The calculator
Angle of view & frame coverage
Select your sensor format, enter the focal length and subject distance. Results update as you type — no submit button needed.
Lens & sensor
The marked focal length of your lens — e.g. 24, 35, 50, 85, 200.
Choose the sensor in your camera body. Sensor dimensions are shown in the selector and detailed in the reference table below.
Frame coverage
Distance from your camera to the subject. Used to calculate the real-world width and height of the area you frame.
horizontal angle of view
Angle of view
Frame coverage at 3 m
How it works — the formulas in full
Nothing here is a black box. The angle-of-view formula comes directly from the geometry of a pinhole model: the sensor dimension is the base of a triangle whose apex sits at the lens's rear nodal point at a distance equal to the focal length. Every step is shown so you can reproduce or verify any result by hand.
Named constants — sensor dimensions (mm)
Sensor format reference
Each format's width, height, and diagonal are physical constants of the sensor.
The diagonal is computed from width and height via the Pythagorean theorem:
diag = sqrt(width² + height²).
All values below are used verbatim in the calculator.
Full frame: 36.0 × 24.0 mm — diagonal 43.27 mm (crop factor 1.0×)
APS-C (1.5×): 23.6 × 15.7 mm — diagonal 28.36 mm (Nikon, Sony, Fujifilm, most third-party)
Canon APS-C (1.6×): 22.3 × 14.9 mm — diagonal 26.82 mm (Canon EF-S and RF-S bodies)
Micro Four Thirds (2×): 17.3 × 13.0 mm — diagonal 21.64 mm (Olympus/OM System, Panasonic)
1-inch (2.7×): 13.2 × 8.8 mm — diagonal 15.86 mm (Sony RX100 series, some compacts & drones)
Formula 1 — Angle of view
AoV = 2 · atan( dimension ÷ (2 · f) )
Where dimension is the sensor width, height, or diagonal in mm and
f is the focal length in mm. The result of atan() is in radians;
multiply by 180 / π to convert to degrees. Run the formula three times — once
with sensor width (horizontal AoV), once with sensor height (vertical AoV), once with sensor
diagonal (diagonal AoV).
The formula assumes the lens is focused at infinity and behaves as a thin ideal lens. At close focus distances, effective focal length increases slightly, making the actual AoV marginally narrower than the formula predicts — the effect is small for most photography but becomes meaningful in macro work.
Formula 2 — Frame coverage at a given distance
coverage = D · sensor_dimension ÷ f
Where D is the subject distance in meters (or any unit — the coverage result comes out in the same unit), sensor_dimension is the sensor width or height in mm, and f is the focal length in mm. The mm units in numerator and denominator cancel, leaving the result in meters.
This formula is exact within the thin-lens model. It tells you the physical size of the scene the frame captures at distance D: run it with sensor width to get frame width, and with sensor height to get frame height.
Sensor dimension reference table
All sensor dimensions are nominal values as commonly specified by manufacturers and industry references. Small variations exist between individual camera models — check your camera's technical specifications for the exact figure if precision matters for your use case.
| Format | Width (mm) | Height (mm) | Diagonal (mm) | Crop factor | Typical cameras |
|---|---|---|---|---|---|
| Full frame | 36.0 | 24.0 | 43.27 | 1.0× | Canon EOS R5/R6, Nikon Z6/Z7, Sony A7/A9 |
| APS-C (1.5×) | 23.6 | 15.7 | 28.36 | 1.5× | Nikon Z30/Z50, Sony A6x00, Fujifilm X-T/X-S |
| Canon APS-C (1.6×) | 22.3 | 14.9 | 26.82 | 1.6× | Canon EOS R50, R10, R7, Rebel series |
| Micro Four Thirds (2×) | 17.3 | 13.0 | 21.64 | 2.0× | OM System OM-5, Panasonic G9/GH6, Lumix S (MFT models) |
| 1-inch (2.7×) | 13.2 | 8.8 | 15.86 | ~2.7× | Sony RX100 series, RX10 series, DJI drones (1-inch) |
Diagonal computed as sqrt(width² + height²). Crop factor is the ratio of the full-frame diagonal (43.27 mm) to each format's diagonal. The 1-inch format uses the 13.2 × 8.8 mm Sony/Nikon standard; some manufacturers spec slightly different dimensions for their 1-inch sensors. All values are nominal — check your camera's official spec sheet for exact figures.
Worked example — 50mm on full frame at 3 m
This is the calculator's default setup. Working through each step by hand shows exactly what the code computes and confirms the results match the expected values.
Look up sensor dimensions for full frame
From the table above: width = 36.0 mm, height = 24.0 mm, diagonal = 43.27 mm. These are the named constants used in all three angle calculations.
Compute horizontal angle of view
AoV_H = 2 × atan(36.0 ÷ (2 × 50)) = 2 × atan(0.36)
atan(0.36) = 0.3481 radians
AoV_H = 2 × 0.3481 × (180 / π) = 2 × 19.944° = 39.6°
Compute vertical angle of view
AoV_V = 2 × atan(24.0 ÷ (2 × 50)) = 2 × atan(0.24)
atan(0.24) = 0.2355 radians
AoV_V = 2 × 0.2355 × (180 / π) = 2 × 13.495° = 27.0°
Compute diagonal angle of view
AoV_D = 2 × atan(43.27 ÷ (2 × 50)) = 2 × atan(0.4327)
atan(0.4327) = 0.4083 radians
AoV_D = 2 × 0.4083 × (180 / π) = 2 × 23.395° = 46.8°
Compute frame coverage at 3 m subject distance
Frame width = 3 m × 36.0 mm ÷ 50 mm = 3 × 0.72 = 2.16 m
Frame height = 3 m × 24.0 mm ÷ 50 mm = 3 × 0.48 = 1.44 m
At 3 m, a 50mm full-frame shot captures a frame 2.16 m wide by 1.44 m tall —
roughly the width of a car door and the height of a seated person.
Common mistakes when thinking about field of view
Field of view is easy to reason about incorrectly. These are the errors that cause real planning mistakes — from equipment selection to composition decisions.
Comparing focal lengths across formats without accounting for sensor size
A "50mm lens" means different things on different bodies. On full frame it gives a roughly normal, 39.6° horizontal view. On an APS-C body (1.5× crop) the same lens gives 26.7° — equivalent to an 75mm lens on full frame. If you read gear reviews written for a different sensor size than your own, every focal length recommendation needs to be adjusted by the crop factor before it applies to your camera. The calculator above makes this concrete: keep the focal length the same and switch the sensor format to see exactly how much the angle of view shifts.
Confusing diagonal AoV with horizontal AoV
Manufacturers and reviewers often quote the diagonal angle of view because it is the largest of the three values and the most impressive-sounding. A lens described as having a "47-degree field of view" is almost always quoting the diagonal — but when you look through the viewfinder, the intuitive sense of "how wide is this" maps to the horizontal angle. For a 36×24mm sensor, a 50mm lens has a 46.8° diagonal AoV, a 39.6° horizontal AoV, and a 27.0° vertical AoV. These are meaningfully different numbers; be clear which axis you are comparing.
Treating angle of view as linear with focal length
Doubling the focal length does not halve the angle of view — the relationship is trigonometric, not linear. Going from 25mm to 50mm (doubling) reduces horizontal AoV on full frame from 73.7° to 39.6°, a drop of 34 degrees. Going from 50mm to 100mm (another doubling) reduces it from 39.6° to 20.4°, a drop of only 19 degrees. The narrowing effect of longer focal lengths is felt much more strongly in the wide-to-normal range than in the telephoto range, which is why a few millimeters of focal length change matter more at 24mm than at 200mm.
Conflating frame coverage (distance-dependent) with angle of view (distance-independent)
Angle of view is a fixed property of the lens-and-sensor combination — it does not change when you step closer or farther from your subject. What changes with distance is the real-world area you capture, the frame coverage. If you need to know whether a person fits in the frame at a given distance, use the coverage output. If you need to know whether a lens will produce a wide or tight look regardless of how far you stand, use the angle of view. Mixing these up is a common source of confusion when planning portrait, event, or architectural shots.
Assuming the focal length engraved on the lens is the effective focal length at close distances
The 50mm marked on a lens is its nominal focal length when focused at infinity. As you focus closer, the lens elements extend outward and the effective focal length increases slightly, which narrows the angle of view relative to what the formula predicts. For general photography this is a negligible effect — at typical portrait or landscape distances the formula is accurate within a fraction of a degree. At true macro distances (1:1 magnification), however, the effective focal length can be nearly double the nominal value, so the actual AoV is substantially narrower than this calculator shows.