Depth of Field Calculator (with a plus)

Want to Blur the Background?
Comparing Depth of Field of Two Lenses

The Depth of Field (DOF) calculator is below, adding some new features.

This subject is of course about adjustable cameras. Determining sensor size (or focal length) is difficult for most compact or phone cameras. The sensor is so small that their lens is necessarily very short, which ensures a great depth of field with little choice. Setting a wide aperture may not be a choice, but choosing more dim lighting can help that. The best chance to blur the background some with a compact camera is to zoom in significantly, and then stand back as necessary (not closer than 5 or 6 feet for a portrait). Choose a background that is very much more distant, hopefully a few hundred feet.

Maximizing Background Blur Without Suffering f/1.8

Both focal length and subject distance are Depth of Field (DOF) factors. We can use them both for our goal. My notion of a portrait at f/1.8 is that there will of course be DOF problems, usually about the hardest possible way to make a good picture, and the last thing I want if I can prevent it. Notions may vary, but studio portraits likely work at f/8 or f/11 (the usual goal is so that the picture will sell well). We do like the sharpness of depth of field. Pros would likely see the advantage of maybe a 200 mm at f/4 for this purpose (of hiding the background in head and shoulders portrait).

Equivalent distance for same FOV

Focal Length A mm, Distance:

Focal Length B mm, Equivalent: 

(distances can be feet or meters)

This is the old adage about the "same DOF for same size image". In this situation with both lens with distances adjusted to be the same Field of View at the subject, if both are also at the same aperture, then they have the Same Depth of Field span too (at the subject they do, it is the same picture, but the background is a different picture). And the longer lens has advantage of being able to stop down a little more, winning with more DOF at the subject, and winning with still less DOF at the background too (if it is far enough back to be a different picture). Where we stand also affects the portrait perspective,. And the long lens, most of the wide background is zoomed out and gone missing, but what's left is even more blurred focus (assuming that is to be a plus here). This standing back at greater distance is little problem to do outdoors, and it possibly need not be that extreme. If both could use the same f/1.8 then, the depth of field at the subject is the Same, both 0.29 feet of DOF in this example (which is only 3.5 inches). DOF does not describe the sharpest necessarily, instead it defines the maximum blur that we can accept. But we don't have to use the same aperture, the 200 mm lens at 24 feet can use say f/4, which has 0.66 feet of DOF (8 inches). That's still not much, but it's sure a lot better, more than twice as much DOF. But again, it is even more blur at the background.

And the overwhelming advantage is even much better yet: We said this Field of View (FOV) at the subject would be the same in either situation (about 2.8x1.9 feet, about right for head and shoulders). But the background field at 40 feet of the 50 mm lens is over 21 feet wide. 21 feet of stuff you want blurred away. However, the field of view of the 200 mm lens is only 7.5 feet wide at 40 feet (behind the subject). So most of the objectionable junk you want to blur is simply missing, simply gone, removed in the best possible way. And better, you can surely simply move the camera a slight step or two to one side to choose to align the best (least objectionable) 7.5 feet of background decently enough, probably even if it were not blurred. But in fact, it is blurred at 200 mm. Probably blurred more than 50mm f/1.8, but 1) the subject DOF is much better, and 2) there is much less of the background even showing. And 3) usually the smaller background that is visible is blurred even more. If this is the goal, then consider using the best tool.

Maybe I'm a purist, but a "portrait lens" means a longer lens to force standing back for proper portrait perspective. Newbies may get strange notions, but "portrait lens" absolutely does NOT mean a f/1.8 lens, which would be a laughable thing in a portrait studio. f/1.8 is more for low light levels, but today, improved high ISO does that better. f/1.8 might be about blurring backgrounds, but we're describing a better choice. A portrait studio (with goal hoping to sell the photo) will be using around f/8, maybe f/11, and will provide the proper light for it. A "portrait lens" for "head and shoulders" means 70 to 85 mm for 1.5x or 1.6x crop APS, or 105 to 135 mm for full size 35 mm frame. That longer length forces us to stand back for better perspective, to NOT enlarge noses, etc. The 50 mm lens standing back properly might do full length well, but is simply too short and close (not the best try) for tighter head and shoulders portraits. A cardinal rule of "Portrait" includes standing back for proper portrait perspective, at least 6 or 7 feet (a couple of meters), or better 8 or 10 feet. Which is very important. We guys are often too dumb to see or realize it, but the wives (may not know why either, but ) will tell us they don't like their too-close portraits. Backing up a few steps and then zooming in is always a good plan.

Example Results for Crop sensor
Background is 40 feet behind subject.
All are Same Field of View at subject.
FOV at subject stays the same.
DOF Span becomes greater (a BIG plus)
FOV at background becomes smaller (a plus)
Background blur becomes greater (the purpose)
OK, you might instead choose 100 mm f/2.8 at 12 feet, but it still offers all of the several advantages over 50 mm f/1.8. It should be obvious that this is a really big deal to know. For head and shoulders portraits, there are four strong advantages often offered by standing back with the longer lens:

What's not to like? Speaking of 200 mm, more than twice as much DOF range at the subject (than 50 mm), yet with greater blur on the background, and only about 1/3 of that background size even showing, which all seem like a big pluses. :) The only downside is we need the longer lens, and to have room to stand back. Flash power could be an issue at extremes.

There are many numerical combinations where the longer lens is simply better in a few ways. And even with a close background, still a few cases where a property or two is still worth consideration. If you also find f/1.8 distasteful, there is this better way.

A Depth of Field calculator
concerned with Blurring the Background

Identify your camera sensor size by entering either actual Sensor Size or Film Size, or Crop Factor or even a final CoC value. Any of those can calculate sensor size. Sensor size can be hard to know, but specifying CoC (and standard divisor) also determines a sensor size, because CoC is about the standard enlargement of sensor size. You can see how to determine your Crop Factor. It's hard to beat precise actual sensor size specifications though.

Film or Sensor Size dropdown box: I have NOT researched every possible camera model for sensor size. The film sizes are known good, but the "1/inches digital sensor size" system for compact and cell phone cameras is a crude approximation, because actuals instead depend on the specific camera models chip. Especially the compact and phone sizes like 1/1.8" CCD are vague (actual sensor sizes are instead described as specifications of XxY mm). Do NOT specify any Equivalent Focal Length. If actual sensor size is not known, I suggest the Crop Factor option may be more accurate. The sensor size computed used is shown in results.

Depth of Field Calculator

  Four ways to specify Sensor Size
Sensor Size WxH x mm
Film or Sensor size
Crop Factor Cropped sensor
Circle of Confusion mm
CoC computes corresponding size sensor
Aspect Ratio
Distance Units ConvertResult is in
same units
CoC DivisorDiagonal / Default 1442
Largest print dimension
10 inches is standard DOF
Sensor pixels x Only for CoC diam in pixels

Lens A

Lens B

Focal length mm mm
Subject distance
Background distance behind subject (same for A & B)
Depth of Field
DOF total span
DOF in front
DOF behind
Background distance
FOV at subject
FOV at background

If you should see results of NaN, it's an error meaning an input is Not A Number (decimal periods are OK, but don't use commas).

If Hyperfocal is new to you, you may like to know more about it, see below. It's importance is that if the focus distance is equal to or greater than hyperfocal, depth of field will reach to infinity (very handy for landscapes).

Including an interesting close and sharp foreground object can have dramatic effect on landscapes. A stopped-down wide angle lens can do this. Try this in the calculator, for example with the default 23.5x15.6 mm sensor, and 18 mm lens at f/16, hyperfocal is 3.456 feet. Then try focus distance at the 3.456 hyperfocal. See? DOF is 1.7 feet to infinity. Three digits helps calculator precision, 3.455 only reaches 23200 feet. So round up slightly, to 3.5 here, call it "at least hyperfocal" that will reach infinity. Note however, if you look closely, focusing at 3.5 feet is not the same thing as focusing at infinity.

That's the same meaning in the hyperfocal chart too. That's pretty awesome to know when you need it.

Using the currently selected sensor size and CoC and feet/meters setup in the first left calculator box immediately above (i.e., your camera), this next button below will compute a chart of hyperfocal distances for various focal lengths and apertures, for that sensor. The chart shows the Hyperfocal distance, but combinations are shaded yellow where half of hyperfocal is arbitrarily less than 7 feet or 2.13 meters (which is up pretty close as compared to infinity). That should be good enough for some generally good approximations, which can be useful.
If you want a printed chart for your camera bag, here's a downloadable zipped printable PDF of it with five sensor sizes (crop factors 1, 1.5, 1.6, 2, 2.71) for both Feet and Meters. Print the page you might be interested in.

Most short lenses are in it, but if desired, you can add up to six other focal lengths to the chart here (the added field is ignored if blank or a duplicate, or if Not a Number).

Add mm  

Hyperfocal Distance Chart

However, while hyperfocal is a strong concept, there is a caution, it may not always be the best choice. Hyperfocal limits are the maximum Depth of Field limits, determined by the Maximum Acceptable DOF blur at both ends. The sharpest point is always the actual focus distance. Let's say maybe hyperfocal comes out as say 12 feet. Then focusing at 12 feet will extend DOF to infinity, and back to 6 feet. Perfect if that's your goal, but of course, focusing at 12 feet is NOT the same as focusing at infinity, or at 6 feet. Or focusing instead at infinity will reach back to 12 feet, which is not the same as focusing at 12 feet. Which end is more important to your picture? It is a choice. More below.

About the DOF calculator:

Abbreviations: DOF is Depth of Field, CoC is Circle of Confusion, and FOV is Field of View.

You can enter 999999 for a distance of infinity.

Yes, I know we can compute much finer precision than the eye can ever see. So yes, I know that computing DOF distances to four significant digits is an unusual thing to do. It's more a two digit concept, if that. :) But humor me, it may be wishful, but not incorrect, and I do it just to be able to enter some results back in to check the calculation consistency. For example, the initial default case shows 200 mm f/4 DOF far limit is 24.34 feet. Then entering a background distance of 0.34 behind the 24 foot focus must compute Background CoC there as 1x CoC (showing concept, because it is at the DOF limit, 1x CoC by definition of DOF). Just 0.3 misses by a little (it is actually 0.33874, which shows even better CoC results). The math distinguishes tiny differences, the eye not so much.

I doubt anyone ever uses a DOF calculator in routine situations. We can't be bothered to stop to actually measure all the distance limits. We can't even accurately set focus to numbers like 11.0 feet. Depth of Field is Extremely Important, but the calculator is more a learning tool, maybe to help learn concept and expectations. What we do need to routinely know and use is how to increase (or decrease) Depth of Field (how to choose settings that give the best try for the situation). The basic DOF factors everyone needs to know are below.

The next page has photo examples of these two initial default cases.

The feet/meters selection is which distance units you are using (the DOF and FOV results are these same units). When it is changed, the checked Convert checkbox will convert previous numbers to keep the same distances. Otherwise that feet/meters change will leave distance values numerically unchanged (but feet and meters are different distance values affecting DOF).

The background distance behind subject will normally be the same for both lenses, since that's where the subject is standing. A relatively long distance behind is good if the goal is for the background.

CoC is Circle of Confusion. It is used two ways.

Blue line is the focus point at S1. Red line is the background at S2. C is the blur circle, c is the reproduced CoC size on the sensor. From Wikipedia.

Background X CoC is the computed actual CoC at the BackGround distance. A larger multiplier means greater relative blur. Normal Depth of Field computes the distance limits where the blur becomes as large as the maximum acceptable CoC limit. Background CoC is shown in the calculator as "X times CoC", meaning actual CoC there is X times size of that maximum acceptable CoC limit entered. This is a relative scale of bokeh and blurring there at the background distance, relative to the just-acceptable CoC at the limit of DOF. However, blur and CoC are vague things, which does not fool calculations, but depending on contrast, our eyes can see it as a bit smaller.

Resolution: If the CoC diameter is 0.02 mm, and is compared to the distance between the lines in a resolution chart, then that diameter distance theoretically represents 1/0.02 = 50 line pairs per mm maximum possible resolution at limits of that DOF span. If at the background distance, 5X CoC for example is 5x0.02 which is 0.1 mm distance, 1/0.1 representing 10 line pairs per mm maximum resolution at that distance. Lenses today can typically resolve 80 to 120 line pairs per mm (a few maybe a bit more).

The DOF concept implies that if the background were located exactly at the computed far limit of DOF, the blur diameter there would be exactly equal to CoC (1X CoC). For example, in the default case B above, 200 mm f/4 at 24 feet, the DOF zone extends 0.339 feet behind. If we put the background only 0.339 feet behind, the Background CoC necessarily computes exactly 1x CoC, or the CoC diameter. Should the background be closer than the far DOF limit, then the multiplier will of course be less than 1 (and be within the DOF range). A larger multiple is a multiplied greater blur. The Background Distance is input here as the distance Behind The Subject, not from the camera. It assumes the subject still stands where it was (with respect to background), but the longer lens steps back.

The classic "Same DOF for same picture image" rule of thumb:   If standing back with longer lens at the longer distance that gives the same Field of View (same subject size), and IF the two cameras have the same sensor size and use the same f/stop, then the Depth of Field "span" is the same for both situations. This works better for telephoto lens, it being true if focus distance is less than 1/4 of hyperfocal of the shorter lens, with longer lens at the longer corresponding distance for same picture. Example for the calculator initial default values (50 and 200 mm, and 6 and 24 feet), same sensor size, and with both at same f/4 f/stop, is the same DOF range span 0.67 feet (see Google). The background CoC will be quite different however (background will not be the same size).

The point: In many cases when wanting to hide the background, standing back with a longer lens can provide the same field of view of subject, but with much less view width of the background, and which also allows stopping down a bit more to provide greater depth of field at the subject, but while still offering greater blur at the smaller background area. Standing back with the longer lens offers better portrait perspective too. These factors can make a significant difference.

CoC Divisor: Maximum CoC limit in DOF calculators is usually computed as (sensor diagonal mm / 1442), which is default here unless CoC or Divisor is directly specified. It is a little arbitrary, and if you decide you want it different, you can change it, and get different results.

Full frame 35 mm cameras often use 0.03 mm for CoC, and APS cameras often use 0.02 mm (due to crop factor). A compact camera or smart phone might have CoC = 0.004 to 0.007 mm (much more enlargement is necessary). Other values have been used, but to get the 0.03 mm value commonly stated requires Sensor Diagonal / 1442. So 1442 is a standard usual value, considered appropriate for viewing a standard 8x10 inch print size. CoC diameter in pixels is shown in the calculator, which may be something to consider if viewing your photos at 100% size. However, Depth of Field is a little bit arbitrary.

Largest Print Dimension is about the relative enlargement of your viewed image. The meaning is that is the "largest dimension" of 8x10 is 10. When we enlarge the viewed image, we enlarge the CoC too, so it's easier to see the blur then, which becomes no longer a suitable indictor. The DOF concept is all about the CoC we can perceive, when enlarged from the sensor size we use. If we are going to enlarge our view more, then we need to start with a smaller CoC. Standard DOF calculations assume viewing a standard 8x10 print size from 10 inches, which is the 10 inch default here (254 mm). This feature is to describe a different image size that you may view, to account for the effect of your enlargement on the Depth of Field calculation.

The CoC used is shown in bold, if and when modified by the Largest Print not being the standard 8x10 inches (254 mm largest). Because, CoC is the largest allowable blur, to still not be perceptible by our eye. If we're going to view an image enlarged bigger, then maximum allowable CoC at the sensor has to be smaller (to not exceed what our eye can perceive). Or vice versa.

However, you can specify any CoC limit directly. Yes, it will then compute and show a sensor diagonal size based on (CoC x Divisor), which is as accurate as those terms. But that sensor size is just for reference, and is used for FOV, but is not further used for DOF. It does Not affect DOF now, since CoC has already been specified directly. The DOF formula computes with only CoC, focal length, f/stop, and focus distance. Sensor size is not in the DOF formula, except that sensor size of course defines CoC (as diagonal / divisor). So, bottom line, you need to know what you're doing if you specify CoC directly. Just because you saw someplace use 0.03 mm CoC, this does NOT mean that is a proper number for your camera and its sensor size. But using smaller CoC (from larger divisor) can make limit the DOF span to be more critically sharp.

If comparing results with numbers from other calculators, make sure the CoC and Sensor Size used are the same value. For those reading this far, Zeiss and Wikipedia suggest the CoC divisor should be 1500 today, a slightly tighter limit on sharpness, but 1442 still seems clearly the standard on the internet, so I went with the flow to avoid confusion. The diagonal of 35 mm film is 43.267 mm, and it divided by 1442 is what makes CoC be 0.03. You can change the divisor as desired. CoC is a little arbitrary anyway, and there's not much difference, being 0.03 or 0.029 mm CoC for full frame 35 mm, perhaps a 4% change in CoC. Other factors like focal length, distance and viewing size probably are larger issues.

Rounding: Note that numerically, real world APS sensors are slightly smaller than 24x16 mm, and their crop factors are actually slightly larger than 1.5 or 1.6. Just for example, the Nikon D5300 DSLR camera manual provides specifications:

Nikon D5300
1.5 crop factor
23.5 x 15.6 sensor


If the sensor is 23.5 mm wide, then the crop factor is 36/23.5 = 1.532 (normally we compare diagonals, but these are same 3:2 aspect ratio). Canon 1.6x would be a similar situation. If Crop Factor or CoC are typical rounded values (0.02 instead of 0.1956), they can slightly skew calculated results in a small way, but the concept should still be clear.

Macro: Depth of Field calculators are not accurate for macro situations. Macro calculations are inaccurate because we don't know extended focal length, and maybe not f/stop reduction, and likely not the location of the front nodal point of the lens to know working distance. At the close focus point, these are large factors. Accuracy depends on knowing the numbers. Macro procedures instead compute DOF from measured magnification. Macro 1:1 means the object image is the same size on the sensor as the object in real life, true regardless of sensor size. For DOF calculators, distances of at least a few feet will be most accurate in any lens calculation.

Adjusting Calculator Depth of Field Limits

When you compute DOF limits, you are specifying that the CoC at those limits will be someone's notion about the size of maximum acceptable blur that a standard enlargement will show. Meaning any more blur would be unacceptable. But there's virtually no difference just either side of that line, and that's not the same meaning as "sharp". The focused point is always sharpest. If focusing at your situations hyperfocal distance, the DOF span is from infinity to a half of hyperfocal. That does not actually mean "sharp", focusing at 8 feet is not the same as focusing at infinity. Instead those limits insure the blur at infinity and at half of hyperfocal will be limited to the maximum CoC diameter still considered to be acceptable blur. And this indeed might often be acceptable, but you should realize it is a compromise, and maybe there are times you may want a more critical calculation. And our enlargements are of variable size.

If interested, you can increase the CoC Divisor higher than 1442, and that will compute more critical DOF limits. This will not then match standard DOF, but if you want it tighter, you can.

For example, if you double the 1442 divisor to 2884, that reduces CoC to half diameter (the maximum allowable blur is now half the blur, so to speak), and it will compute new DOF limits accordingly, half the span of previously. This doubled divisor also doubles the new hyperfocal distance, which then will recompute infinity to half of the new hyperfocal with blur at half of the previous CoC. You'll like that part, except the new DOF span will be substantially less span. But it can be a guide, and increasing the divisor is the way to implement it.

Other Divisors can be considered of course, increasing 10% (to 1586) or 20% (to 1730), and the acceptable CoC will be the same percentage smaller diameter blur, with proportionally smaller new DOF span. The Zeiss company has at times recommended both 1730 and 1500 divisors. Or Leica has used a divisor of 1300 (see below). There's no answer to how much percentage to increase, it's your standards and your goals, what you want, and what you think the situation allows. Japanese companies seem to standardize on the 1442 numbers, which is the standard accepted base today, if not looking too close to the limits. Definitions of "sharp" have been a little bit arbitrary, and again, viewing enlargement is a factor too.

You might do the same increase by directly specifying reduced CoC, like half the size, maybe from 0.02 mm CoC to instead be 0.01 mm CoC. This gives same numbers as doubling the divisor (which is Diagonal = Divisor/CoC mm). DON'T do it that way here though. That will compute a new smaller sensor size, which you could ignore for Depth of Field, except here it will also affect the Field of View numbers (FOV is a big part of the point here, which is about YOUR sensor size). Increasing the divisor is instead much more highly recommended, and you can still see the new CoC number. CoC and DOF and FOV are about enlargement of YOUR sensor size. It will help to understand how DOF Qualifications apply to enlargements (below).

What is Depth of Field and Circle of Confusion?

Circle of Confusion (CoC) is theoretically zero diameter (a point) at the focus point. But this blur circle grows larger when not in focus, and the DOF range is calculated to not exceed the standard limit (sensor diagonal/1442) of acceptable CoC. CoC (and therefore Depth of Field) definitely also depends on the current enlarged viewing size, which is magnification of the DOF blur. We should know that standard CoC is considered to view as acceptable sharpness in the standard 8x10 inch enlarged print viewed at 10 inches.

Depth of Field (DOF) is certainly not ONLY about aperture. DOF is an extremely important basic of photography, however IMO, exact DOF calculators may not be great practical use, other than to get a rough idea. But we certainly do need to know the basic concept. We do need to know this, it should be second nature to you.

DOF is increased by
DOF is decreased by

** The three lens properties above affect the CoC (blurred diameter) in the sensor image. Then the DOF that we perceive relates to how large we enlarge that CoC to view it. In practice, we do think of cameras with smaller sensors giving greater DOF, which might appear to be the opposite of just said above. And they certainly do that, a little cell phone probably does not even adjust focus, yet it is in adequate focus about everywhere. But that is only because the field of view of a tiny sensor is drastically cropped (compared to a larger sensor). Therefore it must use a very short lens to achieve the same normal wider view (Crop Factor). That shorter lens certainly does increase DOF drastically. But even if we could use the Same lens (and ignore the crop), the smaller sensor image still must be enlarged more (to view at same size), which reduces DOF. In the math, a larger sensor computes a larger acceptable CoC limit, which increases DOF (with the same lens). But in practice, the smaller sensor creates the opposite effect, NOT because of size, but due to its necessarily shorter lens, often only 4 or 5 mm focal length on compacts and phones.

Old-timers may remember small Kodak Disc film, or 110 film size. These had quality issues being so small, prohibiting very much print enlargement from film. Compact and phone digital camera sensors have no film grain, but they are about half the dimension of Kodak Disc film, and 1/4 the dimension of 110 film size. DSLR cameras and lenses are significantly larger because some users prefer a larger sensor. A larger sensor reduces the viewing enlargement required.

Many tend to ignore sensor size today, but it's still important. My notion of film size in the past is that:

One thing DOF is NOT is an absolute value computed to a few decimal places. DOF is instead a vague approximation of a vague range of perhaps acceptable focus. Example, a FX 50 mm lens at f/22 computes Hyperfocal as 12.25 feet. Enter 12.25 focus, and DOF will reach infinity. But enter 12.2 feet, and it reaches "only" 3273 feet. These results will be indistinguishable (even if you could set focus to exactly 12.2 feet). Exact numbers are not always as significant as they might appear. :) In practice, we probably guess at the distance, and the actual guess might be 11 feet, which computes DOF to 107 feet. And we might then show it full screen size on our wide screen monitor, which might be about twice the size of the computed standard 8x10 inch print size. So, your DOF results may vary a little, but it is very good to know the concepts (which I would argue are more important than the exact details).

Depth of Field "numbers" are just approximations, not to taken exactly literally. DOF is not actually sharp from one limit to the other. We focus at only one specific distance. Therefore all other distances are NOT in best focus. As the degree of out of focus increases away from the focus point, tiny points in our image grow larger, and appear as larger blobs instead of as the tiniest points. At some point, our eye becomes able to perceive seeing it (depending on our enlargement of it). The diameter of this out-of-focus blob (one from what should have been the tiniest point) is called Circle of Confusion (CoC). We can calculate that actual CoC diameter on the camera sensor image, when at a distance away from the actual focus point. But then we also enlarge that image when we view it. This magnifies any blur, to be easier to perceive it.

Statistical tests have said the average resolution of our eye is to perceive 6 mm of detail at 6 meters distance, called 6/6 vision in Europe, or 20/20 vision in the US (feet = meters x 3.28). This scales to other similar ratios, like 0.025 mm CoC at 25 cm is familiar. For DOF to be judged in a standard way, that was standardized as perceiving 0.025 mm of film detail on an 8x10 inch print when viewed at 25 cm (ten inches). This size print represents substantial enlargement of the small sensor image, so CoC limits at the sensor must be divided by the enlargement factor (from the sensor size to the enlarged print size). Eyes do vary, but someone established this ballpark number, used for DOF as the limit of acceptable CoC diameter (that blurriness limit that we still call sharp). So this 8x10 print viewed at 10 inches is our standard for calculating the DOF blur that will be created.

Is it 1442? You won't see much mention of 1442 anywhere, but I didn't make it up, it is what it must be if consistency is a goal. This judgment is contained in the CoC = Sensor diagonal mm / divisor definition. The Zeiss optical company (long ago, before WWII changed things in East Germany) published using /1730 (20% greater than 1442, 0.025 mm CoC). Then Zeiss has also later said /1500 (4% greater than 1442, 0.0288 mm) - both more strict than 0.03 mm which computes 1442. And Lietz of Leica (90 years ago) used 1/30 mm, also called 1/770 inch, which is 0.033 mm, which computes a 1300 divisor (11% less than 1442). Film was less good back then, but this is a little arbitrary, about what we think our eye can perceive. It is most common today (for Japanese cameras) to say full frame CoC is 0.03 CoC, which computes the divisor 1442 as being the standard value today. That 1500 might be thought of as 1442 rounded up, but the 35 mm film diagonal divided by 0.03 mm is 1442.2 (the diagonal of the 35 mm film frame is 43.26662 mm). Using 0.03 mm CoC concept with Crop Factors is used as CoC = 0.03/Crop Factor, since both CoC and Crop Factor involve the sensor diagonal. If you don't like 1442, then try 1500 (0.0288 mm CoC), but it will not agree precisely with other DOF calculators then. This number is hard to verify in results. The CoC diameter is a scaling factor to scale the blur to what our eye can perceive at this standard 8x10 enlargement. The CoC number is the sensor diagonal / divisor (often 1442, and 0.03 mm CoC in full frame 35mm). Depending on megapixels, this 0.03 mm CoC is typically 4 to 6 pixels diameter.

The Depth of Field is the computed distance zone around the focus point, the span where the CoC remains less than our arbitrary limit for the size of CoC, considered to be in focus. The image is only focused at one distance, and gradually degrades away from that point. Focus just outside the DOF calculation will be hardly different than the focus just inside the DOF calculation. For example, maybe the DOF limit computes 20 feet. But then you probably cannot detect much difference a couple of feet either side of 20 feet, but the exact focus point will be better. DOF is NOT at all magic numbers, it's just where the math precisely computes the CoC size crossed an arbitrary threshold size boundary. The boundary is very vague to our eyes. Sharpest focus is at the one distance where we actually focus. Depth of Field is a vague concept.

If we can see these blurred blobs in the results, that's normally considered bad, when that distance is not in focus well enough. If only slightly out of focus, it may not enough for us to even notice it, much less object about it. Which is good, and while standards vary, DOF is a way to judge it. The exact calculated numbers are rarely important (just a simple guide). But the zone of DOF we perceive is certainly really important, and the big thing to know is what the controls are, and to know how to adjust it. With a little experience, we know what to expect, and this works pretty well.

The name Circle of Confusion is from another era, and Wikipedia quotes work in 1829 and 1832 calculating Circle of Confusion. They had microscope and telescope lenses then, but this was before cameras or film. Still same concept, but maybe if invented today, we might pick a simpler name for CoC (it is the diameter of the blurred circle of an out of focus point source). Camera sensor size is a factor of enlargement. Older work used CoC = (sensor diagonal / 1730), or 0.025 mm for 35 mm film. Today, we often use the computation (sensor diagonal mm / 1442) for acceptable maximum CoC in the final standard print size. These are often rounded numbers, or CoC = 0.03 mm for full frame 35 mm sensors, and CoC = 0.02 mm for smaller APS sensors (because the smaller sensor requires half again greater enlargement).

CoC is arbitrary, and professional level might prefer it smaller, with larger safety factor. Our CoC number choice does not affect the image in any way, it only affects how we might judge it, or plan it. It is an arbitrary notion about when out of focus is judged to become too noticeable. And DOF very definitely also depends on how large you enlarge the image to view it.

What makes DOF even more arbitrary is that the larger we enlarge and view the image, the more noticeable becomes the blur blob of CoC. View it small, and we may not even notice it. The standard of viewing DOF is considered to be an 8x10 inch print viewed from 10 inches. That's about a 9x enlargement of 35 mm film (CoC 0.03 mm), and so the CoC we see then is the 0.03 mm x 9 = 0.27 mm in this print. We enlarge our smaller digital sensors even more to see 8x10, so allowable CoC has to be smaller. Every sensor size has a different CoC (from sensor diagonal mm / divisor) - because we assume to enlarge each to the standard 8x10 inch print to judge it. DOF is a different number after enlargement, BUT the standard maximum CoC value was chosen to be acceptable when viewing this standard print size. Today, we view first on the computer screen, or even a cell phone. But we view different sizes, and this also affects the acceptable CoC goal. There is NOT just one number for DOF of a situation.

If you crop your image significantly before enlarging it, that that's the equivalent of a smaller sensor, with less DOF.

If you print a different size print, you can use the Largest Print Size parameter above to describe a print size (specify the largest dimension, like 20 for a 16x20 print), and it will calculate DOF based on that instead of the standard 8x10 inch print.

Hyperfocal Distance

The Hyperfocal distance is a special idea of DOF. It is sometimes used for landscape photography with wide angle short lenses, when we want an extreme DOF range, extending to infinity, and also back to a rather near foreground object (to emphasize depth). For example, an APS-C sensor (1.5x crop factor) with 18 mm lens at f/16 computes Hyperfocal distance as about 3.5 feet (depending on precise sensor dimensions). What that means is this:

Subject distance is a factor of DOF, but it does not affect hyperfocal distance. But subject distance at hyperfocal is a big effect.

Hyperfocal varies with the square of focal length ratio. Doubling focal length gives 4x hyperfocal distance, or 10x focal length gives 100x hyperfocal. And one half of focal length gives 1/4 hyperfocal distance.

Stopping down two stops more gives half of hyperfocal distance (stopping down one more stop is 0.707 x hyperfocal).

So, doubling focal length AND stopping down four more stops is the same hyperfocal distance.

Aperture is very important, and is often all we can chose to change, but focal length is more important to DOF than aperture. We need to have an idea of what these adjustments do. Photographers don't compute DOF for every picture (probably not for any of them). But we all do need to be aware, and always keep DOF in mind, and experience gives a good idea in our head about what adjustment factors we can use to maximize the effect we want in the shot.

In our calculator example above about standing back with longer lens to better blur the background, the longer lens blurs the background more. But at an "equivalent" subject distance, for the same planned FOV (for the same picture) and at the same f/stop, the subject DOF range is the same overall span. And then stopping down the longer lens a bit more increases the DOF at the subject, but leaves the background DOF still less (if background is sufficiently distant to separate these two zones). Both results can be good goals.

These are basic ideas which have been known for maybe 150 years. The alternative of simply focusing on the near side of the subject zone typically wastes much of the depth of field range in the empty space out in front of the focus point, where there may be nothing of interest. Focusing more into the depth centers and maximizes the DOF range, generally more useful. We hear it said about moderate distance scenes (not including infinity) that focusing at a point 1/3 of the way into the depth range works for this, which is often near true, maybe a little crude, better than knowing nothing, but some situations do vary from that 1/3 depth (below). Close and macro focus situations are closer to the middle at 1/2 way in, and don't include infinity.

The crude distance marking today on our lenses make it hard to set a specific focus distance. If your lens only has a mark at 10 and at 5 feet, setting 6.117 feet won't be easy. But we can approximate it to about 6, at least closer to 5 than to 10, normally close enough. It's all a little vague anyway. Sometimes it might be easy to focus on something at an estimated 6 feet, and then shift your camera aim to the real subject.

Every Depth of Field calculator should show hyperfocal focus distance.

Many prime lenses have a DOF calculator built into them. Speaking of prime lenses (i.e. those lenses that are not zoom lenses) which normally have marks at the distance scale showing the depth of field range at the critical aperture f/stops. In the old days (before zoom lenses), this easy way was the standard procedure to handle DOF. However, this tremendous feature is becoming a lost art today. Zoom lenses cannot mark this for their many focal lengths. Also todays faster AF-S focusing rates can put the marks pretty close together. These 85 mm and 105 mm lenses are AF-S, but it still gives a DOF clue. (the "dots" are the focus mark correction for infrared.)

For example of hyperfocal distance, at right is an older 50 mm FX lens, with focus adjusted to place the f/22 DOF mark at the middle of the infinity mark, which then actually focuses at about 12 feet, and the other f/22 DOF mark predicts depth of field from about six feet to infinity (assuming we do stop down to f/22). This places the focus at about 12 feet. The DOF calculator says this example (FX, 50 mm, f/22, 12.3 feet) DOF range is 6.1 feet to infinity.

Or another case, one not including infinity. If we instead focus this 50 mm lens at 7 feet, then the FX f/11 marks suggest DOF from about 5.5 to 10 feet (at f/11, which is about 1/3 back in this case). The idea of the markings (which appear on prime lenses, zooms are too complex to mark) is to indicate the extents of the DOF range. And done because it can be very helpful. Sometimes f/22 is the best idea, sometimes it is not. f/22 causes a little more diffraction, but it can also create a lot more depth of field. And of course, the lens markings apply to the expected sensor size for that lens.

Those DOF end point extremes will of course Not be as sharply focused as the actual focus point, but they will still satisfy the standard CoC specified. Do realize that DOF just means barely tolerable limits, where the CoC has grown to the maximum limit specified. Focus is always of course sharpest at the exact focused distance. Focus is not necessarily perfect if inside DOF, instead it is assumed unacceptable if outside DOF, but there is no sharp dividing line. If you want really sharp images, include ample safety factor for DOF; pay attention to enlargement size, stopping down at least one more f/stop, and if really important, focus on the important spot that needs to be sharp.

Your DOF calculations may not exactly be realized particularly close in practice, due to your own degree of enlargement, and your viewing distance, and your own eyes, or an inaccurately specified sensor size, and how accurately you guess the actual distances. It is just a large ballpark. You'll have to decide for yourself if your images are as sharp as you want. What you specifically need to know are the factors to increase DOF (stopping down, a shorter lens, and longer distance).

A couple of tricks are to plan on having sufficient DOF with ample safety factor, and then learn to center that DOF around your subject depth. If DOF is limited, don't focus on the nose if you want the ears sharp too. Repeat this to yourself: Focusing on the closest point of your subject wastes the half of the DOF range in front of that point (where there is nothing). Instead, you can plan to better center the DOF zone around your subject. Instead, consciously focus a bit more into the depth of your subject.

To do that centering, we hear about the simple (rough) guide of focusing 1/3 of the way into the scene depth (1/3 of scene in front of focus point, and 2/3 behind). If we think that 1/3 of the DOF range is in front of subject, then it makes sense to focus 1/3 into the scene, instead of at front point, and instead of half way back. There is no good argument for the front point, and half way is true if up focusing pretty close. That focus point may not be where the subject is, and of course that subject will always be sharpest if you actually focus on it (so there are trade offs).

Regardless, hyperfocal becomes interesting.

The fraction of DOF in front of subject

Situations will vary, and the DOF in front of focus might be from 0% to 50% (at extremes). Otherwise, 1/3 is not the worst guess (we are not actually measuring distances anyway). Generally, short lenses have closer hyperfocal, and stopping down any lens brings hyperfocal back closer to us (and brings a short lens back very near). That's a lot to know. Frankly, in practice, we never compute the hyperfocal number, so we just soon learn the general idea of what we need to do when DOF is important. Stopping down some, and focusing somewhat into the scene depth can usually help considerably. Just standing closer with a shorter lens can help DOF, and as discussed here, standing back with a longer lens can reduce DOF range (specifically, will be same DOF at the subject with same f/stop, but greatly different at the background).

For portraits at around 8 or 10 feet, I think a good tip is to focus on the near eye, after ensuring ample DOF, like f/8. IMO, f/1.8 is never the best try, and this article is about an alternative. For full frame portraits, I like about 120 mm at around 10 feet. For DX or APS crop cameras, that would be about 80 mm around 10 feet. Ten feet is very good portrait perspective, and at f/8, that's about a 2x3 foot FOV with around a one foot zone of DOF (again, of course speaking about the standard 8x10 inch print viewed at 10 inches).

Qualifications about Viewing Depth of Field

Depth of Field is NOT an exact number. Depth of Field is computed based on the Circle of Confusion (CoC), which is the arbitrary criteria defining the maximum acceptable blur circle (to be small, not quite perceptible) due to being out of focus. CoC is the diameter of the smallest possible theoretical point after it is defocused to be seen as a larger blur circle (because it focuses in front of, or behind, the sensor plane - then causing a larger out of focus circle on that plane). CoC is the maximum permissible diameter of this blur circle, arbitrarily still judged to be imperceptible in our vision (also assuming a standard viewing enlargement). If the blurred circle is too small for us to perceive it, then we imagine it's not blurred.

Zeiss thought the eye's criteria of visibility of focus blur ought to be a CoC of (frame diagonal divided by 1730, in mm), which computes 0.025 mm today for 35 mm film size. But today, CoC of diagonal divided by 1442 is a common universal value (0.03 mm for 35 mm film). The sensor diagonal is involved because it is a factor of the final print enlargement required, where we see and judge the perception of the enlarged CoC. Enlargement is a big factor of perception. But it's still an arbitrary guess about blur, about what our eyes see after enlargement. Blur diameter cannot be precisely defined... kinda depends. And so a CoC limit is somewhat arbitrary, there's been a few choices. CoC is just a rough guess attempting to measure focus blur, which makes DOF numbers be a vague thing.

The DOF Standard of Viewing is in an enlargement of an 8x10 inch print (near A4 size) when viewed at a distance of 10 inches (25 cm). You should know that DOF calculators use a CoC which assumes this standard enlargement, regardless if you assume it or not. If you view it up close on a large HDTV screen, DOF will appear much less than you calculated. If you view it on a smaller wallet or 4x5 inch photo, DOF should appear better than you calculated.

Viewing the enlargement size is an important factor in what we see, and in CoC and the Depth of Field calculations. This viewing enlargement factor makes small sensor diagonal be an important factor of DOF. It's the reason smaller sensors have a smaller CoC, and larger sensors have a larger CoC (sensor size requires enlargement of CoC). But standard DOF calculations assume a standard 8x10 inch print is viewed. So this affects viewing a smaller print or a larger print:

Computing on the diagonal attempts to equalize for different sensor or print shapes, but many vague assumptions are included. You should include a safety factor, especially for large prints, one extra f/stop for safety.

Depth of Field is an angular size concept, and the math is very precise, EXCEPT for the main factor of CoC, which is rather vague and arbitrary. So there are no hard answers about Depth of Field. And since Depth of Field GRADUALLY changes with distance, there is of course no sharp line at the computed limit. There will be virtually no difference seen slightly either side of the computed limit. Numerical Depth of Field is at very best, an extremely rough guide.

Depth of Field is a fundamentally important principle of photography. However using it is MUCH LESS ABOUT any computed numbers, and VERY MUCH MORE ABOUT understanding how to use the factors that increase or decrease it (above, f/stop, distance, focal length, and sensor size). Normal situations are not much concern, but sometimes we're aware we want a lot of depth of field, or don't want much of it, and we should know how to control that, to do what we can.

Continued - Part Two, Examples about background

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