The Angle of Field of View is independent of the field distance. The angle is computed from sensor size and focal length. The Field Distance is not limited to be only the subject or focus distance. Here it means the distance to the point where you want field size calculated. It might be the background distance for example (which then would show the Field of View at the background distance). A 2nd distance can be entered for convenience, but it is the same result as simply changing the first distance.
When you specify a different embedded format (like 16:9 video on your 3:2 or 4:3 camera sensor, or a photo 4:3 format on your native 16:9 camcorder), this changes the effective sensor area and size from the format's original native value (usually a different image height), and changes the Crop Factor and the Field of View too. The calculator can show this.
If using options 1 to 4, do pay attention to properly specify Aspect Ratio. The crop factor determines sensor Size, and then native aspect ratio specifies the Shape of it. This in turn specifies the size of any embedded formats contained within it, so it is important to compute the correct numbers. embedded format is a complication, but it is necessary to know the sensor area used.
A red warning may be shown if the Aspect Ratio specified does not match the native Crop Factor computed in Option 3 or 4 (native Aspect Ratio in Option 1 or 5 is computed from actual sensor size). The warning means that an aspect ratio with the correct base aspect ratio (the native sensor size) was likely not selected, which seems an easy oversight, not likely intended, but mistakes change active sensor size and the DOF numbers. Verify, but the warning can be ignored if it's actually correct (you could let me know about the facts of that situation). But meaning, if you select a 16:9 movie aspect ratio in a 4:3 camera, this correct aspect ratio selection specifies both, as "16:9 in 4:3 camera". The warning makes the standard assumption that native crop factors less than 2x should be 3:2, or equal or larger than 2x should be 4:3 (with exception for 2.7x), which are the normal expected and required camera values. Actually, I use 1.9x as that warning boundary.
Rounding: Four or five significant digits may be shown, but inputs of focal length or distance or sensor size or aspect ratio values are rounded values, not that precise (the math is accurate, but camera specifications round things). In math, the final answer can only contain as many significant digits as the least precise value. Only couple of significant digits is not very precise, but should be somewhat close. Still multiplying a 5 mm sensor width into a 30 foot field width multiplies any error too. Excessive digits are shown just in case those results are reentered to recompute back to original values, avoiding additional round-off (for example in Option 9). That's just my whim to aid verifying all results are accurate.
But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem.
| Accepted Ft' In"
|
|---|
| Input | Value
|
|---|
| 8 | 8
|
| 8.25 | 8.25
|
| 8' 6" | 8.5
|
| 8 6.5 | 8.542
|
| 8.1' 6.25" | 8.621
|
Units of either feet or meters work, but clicking the green Ft' In" button will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on.
The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results.
The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size.
Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5.
- Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them.
- Option 2 - Was deleted, unneeded following improvements.
Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor).
- Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor.
- Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results.
- Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more.
If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3.
The orange Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC.
Options 6-8 still use the sensor size currently described in Options 1-5.
The blue Flip button (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip.
- Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length.
- Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length.
- Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it.
Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits.
- Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that.
The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results.
There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras.
See this summary of Issues determining Sensor Size for more, if any issues.
Scaling Field of View
Greater focal length magnifies, and smaller sensor size crops.
Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera.
However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math).
Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors".
Magnification
Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being:
- Magnification (of object at focus distance) = object image size on sensor / object size in real life.
- Magnification = sensor size / external field size at focus distance.
- Magnification at 1:1 macro is 1 (same size image on sensor as the object real size).
- Magnification of object at Infinity is 0 (infinitesimal in image).
The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths.
Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then:
The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers.
Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same).
Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then:
- Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example.
Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method.
- Magnification = (focal length / field distance) computes same number (similar triangles).
Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension.
When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1.
Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor.
Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses).
Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept.
If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept.
The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification.
Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there.
But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor.
In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance).
Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, 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 field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle.
Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too).
Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors.
And there is also a FoV Math section for FoV.
Menu of the other Photo and Flash pages here
