UTILS.
100% in-browser
📐

Angular Size Calculator

Solve any of physical size, distance, or apparent angle from θ = 2·arctan(size/2·distance); results in degrees, arcminutes, and arcseconds.

Enter any two of size, distance, and angle; leave one blank to solve for it. Size and distance must share one length unit.

About this tool

The Angular Size Calculator is a free, in-browser astronomy tool that relates an object's true physical size, its distance, and the apparent angle it subtends in the sky. It uses the exact relation θ = 2·arctan(size / (2·distance)); for the small angles common in astronomy this matches the handy approximation θ(arcsec) ≈ 206,265 × size / distance. Leave any one of the three quantities blank and the calculator solves for it.

All of the trigonometry runs locally in your browser, so the values you type are never uploaded or stored. The physical size and distance must be entered in the same length unit — metres, kilometres, light-years, whatever you like — because only their ratio matters; the apparent angle can be entered or read out in degrees, arcminutes, or arcseconds.

The angular result is always reported in all three angular units at once (1° = 60′ = 3,600″), which makes it easy to check, for example, that the Moon and the Sun both subtend roughly half a degree from Earth, or to work out how large a planet or galaxy appears through a telescope. The small-angle form is accurate to better than 1% for angles under about 10°.

Frequently asked questions

What is the angular size formula?
The exact form is θ = 2·arctan(size / (2·distance)). For small angles it reduces to θ(radians) ≈ size / distance, or θ(arcsec) ≈ 206,265 × size / distance, which is accurate to under 1% below about 10°.
Do size and distance need the same units?
Yes. Because only the size-to-distance ratio enters the formula, both must use the same length unit — metres, kilometres, AU, light-years — and the units cancel out. The angle is unit-independent.
Which value can I solve for?
Leave exactly one of physical size, distance, or angle blank. Blank angle gives θ = 2·arctan(size/2·distance); blank size gives size = 2·distance·tan(θ/2); blank distance gives distance = size / (2·tan(θ/2)).
How big does the Moon look from Earth?
The Moon's diameter is about 3,474 km at a distance near 384,400 km, giving an angular size of roughly 0.52°, or about 31 arcminutes — close to the Sun's, which is why total solar eclipses are possible.

More tools