📐 Angular Size Calculator
Enter an object's diameter and distance to get its angular size — how big it appears — in degrees, arcminutes and arcseconds.
Degrees
0.518°
Arcminutes
31.1′
Arcseconds
1860″
Angular (apparent) size is how large something looks: θ = 2·arctan(diameter ÷ 2·distance). For distant objects this is the small-angle rule, θ(arcsec) ≈ 206,265 × size ÷ distance. The Moon and Sun both span about half a degree — which is why eclipses fit so neatly. 1° = 60′ = 3,600″. 🔒 In your browser.
How the angular size calculator works
Angular size is how large something looks in the sky, regardless of its true size — it depends on the ratio of diameter to distance. The tool uses θ = 2 × arctan(diameter ÷ (2 × distance)), which for small angles reduces to the astronomer's rule θ(arcseconds) ≈ 206,265 × diameter ÷ distance. Enter the diameter and distance in the same units.
The Moon and the Sun both appear about half a degree across — a coincidence that makes total solar eclipses possible. Angular sizes are given in degrees, arcminutes (1⁄60 of a degree) and arcseconds (1⁄60 of an arcminute).
Frequently asked questions
What is angular size?
The apparent size of an object as an angle in the sky — how much of your field of view it fills. A nearby small object and a distant large one can have the same angular size. It depends on diameter ÷ distance.
How do I calculate angular size?
θ = 2 × arctan(diameter ÷ (2 × distance)). For distant objects this simplifies to θ in arcseconds ≈ 206,265 × diameter ÷ distance (in the same units). The tool does both.
How big is the full moon in the sky?
About 0.5° (half a degree), or roughly 31 arcminutes across. Surprisingly small — you can cover it with the tip of your little finger held at arm's length.
Why do the Sun and Moon look the same size?
By coincidence, the Sun is about 400× larger than the Moon but also about 400× farther away, so both span roughly half a degree. That near-match is why the Moon can exactly cover the Sun in a total eclipse.
What are arcminutes and arcseconds?
Subdivisions of a degree for measuring small angles: 1 degree = 60 arcminutes, and 1 arcminute = 60 arcseconds. Planets and stars are measured in arcseconds.
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