How do I calculate horizontal and vertical field of view from sensor size, focal length, and working distance?
Asked 9/25/2017
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I need a standard way to calculate field of view for an imaging setup. My inputs include pixel dimensions, pixel size, sensor dimensions, focal length, working distance, and angle of view. Specifically, I want to calculate horizontal and vertical field of view in millimeters.
I found these two formulas:
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Similar-triangles form: f = (h × WD) / HFOV where h is the sensor width, f is focal length, WD is working distance, and HFOV is horizontal field of view in mm.
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Angle-of-view form: HFOV = WD × 2 × tan(horizontal AOV / 2)
These seem to give different results in my spreadsheet. What is the accepted way to calculate horizontal and vertical field of view, and how do these formulas relate?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
8y ago
2 Answers
1
The formula I use in Excel
f = focal length d = format dimension (sensor height or width)
=((ATAN((d/2/f)))*180/PI())*2
Using the above for a 50mm lens mounted to a 35mm full frame measuring 24mm height by 36mm diagonal measure 43.27mm
The vertical angle of view is 27°
The horizontal angle of view is 39.6°
The diagonal angle of view is 46.8°
I use 1000 yards as the distance as to field of view, answer in feet.
=(TAN(d*PI()/180))*1000*3
The vertical distance @ 1000 yards is 1528 feet
The horizontal distance @ 1000 yards is 2482 feet
The diagonal distance @ 1000 yards is 3194 feet
Easy to covert feet to mm
Originally by user44949. Source · Licensed CC BY-SA 4.0
user44949
8y ago
0
Generated from our catalog & community — verify before relying on it.
Both formulas are valid; they describe the same geometry in different ways.
Use sensor dimension and focal length to get angle of view: AOV = 2 × atan(d / (2f)) where d is the relevant sensor dimension (width for horizontal, height for vertical, diagonal for diagonal AOV).
Then convert angle of view to field of view at a given working distance: FOV = 2 × WD × tan(AOV / 2)
You can also go directly by similar triangles: FOV = (d × WD) / f This is the same result as the trig form under the thin-lens approximation.
Typical cause of mismatched answers: mixing units or angle modes. Sensor size, focal length, and working distance must use consistent length units, and trig functions in spreadsheets often expect radians unless you explicitly convert.
So for horizontal and vertical FOV:
- HFOV = (sensor width × WD) / f
- VFOV = (sensor height × WD) / f
Or equivalently:
- horizontal AOV = 2 × atan(sensor width / (2f))
- vertical AOV = 2 × atan(sensor height / (2f))
- then FOV = 2 × WD × tan(AOV / 2)
If Excel was the issue, the likely problem was degrees vs radians in TAN/ATAN.
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