Angular Size Calculator

What the Angular Size Calculator Does

This angular size calculator works out how large an object appears in the sky from a given distance. You enter the object's true (physical) size and how far away it is, and the tool returns the apparent size as an angle, expressed in arcseconds, arcminutes, or degrees.

It is useful for amateur astronomers planning what fits in an eyepiece or camera field, students learning the small-angle approximation, and anyone curious why the Moon looks the same width as the Sun. Photographers and surveyors can also use it to estimate how big a distant object will appear in a frame.

How It Works: The Angular Size Formula

Angular size depends only on the ratio of an object's actual size to its distance. For the small angles common in astronomy, the apparent size in arcseconds is:

angular size (arcsec) = 206265 x actual size / distance

The actual size and distance must be in the same units (both kilometers, both light-years, and so on) so the units cancel. The constant 206265 is the number of arcseconds in one radian, which converts the raw ratio into arcseconds. To get other units, divide by 60 for arcminutes (60 arcsec = 1 arcmin) or by 3600 for degrees (3600 arcsec = 1 degree). This small-angle formula is accurate for angles up to a few degrees; for very large angles the exact form uses the arctangent of (size / distance).

Worked Example: The Moon

The Moon has a diameter of about 3,474 km and sits roughly 384,400 km away. Plugging into the formula:

angular size = 206265 x 3,474 / 384,400 = 206265 x 0.009037 = 1,864 arcsec.

Converting: 1,864 / 3600 = 0.518 degrees, or about half a degree. The Sun is roughly 400 times larger than the Moon but also about 400 times farther away, so its apparent size works out to nearly the same ~0.5 degree. That near-match is exactly why total solar eclipses are possible: the Moon can just cover the Sun's disk.

Tips, Common Mistakes, and Factors That Affect the Result

A few practical points keep your answers accurate:

• Match your units. The single most common error is mixing units, such as size in kilometers and distance in astronomical units. Convert both to the same unit first.
• Use diameter, not radius, when you want the full apparent width of a disk like a planet or the Moon.
• Remember the conversions: 1 degree = 60 arcminutes = 3600 arcseconds. Reporting 0.5 as arcseconds instead of degrees is off by a factor of 3600.
• Distance dominates. Because angular size scales as 1 / distance, doubling the distance halves the apparent size, while doubling the physical size only doubles it.
• Stick to the small-angle range. The 206265 formula is precise for sky objects but loses accuracy for nearby, very wide objects; switch to the arctangent form there.

Quick Reference and Practical Uses

For perspective, Jupiter spans roughly 30 to 50 arcseconds depending on Earth's distance from it, Venus ranges from about 10 to 60 arcseconds across its phases, and a typical full Moon or Sun is near 1,800 arcseconds (0.5 degrees). The smallest detail a sharp human eye can resolve is around 60 arcseconds (1 arcminute), which is why planets look like points without a telescope.

You can run the calculation in reverse too: if you know an object's distance and measure its apparent angular size, rearrange the formula to find its true diameter. This is the same principle astronomers use to size craters, sunspots, and distant galaxies.