Space · Sky
Angular size calculator.
Enter how big something is and how far away it is to see how large it appears in the sky.
Inputs
Angular size
Enter a size and a distance.
How angular size is worked out
Angular size is the angle an object covers in your field of view. For an object of width d at distance D, the exact relation is δ = 2 · arctan(d / 2D). When the object is far smaller than its distance, this shrinks to δ ≈ d / D radians (Wikipedia, Angular diameter). The tool uses the exact form, so it also works for very close or very wide objects. An arcminute is 1/60 of a degree and an arcsecond is 1/60 of an arcminute.
Worked example, the Moon. The Moon's mean diameter is 3,474.8 km (from NASA's radii) and its mean distance is 384,400 km. The tool gives 0.5179°, which is 31.08 arcminutes. Wikipedia lists the Moon's apparent diameter as ranging from 29.33 to 34.10 arcminutes as its distance changes, so the mean-distance figure sits inside that range. NASA's fact sheet gives a mean apparent diameter of 1,896 arcseconds, the yardstick used for the “Compared with the Moon” line.
Worked example, the Sun. With a diameter of about 1,391,400 km at 149.6 million km the result is 1,918 arcseconds, within an arcsecond of NASA's listed 1,919 arcseconds at 1 AU (range 1,887 to 1,952). That is why the Sun and Moon look about the same size in our sky.
Safety: never look at the Sun without certified solar eclipse glasses or a proper solar filter.
Frequently asked questions
How do I find the angular size of the Moon?
Enter its diameter (3,474.8 km) and its distance (384,400 km on average). The result is about 31.08 arcminutes, or 0.518 degrees. Wikipedia gives the range over its orbit as 29.33 to 34.10 arcminutes.
What is the small-angle formula?
When the object is much smaller than its distance, the angle in radians is about size divided by distance. Multiply by 206,265 to get arcseconds. This calculator uses the exact arctangent form instead.
How many arcseconds are in a degree?
There are 3,600 arcseconds in one degree: 60 arcminutes per degree and 60 arcseconds per arcminute.
Can I use it to find the real size of a distant object?
Not directly. Rearranged, the size is roughly the angle in radians times the distance. For example, a 1 arcminute angle at 1,000 m is about 0.29 m wide (1 arcminute = 0.000291 radians).
Sources
Checked
Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Treats the object as a flat disc facing you and ignores atmospheric refraction. A sphere seen from close range subtends a slightly different angle than the disc formula gives.