ClarityHow to use this tool
- Choose which direction you need: horizontal, vertical or diagonal.
- Enter the matching active sensor dimension in millimetres and the actual lens focal length in millimetres.
- Calculate the angle in degrees. Use a different sensor dimension to calculate another direction.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| Sensor dimension | Numeric value. Unit: mm. Must be greater than zero. | 36 |
| Focal length | Numeric value. Unit: mm. Must be greater than zero. | 50 |
Result for these sample inputs
39.5977527 degrees
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
Angle = 2 arctan(sensor dimension/(2 × focal length)).
A 36 mm sensor width with a 50 mm lens gives 2 × arctan(36 / 100) ≈ 39.5978° horizontally. Using a 24 mm sensor height with that lens gives approximately 26.9915° vertically.
Understanding your result
Larger sensor dimensions widen the angle at a fixed focal length. Longer focal lengths narrow it at a fixed sensor size. Use actual focal length with actual active sensor dimensions; combining an equivalent focal length with a cropped sensor dimension applies the crop twice.
What to keep in mind
Rectilinear lens model. Fisheye projection, digital cropping, stabilization, distortion and close-focus changes are not modeled. Width, height and diagonal produce different angles. Both input dimensions must be positive and in millimetres.
Common questions
Should I enter 35 mm-equivalent focal length?
Use actual focal length with the actual sensor dimension. Equivalent focal length is useful for comparison but is not paired with a smaller sensor in this formula.
Does this calculate the width of the scene?
It returns an angle. To find a scene width you also need the distance and an appropriate projection model.
Methodology maintained by ClarityKit. How these tools are built and checked.