About

Incorrect field of view estimates lead to missed framing, wasted lens purchases, and failed surveillance coverage. This calculator computes horizontal, vertical, and diagonal FOV angles from physical sensor dimensions and focal length using the standard arctangent projection model: θ = 2 ⋅ arctan(d ÷ 2f). It derives crop factor relative to the 35mm full-frame diagonal of 43.27mm, and projects real-world scene coverage at a user-specified distance. The tool assumes rectilinear lens projection. Results diverge from reality for fisheye or ultra-wide lenses below 10mm equivalent, where barrel distortion dominates.

Pro tip: manufacturer-stated focal lengths are nominal. Actual values shift with focus distance due to focus breathing, particularly on cinema lenses. For security camera placement, always add a 10 - 15% margin to your calculated coverage width to account for lens tolerances and mounting alignment errors.

Formulas

The rectilinear field of view angle θ for any sensor dimension d and focal length f is derived from simple trigonometry of the imaging triangle:

θ = 2 ⋅ arctan(d2 ⋅ f)

where d is the sensor dimension (width, height, or diagonal) in mm, and f is the lens focal length in mm. Substitute the appropriate dimension to obtain horizontal (θ_H), vertical (θ_V), or diagonal (θ_D) FOV.

The sensor diagonal is computed via the Pythagorean theorem:

d_diag = √w² + h²

The crop factor C relates a sensor to the 35mm full-frame reference diagonal of 43.27mm:

C = 43.27d_diag

Scene coverage (width or height of the visible area) at a given distance D:

W_scene = 2 ⋅ D ⋅ tan(θ2)

where D = distance to subject, W_scene = coverage dimension in matching units, θ = the corresponding FOV angle, C = crop factor (dimensionless), w = sensor width in mm, h = sensor height in mm, f = focal length in mm.

Reference Data

Sensor Format	Width mm	Height mm	Diagonal mm	Crop Factor	Common Use
Medium Format (Fuji GFX)	43.8	32.9	54.78	0.79	Studio / Landscape
Full Frame (35mm)	36.0	24.0	43.27	1.0	Professional Photo/Video
APS-H (Canon 1D)	28.7	19.0	34.42	1.26	Sports Photography
APS-C (Canon)	22.3	14.9	26.82	1.61	Consumer DSLR
APS-C (Nikon/Sony)	23.5	15.6	28.21	1.53	Consumer DSLR/Mirrorless
Micro Four Thirds	17.3	13.0	21.64	2.0	Mirrorless / Drone
1 inch (Sony RX100)	13.2	8.8	15.86	2.73	Compact / Drone
Super 35mm (Cinema)	24.89	18.66	31.11	1.39	Cinema Cameras
2/3 inch	8.8	6.6	11.0	3.93	Broadcast / Security
1/1.7 inch	7.6	5.7	9.5	4.55	Premium Compact
1/2 inch	6.4	4.8	8.0	5.41	Security Cameras
1/2.3 inch	6.17	4.55	7.66	5.64	Action Cameras
1/2.5 inch	5.76	4.29	7.18	6.02	Dashcams / Webcams
1/3 inch	4.8	3.6	6.0	7.21	CCTV / IP Cameras
1/4 inch	3.6	2.7	4.5	9.62	Miniature / Endoscope
iPhone 15 Pro Main	9.8	7.3	12.22	3.54	Smartphone
Samsung S24 Ultra Main	9.57	7.22	11.99	3.61	Smartphone
Hasselblad X2D	43.8	32.9	54.78	0.79	Medium Format
Phase One IQ4 150MP	53.4	40.0	66.73	0.65	Large Medium Format
RED Komodo (S35)	27.03	14.26	30.56	1.42	Cinema 6K
ARRI Alexa 35	27.99	19.22	33.96	1.27	Cinema 4.6K
DJI Mavic 3 (4/3)	17.3	13.0	21.64	2.0	Drone
GoPro Hero 12	6.17	4.55	7.66	5.64	Action Camera
Blackmagic Pocket 6K	23.1	12.99	26.51	1.63	Cinema

Frequently Asked Questions

Crop factor multiplies the focal length to give a 35mm-equivalent value. A 50mm lens on an APS-C sensor (crop factor 1.5) produces the same field of view as a 75mm lens on full frame. The actual focal length does not change - only the captured portion of the image circle narrows, which mimics a longer lens. This matters when matching lenses across systems: a 35mm f/1.4 on Micro Four Thirds (crop 2.0×) frames like a 70mm on full frame.

Manufacturers typically quote diagonal angle of view measured at infinity focus. At closer focus distances, many lenses exhibit focus breathing - the effective focal length shortens or lengthens, shifting the FOV by 5-20%. Cinema lenses are specifically designed to minimize breathing. Additionally, some cameras crop the sensor area for video modes (e.g., Sony 4K crop on APS-C bodies), further reducing the effective sensor dimensions.

No. The arctangent formula models rectilinear projection, where straight lines in the scene remain straight in the image. Fisheye lenses use equidistant, equisolid, or stereographic projections that compress peripheral rays. A rectilinear 8mm lens on full frame would calculate to approximately 153° - but physical rectilinear lenses cannot exceed roughly 120° before distortion becomes extreme. For fisheye lenses, use the manufacturer's stated angle or apply the specific projection equation for that lens design.

Rearrange the coverage formula. If you need to cover a width W at distance D, the required focal length is: f = (sensor width × D) / W. For example, to cover a 10-meter-wide scene at 20 meters with a full-frame sensor (width 36mm): f = (36 × 20) / 10000 = 0.072, which gives 72mm. Always convert W and D to the same units (millimeters) before dividing, or keep them both in meters and the sensor width in mm to get the focal length in mm directly.

A wider aspect ratio (e.g., 16:9 vs 3:2) increases horizontal FOV but reduces vertical FOV for the same diagonal measurement. Two sensors with identical diagonals but different aspect ratios produce different horizontal and vertical coverage. The 16:9 crop common in video mode on a 3:2 sensor discards top and bottom rows, reducing vertical FOV by roughly 12% compared to full-sensor readout while keeping horizontal FOV nearly unchanged.

The coverage formula assumes a flat plane perpendicular to the optical axis. At short distances (under 2 meters), parallax and lens-to-sensor distance (which increases during close focusing) introduce errors of 3-8%. At very long distances (over 500 meters), atmospheric refraction can slightly bend light paths, though this effect is negligible for most photography. For macro photography, the effective focal length can double at 1:1 magnification, halving the calculated FOV.