Enter the visual size and the distance into the Visual Angle Calculator. The calculator will evaluate the Visual Angle. 

Visual Angle Calculator

Choose what you know, then calculate the missing value.

Angle
Size
Distance
Screen FOV
Solve visual angle
Solve object size
Solve viewing distance
Solve screen field of view

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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.

  1. First, determine the visual size (full height/width/diameter) of the object.
  2. Next, determine the viewing distance (from the eye to the object).
  3. Next, gather the formula from above: VA = 2×atan(S/(2D)).
  4. Finally, calculate the Visual Angle (and convert to degrees if needed).
  5. 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°