Camera FOV Calculator: Field of View by Sensor & Lens

What is a camera field of view calculator?

A camera field of view (FOV) calculator works out how wide a scene a camera can capture. It uses two numbers: the size of the camera's sensor and the focal length of the lens. The result is an angle, usually given in degrees, for the horizontal, vertical, and diagonal directions.

Field of view matters because it decides what fits in the frame. A wide field of view captures a broad scene, such as a landscape. A narrow field of view captures a small slice of a scene but makes distant subjects look larger.

How to calculate field of view

Field of view depends on two things: the sensor dimension (width or height, in millimeters) and the lens focal length (also in millimeters). The formula uses the arctangent function, written as arctan or tan⁻¹:

FOV = 2 × arctan(d / (2 × f))

• d is the sensor dimension: width for horizontal FOV, height for vertical FOV.
• f is the focal length of the lens, in millimeters.
• The result comes out in radians and is converted to degrees for display.

The formula assumes a rectilinear lens focused at infinity, which is the usual reference case. Focusing on a close subject moves the lens further from the sensor and narrows the real field of view slightly.

The diagonal FOV uses the same formula, but with the sensor's diagonal length in place of width or height. The diagonal is found with the Pythagorean theorem:

diagonal = √(width² + height²)

Sensor height, when only the width and an aspect ratio are known, is found by dividing width by the aspect ratio:

height = width ÷ aspect ratio

A 3:2 aspect ratio (aspect ratio value 1.5) is standard for most DSLR and mirrorless photos. A 16:9 ratio (1.778) is standard for video. A 4:3 ratio (1.333) is used by Micro Four Thirds cameras and many older compacts. Cinema productions sometimes use a 2.39:1 ratio for a widescreen look.

Common sensor sizes

Sensor size changes the field of view even when the focal length stays the same. A larger sensor captures a wider angle from the same lens.

The calculator lists these sizes, in width × height:

• Medium format: 43.8 × 32.9 mm
• Full frame (35mm): 36 × 24 mm
• APS-H: 28.7 × 19.0 mm
• APS-C (Nikon/Sony): 23.5 × 15.6 mm
• APS-C (Canon): 22.3 × 14.9 mm
• Micro Four Thirds: 17.3 × 13.0 mm
• 1-inch: 13.2 × 8.8 mm, used in high-end compact cameras and many drones
• 2/3-inch: 8.8 × 6.6 mm
• 1/1.7-inch: 7.6 × 5.7 mm
• 1/2.3-inch: 6.17 × 4.55 mm, common in smartphones and action cameras

Any other sensor can be entered by choosing "Custom" and typing its width and height.

The full-frame diagonal (43.3 mm) divided by a sensor's diagonal is called the crop factor. It is used to compare lenses across different cameras, and is described in the FAQ below. APS-C (Nikon/Sony) works out at about 1.5, APS-C (Canon) at about 1.6, and Micro Four Thirds at 2.0.

Example calculation

Take a full-frame camera (36 × 24 mm sensor) fitted with a 50mm lens.

Horizontal FOV: HFOV = 2 × arctan(36 / (2 × 50)) = 2 × arctan(0.36) ≈ 39.60°

Vertical FOV: VFOV = 2 × arctan(24 / (2 × 50)) = 2 × arctan(0.24) ≈ 26.99°

Diagonal FOV: Diagonal = √(36² + 24²) ≈ 43.27 mm DFOV = 2 × arctan(43.27 / 100) ≈ 46.79°

A 50mm lens on full frame is called a "normal" lens because its focal length is close to the 43.3 mm sensor diagonal. Lenses shorter than the diagonal are wide angle; longer ones are telephoto.

Quick reference: full-frame focal lengths

A shorter focal length always gives a wider field of view. A longer focal length always narrows it.

How to use the calculator

1. Pick a sensor size from the list, or choose "Custom" and enter the exact width and height in millimeters.
2. Enter the focal length of the lens, in millimeters.
3. Derive the height from an aspect ratio if the sensor height is unknown. This option appears only for a custom sensor: tick "Calculate height from aspect ratio" and pick 3:2, 4:3, 16:9, 1:1 or 2.39:1. The calculator then sets height = width ÷ ratio.
4. Read the results: sensor dimensions, then horizontal, vertical and diagonal FOV, shown in degrees or in radians, whichever unit is selected.

Every measurement must be a positive number. A focal length of zero or less, a sensor width or height of zero or less, and any value that is not a real number are all refused, and the calculator shows a message instead of a result.

Why field of view matters

Photographers use FOV to choose a lens before a shoot. A wide lens (14-35mm on full frame) fits more of a room or landscape into the frame. A telephoto lens (85mm and longer) isolates a distant subject and compresses the background.

Cinematographers calculate FOV when planning shots, so that camera position and lens choice match the intended framing. Security installers use it to work out how much of a room or parking lot a single camera covers. Drone pilots use it to plan flight paths that fully cover a survey area without gaps.

Sensor size changes these numbers too. A smaller sensor narrows the field of view for a given lens, which is why the same 50mm lens looks like a longer telephoto on an APS-C camera than on a full-frame camera.

Frequently asked questions

What is field of view in photography?

Field of view is the angle of the scene a lens and sensor capture together, measured in degrees. A wide angle, such as 74°, covers a broad scene. A narrow angle, such as 10°, covers a small slice of the scene but magnifies distant subjects.

How does sensor size affect field of view?

A larger sensor captures more of the image a lens projects, giving a wider field of view. A smaller sensor crops that same projected image, narrowing the field of view. This is why a 50mm lens has a different field of view on a full-frame camera than on an APS-C camera.

What is crop factor?

Crop factor is the full-frame diagonal of 43.3 mm divided by a sensor's diagonal. An APS-C (Nikon/Sony) sensor has a crop factor near 1.5×, an APS-C (Canon) sensor near 1.6×, and Micro Four Thirds near 2×. Multiplying a lens's focal length by the crop factor gives its full-frame-equivalent focal length, useful for comparing lenses across camera systems. It should not be used in place of the actual sensor dimensions when calculating the real field of view of that camera.

What focal length gives a "normal" field of view?

A normal lens has a focal length close to the sensor diagonal, so the picture looks neither stretched nor compressed. On full frame the diagonal is 43.3 mm, and the common 50mm lens is near enough: it gives a horizontal field of view of about 39.6° and a diagonal field of view of about 46.8°. On smaller sensors a shorter lens is needed to match that view, because the diagonal is shorter.

How does aspect ratio change the field of view?

Aspect ratio sets the relationship between sensor width and height, which changes the vertical field of view for a fixed width. A wide ratio like 16:9 gives less vertical coverage than 4:3 at the same width and focal length, because the sensor is relatively shorter.

Can field of view be changed after a photo is taken?

Cropping an image narrows its effective field of view but cannot widen it beyond what the lens originally captured. Techniques such as panorama stitching can combine multiple photos into a wider field of view, but this requires taking several shots at the time of capture, not just editing afterward.

References

1. "Angle of view." Wikipedia, Wikimedia Foundation. https://en.wikipedia.org/wiki/Angle_of_view
2. Ray, Sidney F. Applied Photographic Optics. Focal Press, 2002.
3. Jacobson, Ralph E. The Manual of Photography. Focal Press, 2000.