What is angular size?

Angular size (also called angular diameter or apparent size) is the angle an object subtends at the observer's eye. It tells you how large the object looks in the sky, regardless of its true physical dimensions.

What formula does this calculator use?

The exact formula is: angular size = 2 × arctan(physical size / (2 × distance)). For objects much smaller than their distance, this reduces to the small-angle approximation: angle ≈ physical size / distance (in radians).

Why does the Moon look the same size as the Sun?

The Sun is about 400 times larger than the Moon, but it is also about 400 times farther away. Their angular diameters are therefore nearly identical — roughly 0.5° — which is why total solar eclipses are possible.

What is the angular size of the full Moon?

The Moon's angular diameter ranges from about 29.4 arcminutes (at apogee) to 33.5 arcminutes (at perigee). Its average is roughly 31 arcminutes, or about 0.52°.

What units can I use for size and distance?

The calculator accepts kilometers, meters, miles, astronomical units (AU), light-years, and parsecs for both size and distance. All units are converted internally to a common base before computing the angle.

What is an arcsecond?

One degree is divided into 60 arcminutes, and one arcminute is divided into 60 arcseconds. So 1° = 3,600 arcseconds. Most planets and many galaxies have angular sizes measured in arcseconds when observed from Earth.

Angular Size Calculator

Name: Angular Size Calculator
Availability: InStock
Author: Nham Vu

Calculate the angular size of any astronomical object from its physical size and distance.

Object Parameters

Physical Size (diameter)

Distance from Observer

Common Objects

Enter values and click Calculate to see results.

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Summary

Calculate the angular size of any astronomical object from its physical size and distance.

How it works

Enter the physical size (diameter) of the object and choose the appropriate unit.
Enter the distance from the observer to the object and choose the appropriate unit.
The calculator applies the small-angle formula: angle = 2 × arctan(size / (2 × distance)).
Results are shown in degrees (°), arcminutes ('), and arcseconds ('').
Use the "Presets" panel to load common astronomical objects instantly.

Use cases

Find the apparent angular diameter of the Moon, Sun, or planets.
Estimate the angular size of a galaxy or nebula for astrophotography framing.
Check whether a deep-sky object fits within a telescope eyepiece field of view.
Calculate the angular size of exoplanets relative to their host star.
Convert a known angular size back to a physical size using the formula in reverse.
Teach the small-angle approximation in physics or astronomy classes.

Frequently Asked Questions

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Last updated: 2026-05-29 · Reviewed by Nham Vu