How do you calculate angle of view from sensor size and focal length?
Asked 7/27/2013
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How can I calculate a camera's field of view (angle of view) in degrees from the sensor size and focal length? For example, with a 1-inch sensor and a 30mm lens, how do the common online calculators work? Also, does subject distance matter, and should I use horizontal, vertical, or diagonal sensor size?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
13y ago
2 Answers
17
The calculators you posted are for fairly standard, rectilinear lenses. This means you can use the Pinhole camera model to calculate the information.
This graphic fairly well shows what is going on:
On the horizontal axis you see f. This is the focal length of the lens. Then, the arrow labeled Y1 is the image plane (where the sensor sits). If the sensor has the half-size of y1, then the angle of the green line with the horizontal is half your field of view.
Basic geometry can give you the FOV: FOV = 2 * arctan(y1 / f)
Mind two things:
- Units.
y1is the half-size of your sensor. If you have a 1" sensor, the half-size would be 8mm (as mattdm pointed out in the comments), and your calculation would give you the FOV along the diagonal of the sensor. If you want it along the horizontal, then you need to calculate the width of the sensor and use that as the value fory1.
Originally by user7718. Source · Licensed CC BY-SA 4.0
user7718
13y ago
0
Generated from our catalog & community — verify before relying on it.
For a standard rectilinear lens, the usual calculators are based on simple pinhole-camera geometry.
Use: angle of view = 2 × arctan(sensor dimension / (2 × focal length))
Pick the sensor dimension that matches the view you want:
- horizontal AoV: sensor width
- vertical AoV: sensor height
- diagonal AoV: sensor diagonal
Equivalently, if you use half the sensor size y and focal length f: AoV = 2 × arctan(y / f)
Important notes:
- Keep units consistent. If focal length is in mm, sensor size must also be in mm.
- A “1-inch” sensor is not actually 1 inch across, so use its real dimensions.
- Subject distance is not needed to calculate angle of view itself. Distance is only useful if you want to know how much of the scene fits into the frame at that distance.
- The result depends on whether you mean horizontal, vertical, or diagonal AoV.
- This simple formula assumes a rectilinear lens. Strongly distorted lenses such as fisheyes may not match it well.
If you need the real-world framed width at a given distance, taking a test photo of an object with known size is a practical way to verify it.
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