Angular Size Calculator
The angular size of an object tells you how large it appears in the sky, regardless of its true physical size. An object can appear large because it is physically big, or because it is close. The exact formula is theta = 2 arctan(physical size / (2 times distance)), with both measurements in the same unit. This calculator accepts any consistent units (km, AU, parsecs) and converts the output to degrees, arcminutes, and arcseconds simultaneously, so you can compare results directly with telescope eyepiece fields of view and star atlas charts.
Angular size formula
theta (rad) = 2 * arctan(size / (2 * distance))
1 degree = 60 arcmin = 3,600 arcsec
For small angles where size is much less than distance (common in astronomy), theta in radians approximately equals size / distance. This small-angle approximation is accurate to better than 1% when the ratio size/distance is less than 0.1. The exact formula is always used here.
Angular size reference values
Moon: 0.50 degrees (30 arcmin). Sun: 0.53 degrees (32 arcmin). Jupiter at opposition: about 45 arcsec. Mars at closest approach: about 25 arcsec. Andromeda Galaxy: about 3 degrees visible extent. Human full Moon finger-width at arm's length: about 1.5 to 2 degrees. Field of binoculars (7x50): typically 7 degrees.
Angular size: frequently asked questions
What is angular size?
Angular size (also called angular diameter) is the angle subtended by an object at the observer's eye. It depends on both the object's physical size and its distance. The full Moon, for example, subtends about 0.5 degrees (30 arcminutes) as seen from Earth.
What is the formula for angular size?
The exact formula is theta = 2 arctan(d_phys / (2 * dist)), where d_phys is the physical diameter and dist is the distance, both in the same units. For small angles (common in astronomy), theta approximately equals d_phys / dist in radians.
What are arcminutes and arcseconds?
One degree is divided into 60 arcminutes (arcmin), and one arcminute into 60 arcseconds (arcsec). So 1 degree = 3,600 arcseconds. The angular resolution of the Hubble Space Telescope is about 0.05 arcseconds. The human eye resolves about 1 arcminute.
Why does the Moon appear the same size as the Sun?
The Moon's diameter is about 3,474 km and it is about 384,400 km away; the Sun is about 1,392,700 km in diameter and about 149,600,000 km away. Both subtend almost exactly 0.5 degrees, which is why solar eclipses can be total.
How do astronomers measure angular sizes of distant objects?
For nearby stars, interferometry achieves arcsecond or sub-arcsecond resolution. For galaxies and other extended objects, angular size is measured directly from images. The Rayleigh criterion gives telescope angular resolution as 1.22 lambda / D, where lambda is wavelength and D is aperture.
Official sources
- USNO Astronomical Almanac: aa.usno.navy.mil.
- NASA Solar System Exploration: solarsystem.nasa.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.