Calculate visual angle, object size, viewing distance, and screen field of view from size, angle, distance, aspect ratio, and resolution.

Centered flat object or screen. Viewing distance is perpendicular from the eye to the objectโ€™s plane.

Related Calculators

Visual Angle Formula

The following example problem outlines the steps and information needed to calculate the Visual Angle.

VA & = 2arctan((S) / (2D)) \ VA & โ‰ˆ (S) / (D) (small angles, in radians)

Variables:

  • VA is the Visual Angle (radians; multiply by 180/ฯ€ 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 perpendicular distance from the eye to the plane of a centered flat object

For a flat extent centered on a perpendicular sightline, calculate twice the inverse tangent of half the full size divided by viewing distance. Off-center, tilted, curved or spherical objects require different geometry. For small angles (S much smaller than D), VA โ‰ˆ 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 = 2ร—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.

full visual size = 30 cm

perpendicular viewing distance = 20 cm

VA = 2ร—atan(S/(2D)) = ?

VA = 2ร—atan(30/(2ร—20)) = 2ร—atan(0.75) โ‰ˆ 1.2870 radians โ‰ˆ 73.7398ยฐ