Enter the visual size and the distance into the Visual Angle Calculator. The calculator will evaluate the Visual Angle.
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Visual Angle Formula
The following example problem outlines the steps and information needed to calculate the Visual Angle.
\begin{aligned}
VA &= 2\arctan\!\left(\frac{S}{2D}\right) \\
VA &\approx \frac{S}{D}\quad \text{(small angles, in radians)}
\end{aligned}Variables:
- VA is the Visual Angle (radians; multiply by 180/π to convert to degrees)
- S is the visual size (the full linear size/extent of the object, e.g., height or diameter)
- D is the distance from the eye (or viewpoint) to the object
To calculate the full visual angle of an object, take 2 times the inverse tangent of the object size divided by 2 times the distance. For small angles (when S is much smaller than D), you can use the approximation VA ≈ S/D (in radians).
How to Calculate Visual Angle?
The following steps outline how to calculate the Visual Angle.
- First, determine the visual size (full height/width/diameter) of the object.
- Next, determine the viewing distance (from the eye to the object).
- Next, gather the formula from above: VA = 2×atan(S/(2D)).
- Finally, calculate the Visual Angle (and convert to degrees if needed).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
visual size = 30
distance = 20
VA = 2×atan(S/(2D)) = ?
VA = 2×atan(30/(2×20)) = 2×atan(0.75) ≈ 1.2870 radians ≈ 73.7398°
