Angular Size Calculator

Angular size, also called angular diameter or apparent size, is the angle an object appears to span from where you stand. It is not a length but an angle, so the same object looks larger up close and smaller far away. Two objects of very different real sizes can share an angular size if their distances scale to match.

This tool uses the exact form theta = 2 x arctan(size / (2 x distance)), where size is the object's real width and distance is measured to it. The angle comes out in radians and is then converted to degrees, arcminutes and arcseconds. Only the ratio of size to distance matters.

The simple ratio size / distance is the small-angle approximation and it is only accurate when the object is far smaller than its distance. The arctangent version is exact at every angle, so it stays right for a wide object seen from close up, where the shortcut would overstate the angle.

They subdivide a degree the way minutes and seconds subdivide an hour. One degree is 60 arcminutes and one arcminute is 60 arcseconds, so a degree holds 3600 arcseconds. Astronomers use these finer units because most objects in the sky span far less than a whole degree.

Yes, and that is the only rule. Because the formula depends on the ratio size to distance, the units cancel, so kilometres over kilometres or metres over metres both give the same angle. Mixing units, such as a size in metres and a distance in kilometres, produces a wrong answer.

From Earth the Moon spans roughly 0.5178 degrees and the Sun roughly 0.5327 degrees, close enough that the Moon can just cover the Sun's disc. That near match is exactly why total solar eclipses are possible, and why the fit is sometimes snug and sometimes ring-shaped as the distances vary.

Both the size and the distance must be finite numbers greater than zero. A zero or negative value has no physical meaning here and is rejected with a message, so you always work from a real object at a real distance.

Not directly in this tool, but the relationship rearranges easily. If you know the angle and the distance, the real size is 2 x distance x tan(theta / 2). Knowing the angle and the size instead lets you solve for distance the same way.

Yes. The trigonometry runs in your browser, so the size and distance you enter never leave your device and the tool keeps working with no internet connection.