Angular Size Calculator
Angular diameter from physical size and distance (or size from angle), in degrees, arcminutes and arcseconds — with comparisons to the Moon, a fist at arm’s length and telescope resolution.
How it works
θ = 2·arctan(size ÷ 2·distance) ≈ size ÷ distance (radians) for small angles; 1° = 60′ = 3,600″
Angular size is what actually determines how big something looks: the Sun is 400 times wider than the Moon but 400 times further, so both span half a degree — the coincidence that makes total eclipses possible. Astronomers work in arcseconds; the Hubble telescope resolves about 0.05″, ground-based seeing rarely beats 1″. The same geometry sizes a distant building, checks whether a sign is legible from the road or whether a planet is resolvable in a telescope.
Worked example
The Moon: 3,474 km at 384,400 km → 0.518° = 31.1′. Jupiter at opposition: 143,000 km at 630 million km → 47″, a clear disc in a small telescope.
Frequently asked questions
When does the small-angle approximation fail?
Beyond about 10° the error passes 0.3%; the calculator uses the exact arctangent throughout.
How small can the eye resolve?
About one arcminute for high-contrast detail — Venus (up to 1′) is the only planet that is marginally a disc.
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This calculator is for educational purposes. Double-check important results before acting on them.