Calculate Angular Diameter

Name: Calculate Angular Diameter
Author: Jürgen Kummer

Visualisation

Calculator for the apparent size of distant objects in degrees, from real size and distance. This is the angular size that we see.

g = real size, r = distance, α = angular diameter or apparent size, parallax

g and r have the same unit, regardless if centimeters or light-years. You can convert length units here.
The unit of the angle is degrees or radiant. You can convert angle units here.

Formulas: g = |2r*tan(α/2)| ; r = |g/(2*tan(α/2))| ; α = 2*arctan(g/(2r))

The visual angle describes how big something appears, i.e. the extent it occupies in the field of vision. The link between apparent size and real size is distance. Without knowing the distance, you can only estimate the real size from experience and this can be very deceptive.
The visual angle is usually given in degrees. 360 degrees would go all the way around, but we can't see that because our visual field is smaller. The full moon and the sun have a size of half a degree, although of course you shouldn't look directly at the sun. A house ten meters wide and one hundred meters away, viewed straight on, is about six degrees wide.

Examples from astronomy: the moon has a size of approximately 3500 km (g) and a distance of 400000 km (r). It has an apparent size of about 0.5 degrees (α). The galaxy M51 is about 31 megalight-years away from us and has an angular diameter of 0.19 degrees, which corresponds to 103000 light-years diameter.
At distances above hundreds of millions of light-years, the curvature of space plays a role, which is neglected here.

Parallax is the technical term for an apparent change in position of an object when the position of the viewer changes. This can also be calculated here.
Example for a parallax: a mountain in a distance of 50 km, seen from two points 100 m away from each other (line between the points upright to the distance), changes its apparant position for 0.115°.

Last updated on 06/23/2025. Author: Jürgen Kummer

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