Angular Size Calculator — Size, Distance and Apparent Size Online

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What is angular size?

Angular size is how big something looks in the sky, measured as an angle rather than in metres or kilometres. The Moon looks about half a degree wide. Your fist held at arm’s length covers about ten degrees. Two objects can have the same angular size while being wildly different in real size: the Sun and the Moon look almost the same size in our sky, yet the Sun is about 400 times wider than the Moon — it is also about 400 times farther away.

This is why astronomers talk about angles. When you look through a telescope or with your naked eye, you never see kilometres. You see angles. Angular size is the bridge between what you see and what is really there, and this calculator walks across that bridge in all three directions.

The three modes

The calculator has three modes. In the first mode, you enter a real size and a distance, and it returns the angular size in degrees, arcminutes, and arcseconds. An arcminute is one sixtieth of a degree, and an arcsecond is one sixtieth of an arcminute. The full Moon is about 31 arcminutes wide, which is why old star charts often describe small objects in arcminutes.

In the second mode, you enter an angular size and a distance, and it returns the real size. This is how astronomers measure things they cannot touch: if a crater looks 30 arcseconds wide on the Moon and you know the Moon’s distance, you can work out the crater’s real width. In the third mode, you enter an angular size and a real size, and it returns the distance. This is the classic parallax-style trick behind many distance estimates in astronomy.

The formula behind all three modes is exact geometry, not the small-angle shortcut: angular size equals twice the arctangent of size divided by twice the distance. For small angles the shortcut answer and the exact answer agree to many decimal places, but the exact form stays correct even for wide angles, like the size of a building seen from across the street.

A worked example: the Moon

The Moon is about 3,474 kilometres wide and sits about 384,400 kilometres away on average. Enter those two numbers and the calculator returns about 0.518 degrees, or about 31.1 arcminutes. That matches what observers measure. Because the Moon’s orbit is elliptical, its distance varies between about 356,500 and 406,700 kilometres, so its angular size swings between about 0.49 and 0.56 degrees. That is why some full Moons look a little bigger than others — the famous supermoon is just the Moon near its closest point.

Try the reverse direction. Suppose a lunar crater spans 30 arcseconds. Convert that to degrees (30 divided by 3600, or 0.00833 degrees) and combine it with the Moon’s distance, and you get a crater about 56 kilometres wide. That is roughly the size of the crater Copernicus, which is an easy telescopic target.

Everyday uses

Angular size is not only for astronomy. Photographers use it to work out what focal length they need to frame a subject: a building of known height at a known distance subtends a known angle, and the lens must cover that angle. Hikers use a rough version of the same idea when they judge distances by holding a thumb at arm’s length. Surveyors, drone pilots, and archers all meet the same geometry in different clothes.

For stargazers, angular size answers practical questions. Will this galaxy fit in my eyepiece’s field of view? Is that pair of stars wide enough to split with my telescope? How big will Jupiter’s disc look at this magnification? A planet’s angular size in arcseconds, divided by your telescope’s magnification, gives you a feel for the view before you step outside.

Common mistakes

The biggest mistake is mixing units. The calculator requires the size and the distance in the same unit — kilometres with kilometres, metres with metres. If you enter a size in metres and a distance in kilometres, the answer will be wrong by a factor of a thousand. The second mistake is confusing angular size with area. An object that is twice as wide covers four times the area of sky, not twice, because area grows with the square of the width.

The third mistake is forgetting that angular size says nothing about brightness. A small, bright star and a large, dim galaxy can have very different angular sizes and very different visibility. Angular size tells you how much sky something covers, not how easy it is to see.

Frequently asked questions

Why do the Sun and Moon look the same size? Because the Sun is about 400 times wider and about 400 times farther away, so the two ratios cancel. That coincidence is why total solar eclipses happen at all.

What is an arcsecond in plain terms? It is a very small angle: 1/3600 of a degree. A coin held about four kilometres away would span about one arcsecond.

Does the calculator work for very close objects? Yes. The exact formula stays correct at any distance, unlike the small-angle approximation, which starts to drift for wide angles.

Can I use it for camera framing? Yes. Enter the subject’s size and distance to get the angle it covers, then compare that angle with your lens’s field of view.