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Calculator for Field of View (FOV)
of a Camera and Lens

Computes Field of View seen by camera and lens, for any sensor size or aspect shape (film or digital). Computes both the dimensional size of the Field Of View seen at a specified distance, and also Angle Of View (degrees, which is independent of distance).

Uses of course include computing dimensional field of view size at the subject distance. We don't often care about precise field size, but suppose you plan a portrait to include a 2x3 foot subject area. You know you need to stand back six or eight feet for proper portrait perspective. What focal length is that field size and distance going to require? (Option 5, and it depends on your sensor size). And the background may be six feet farther back yet, then how large is it? This calculator can plan or verify your choice. It can also compare expected fields seen by different lenses or sensors or distances.

There's a large table of Field of View (angular, in degrees) for many lens focal lengths and a few popular sensors on the next page (or Option 1 to 4 below shows more specific cases). Perhaps somewhat related, another calculator can compute distance or size of an object in a photo.

This calculation requires accurate sensor size and focal length. These values may be difficult to determine for compact cameras and phones and camcorders, but DSLR values should be more easily known. You can specify crop factor as a way to compute actual sensor size. The Exif data often reports focal length. Do NOT specify 35 mm Equivalent focal length (at least Not unless you also specify 35 mm film size, 36x24 mm, or crop factor 1, which is 3:2 aspect ratio). Use the actual lens focal length with the actual sensor size.

Options 1-4 are four ways to specify sensor size. Enter Focal Length and Distance, select a sensor size in Option 1-4, and click Compute. Then FOV is computed from focal length, distance, and sensor size. Or Options 5-8 are more special purpose.

Numbers only (a NaN result means input is Not A Number). Periods as decimal points are OK.

Field of View CalculatorField DimensionAngle of View
Focal Length mm Width
Dimension
Width
Degrees
Subject Distance Height
Dimension
Height
Degrees
Any units for Distance, feet or meters. Dimension results are the same units Diagonal Dimension Diagonal Degrees
1 Sensor size
Width mm
Sensor size
Height mm
2 Sensor Width mm Aspect Ratio
Width: Height
3 Crop Factor Aspect Ratio
Width: Height

4

Film and
Sensor Size Description
  (Option 4)
Mostly this is Film Size. The size of a CCD sensor is NOT the 1/x inch number (the size is WxH mm)
5

and the Sensor Size in Option above

Dimension
units in the
Width

Height

Diagonal

  Direction

6 (Subject Distance is optional) Find Focal Length giving Field of View of
Angular Degrees in
7 Magnification Feet
Meters
8 Compute the Sensor Size from the measured Field Width and Height Dimensions that you enter at top above, measured AT the Focal Length and Distance entered.

Please report ( Here ) any problems with the calculator, or with any aspect of this or any page. It will be appreciated, thank you.

Distance units can be feet or meters, miles or cubits, any units, your choice. Dimension results will be those same units.
Clicking the little green button (by Distance, marked In for Inch) will assume feet, and will repeat Dimensions in feet ' and inches " format. You can click the green button again to toggle this option off or on.

The blue Flip button at Option 5 will toggle to swap finding either Focal Length or Distance in option 5 and 7, to compute either one from the other. Options 5-7 requires first specifying correct sensor size in options 1-4.

The calculator is NOT for fisheye lenses (their view will be wider), and it is not for close macro distances (at end below). Field accuracy will be better at distances of at least a couple of feet (magnification 0.1 or less), because the lens focal length number increases with closer distance. The marked value of focal length applies to Infinity focus, but at normal distances, the focal length difference is small for the focus range of regular lenses.

Select an Option, and click the Compute button (for all Option numbers).
Options 1-4 are four ways to specify sensor size.

Magnification is a related property here. Greater magnification reduces FOV, and also, FOV calculation becomes inaccurate if magnification exceeds about 0.1 (if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus quite that close. This FOV calculation is not accurate for macro distances. Macro purposes use Magnification for calculations instead of FOV.

Magnification (for cameras) can be computed two ways. The obvious way is (Sensor dimension / FOV dimension), using horizontal dimension for example. Or (focal length / subject distance) computes the same number (similar triangles). When these dimensions or distances are equal (when image size on sensor is equal to subject real life size), this is 1x magnification, called 1:1 reproduction. But camera "magnification" is normally a reduced size on the sensor, < 1. If our Moon is 3474 km diameter, and its image is 0.5 mm, that's an extreme size reduction.

Note that binocular and telescope magnification numbers are a different system, being "viewing devices", and their magnification number is relative to the size our naked eye sees at 1x. If a magnifying eye piece is used (like binoculars use), then magnification is (main lens focal length / eye piece focal length). If no eye piece is used (if scope is attached like a camera lens, called prime focus photography), then some astronomers do compare it as if a 50 mm lens gives 1x magnification (so 2000 mm would give 2000/50 = 40x). That's an approximation, based on a 50 mm lens being the "normal lens" or view if on 35 mm film. But at best, it would be a different number on another size sensor.

But cameras are a "reproduction device" and the magnification number is relative to the actual real life size of the subject being reproduced. So obviously, sensor dimension / FOV dimension is the actual magnification. Reproduction size of 1/100 is 0.01x or 1:100. In contrast, the DSLR "viewfinder" magnification rating is compared to the eye's view (called 1x), but the lens images are compared to the size of the distant field of view (affected by focal length and distance). Live View LCD zoom magnification is compared to size of the LCD screen, so there are different meanings.

Magnification is Not affected by a cropped sensor or smaller sensor size. Both sensor and field of view are cropped proportionally smaller, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of subject size. 2x distance is 1/2 the magnification of subject size. Therefore 2x focal length AND 2x distance together combine to remain the same magnification and same subject size. See the Depth of Field page for more about using that.

The most usable general understanding to compare magnification of focal lengths (for a given sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. A 400 mm lens will show an enlarged view 4x the subject size and 1/4 the field of view of a 100 mm lens (100/400 = 1/4). This example 1/4 is true of frame dimensional field of view, or 4x for subject size, however the numeric angle of view number (in degrees) is Not linear for short focal lengths.


The biggest risks to FOV accuracy are in not actually knowing the specific accurate sensor size, or not actually knowing the specific accurate focal length, or your guess about distance. Compact and phone cameras may be difficult to know (and Crop Factor might be your best tool). DSLR cameras do better describing those specifications.


Determine Crop Factor:

Crop factor is about the corresponding Field of View due to a smaller sensor size, as compared to 35 mm film size results. The smaller sensor size simply crops the view that a larger sensor would see. Computing Field of View requires knowing sensor size and focal length. Focal length used is normally in the DSLR Exif data (compact Exif may at least show Min and Max zoom focal length). Sensor size might be found in the camera specs, but it can sometimes be difficult to know. Sensor size can be computed from Crop factor.

Crop Factor =  

Diagonal dimension of 35 mm film
Diagonal dimension of THIS camera sensor

If THIS sensor size division computes the Crop Factor to be 1.5x, it means that the 35 mm film frame is 1.5x larger. THIS smaller frame is 1/1.5 or 2/3 the dimensions of the 35 mm film (measured on the diagonals if different shape sensors).

We might not be told Crop Factor for our camera, however we are often told its Equivalent focal length relationship of a comparison lens for 35 mm film, which can tell us Crop Factor and sensor size:

Crop Factor =  

Equivalent focal length with 35 mm film
Actual focal length of THIS camera

For a random example, the specification for some compact camera's zoom lens might say:

Focal Length: 4.5 - 81.0 mm   (35 mm film equivalent: 25 - 450 mm)

THIS lens says its zoom focal length is 4.5 to 81.0 mm. It also says that a 35 mm film camera would see the same field view if it used a 25-450 mm lens. That says THIS cameras 4.5 mm lens is the equivalent view of a 25 mm lens on a 35mm film camera (the tiny compact sensor has to use a very short lens to fill it with the same field of view). So it computes crop factor to be (25 mm / 4.5 mm), or (450 mm / 81 mm), either of which compute the same 5.55 crop factor.

The 35 mm diagonal is 43.27 mm. When we know THIS crop factor is 5.55, then the diagonal dimension of THIS sensor is 43.27 mm / 5.55 = 7.8 mm.
If the aspect ratio is the common 4:3, then it's a 345 triangle. In which case, Sensor Width is Diagonal x 4/5 = 6.24 mm, and Height = Diagonal x 3/5 = 4.68 mm.

So Equivalent focal length is NOT about what this lens does. The focal length of this lens is as specified, it only does what it does. Equivalent focal length only describes the lens that a 35 mm film camera would use to see the same field of view as this lens sees on this camera. If you are used to 35mm film lenses, this will be convenient information, to compare the expected field of view of this lens. But it does not change what this lens does on this camera (meaning, if this lens specifies X mm focal length, then the focal length is X). Crop Factor is the degree that the smaller sensors reduce the field of view, as compared to the field of view of the same focal length on a 35 mm film cameras used as a comparison standard.
FWIW, IF you do incorrectly specify the Equivalent focal length in this calculator, then you also must only specify the 35mm film full frame 36x24 mm sensor size that it applies to. That would use 3:2 aspect ratio, but will otherwise work to show FOV, although roundabout.

Crop factor is also the ratio of the 35 mm film diagonal divided by this sensors diagonal. We know 35 mm size, so knowing crop factor can tell us sensor size. So computing sensor size will be as accurate as your data numbers. However, the focal length actually used in compacts is probably not known except at the extremes that the zoom spec mentions (and default power up zoom is probably some unknown intermediate point).

Smart phones don't zoom, but official specs are rare. Sensor size can be computed from crop factor, if known. Sources differ, and Apple specs don't say, but one estimate is that an iPhone 5s sensor size is 4.54 mm * 3.42 mm and crop factor 7.93x. If you can determine either sensor size or crop factor, the calculator above will compute the other. iPhone 5s Exif reports focal length of 4.2 mm.

Crop factor is often specified as a slightly rounded number. For example, the 35 mm film frame is 36 mm wide, and if the DX sensor is 23.5 mm width, then it is actually 36 mm/23.5 mm = 1.53 crop, but called 1.5x. But, the focal length number is also rounded anyway.

Entering exact sensor dimensions above would be the most precise. The camera manufacturers specify the equivalent 35 mm crop factor from the diagonal ratio to 35 mm film (because many of us are very familiar with 35 mm film, and crop factor tells us what view to expect now). We may not know sensor size or focal length on compacts, except at either end of the zoom range, but then we can determine crop factor, for example, if they specify their 6.1 mm lens is equivalent of 24 mm lens on a 35 mm camera, then obviously their crop factor is 24/6.1 = 3.93. And after the fact, the Exif (Manufacturers Data section) often shows the zoom focal length used for the picture (see a viewer that will show this).

Aspect Ratio: Aspect ratio is the SHAPE of the sensor. Numerically it is the ratio of width to height. If Aspect Ratio is unknown, look at the size of your images (pixels) straight from the camera. For example, maybe the size is 4320x3240 pixels. Divide Width by Height. For example, 4320 / 3240 is 1.3333. Common camera Aspect Ratio values are:

1.3333 is 4:3 (also = 4/3) - Compacts and phones
1.5     is 3:2 (also = 3/2) - DSLR
1.7778 is 16:9 (also = 16/9) - Camcorders

HDTV 16:9 movies: Special considerations. The differences in the Aspect menu in Option 3 above is about the difference in camcorders from DSLR, compacts and phones. Someone might find some exception about some camcorder, but generally:

Still cameras (including DSLR, compacts, phones) today are usually more or less around 10 to 24 megapixels. They have 3:2 or 4:3 sensors, and take 3:2 or 4:3 photos of that size, and their diagonal fits the diameter of the lens circular view. Their HDTV movies possibly might be slightly smaller than sensor width, but can't be larger - and of course will necessarily be resampled to 1920x1080 or 1280x720 pixels, up to about 2 megapixels - which is the maximum that HDTV can use. The 16:9 movies in still cameras are constrained within that still camera sensor size, limited to the same width.

Whereas camcorders are typically only about the necessary HDTV 2 megapixels (a 4K camcorder might be 12 to 18 megapixels). They have 16:9 sensors, which fits the full diagonal, not constrained by any 3:2 or 4:3 sensor width. Generally, if camcorders also take still pictures, those are 16:9 too. But if they provide 4:3 still photos (Sony does), and if less than 2 megapixels, those are necessarily horizontally cropped to be constrained within the height of the 16:9 sensor, limited to the same height. These situations will require some attention to know what you have.

This is a complication about the field of view of movie recordings in still cameras, and in still pictures from camcorders. We're not always too sure about the sensor area used. Option 3 above can differentiate these differences (aspect can match the yellow drawings).

In this image at right, the blue circle represents the diagonal of the image that the lens projects. 16:9 in camcorders is wider, but not if constrained within the more narrow frame sizes. I suppose there could be some exception, but camcorders should have a 16:9 sensor, and DSLR, compacts and phones typically have 4:3 or 2:3 camera sensors. Their 16:9 width will be the same as the 4:3 width, but then the height is less.

Determine aspect ratio by dividing image width by the height (both in pixels), which is its aspect ratio. 3:2 divides as 1.5, 4:3 divides as 1.3333, and 16:9 divides as 1.7778. So if your camera takes still pictures of aspect 1.7778, then it is probably a camcorder with a 16:9 chip.

Some photo cameras will use their full sensor width for their HD movie width (Nikon D7100, D600, D750 do specify their movies are full sensor width) and that is assumed here. But for example, the Nikon D800/D810 use slightly less width (these D8xx manuals specify the sensor image area for FX HD movies is 32.8 x 18.4 mm FX, and DX HD is 23.4 x 13.2 mm). That is 35.9/32.8 = 91% of full width. An iPhone 5S (on a tripod) measures the movie field of view to be 91% less too. This field of view reduction could be computed by using effective Focal Length = 1/0.91 times longer (10% longer), OR a crop factor 1/0.91 times larger (10% larger).

But actually knowing the actual sensor size is the key to FOV accuracy.


There are approximations in calculations. The math is precise, but the data is less so. Focal length is a little vague, as might be the precise sensor size. However, the results certainly are close enough to be very useful in any practical case. My experience is that the field is fairly accurate (at distances of at least a meter or so), assuming you actually know your parameters. Some problems are:

The Marked focal length of any lens is a rounded nominal number, like 50 or 60 mm. The actual can be a few percent different. Furthermore, the Marked focal length is only applicable to focus at infinity. Focal length necessarily increases when lens is extended forward to focus closer. Also zoom lenses can do other internal tricks with actual focal length (some zooms can be shorter when up close, instead of longer). Focal length will be less accurate at very close distances, and field of view becomes a little smaller. So this calculation does not include macro distances (if magnification > 0.1). You also have to measure your distance and field dimensions accurately too. And of course, we are only seeking a ballpark number anyway, we adjust small differences with our subject framing.

And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting.

Actual focal length can be determined by the magnification (Wikipedia). Or, the focal length (f), the distance from the front nodal point to the object to photograph (s1), and the distance from the rear nodal point to the image plane (s2) are related by this Thin Lens equation:

If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy.

In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This says that the marked focal length applies when focused at infinity.

Also if at 1:1 magnification, then s1 = s2, saying that the working macro distance in front of the lens is equal to the (extended at 1:1) focal length of the lens.

fov

The focal length measures from lens node to sensor. We compute the right triangle on center line, of half the sensor dimension, so the half lens angle = arctan (sensor dimension / (2 * focal length)). The Subject distance is in front of lens node, with same opposite angle. One way is that field dimension = 2 * distance * tan (center line half angle). The problem is that focal length f becomes longer when focused at close distances (but the opposite can be true of a few zoom lenses). That becomes an insignificant field of view difference at normal distances, 1 meter or more.

Multi-element camera lenses are "thick" and more complex. We are not told where the nodes are designed, normally inside the lens somewhere, but some are outside. For telephoto lenses, the rear node (focal length from sensor plane) is in front of the front lens surface. The designer's term telephoto is about the reposition of the nodal point so that the physical lens is NOT longer than its focal length. Yet, this rear node is generally behind the rear lens surface of a wide angle lens (lens moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens, 24 mm mirror, etc). This nodal difference is only a few inches, but it affects where the focal length is measured. And it shifts a bit as the lens is focused closer. Repeating, the focal length marked on the lens is specified for focus at infinity.

The Subject distance S is measured to the sensor focal plane (it is the "focus distance"), where we see a line symbol like Φ marked on the top of the camera (near rear of top LCD). The line across the circle indicates the location of the sensor plane (for focus measurements). However, the Thin Lens Equation uses the distance d in front of lens. This is why we often see in equations: (S - f) used for d.

For Macro, computing magnification is more convenient than focal length (since we don't really know focal length at macro extension). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:
    m = s2/s1.   Or m = f/d.   Or m = f/(S-f).

So from this, we know macro field of view is simply the sensor dimensions, divided by the magnification. Let's say it this way:

1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node).

1:1 macro (magnification 1), the field of view is exactly the same size as the sensor.
1:2 macro (magnification 0.5), the field of view is twice the size of the sensor.
1:4 macro (magnification 0.25), the field of view is four times the size of the sensor.

This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro.

The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity).

The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why.

But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant.

Next page is a table of angular Field of View (degrees) for many lens focal lengths and a few popular sensors.

Menu of the other Photo and Flash pages here


Copyright © 2014-2017 by Wayne Fulton - All rights are reserved.

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