Angular Size Calculator
Enter the real size of an object and how far away it is to get its angular size — the apparent size it covers in your field of view — in radians and degrees.
Radians and degrees at once
Enter the physical size and the distance and the calculator returns the angular size in radians (size ÷ distance) and in degrees together.
Match the units
The size and the distance must use the same length unit — metres, kilometres, light-years — because only their ratio matters and the units cancel.
What is angular size?
How big something looks, not how big it is
The angular size calculator finds how large an object appears from a given distance — the angle it spans in your field of view. A distant mountain and a nearby coin can cover the same angle, so angular size depends on the ratio of real size to distance, not on the size alone. Using the small-angle approximation, the angle in radians is simply the object's physical size divided by its distance, and multiplying by 180/π converts that to degrees. Astronomers use it to describe how big the Moon, Sun, or a planet looks in the sky.
Enter the real size of an object and its distance to get the angular size in radians and degrees instantly.
The small-angle approximation says the angular size in radians equals the physical size divided by the distance, and you convert to degrees by multiplying by 180/π.
θ = size ÷ distanceSuppose an object is 1 metre wide and sits 1000 metres away. Dividing the size by the distance gives 1 ÷ 1000 = 0.001 radians. To express that in degrees, multiply by 180/π: 0.001 × 57.29578 ≈ 0.057296°. Because the formula uses only the ratio, the same answer holds whether you measure in metres, kilometres, or light-years — as long as the size and distance share the same unit.
The formula is a fast, accurate shortcut, but it is an approximation with a clear range of validity.
Only accurate for small angles
The small-angle approximation (θ ≈ size ÷ distance) is accurate only when the object is much smaller than its distance — roughly when the angle is below about 10°. For larger angles you should use the exact form, θ = 2 × arctan(size ÷ (2 × distance)), which accounts for the curvature the approximation ignores. Keep the size and distance in the same length unit, and remember this gives the angular size for a flat, head-on object, not a curved or tilted one.