Angular Size Calculator
Angular size is how big something looks, measured as an angle across the sky. Give any two of size, distance and angle to find the third.
Angular size
How big an object looks in the sky, its true size from an angle, or its distance.
Angular size
31.1′
About the same width as the full Moon.
- Degrees
- 0.517924°
- Arcminutes
- 31.0754′
- Arcseconds
- 1,864.53″
- Diameter in km
- 3,474.8
- Distance in km
- 384,400
Uses the exact formula for a sphere seen from its centre distance. The Moon and planets change size a little as their distance changes.
How this is calculated
- 1
Angular size from size and distance
α = 2 × atan(d ÷ 2D), where d is the object's diameter and D its distance, both in the same unit. The Moon, 3,474.8 km across at 384,400 km, comes out at 0.518°, or 31.1 arcminutes.
- 2
Size from the angle
Rearranged, d = 2D × tan(α ÷ 2). Measure a crater's angle in a telescope image, enter the Moon's distance, and you get its width in kilometres.
- 3
Distance from the angle
D = d ÷ (2 × tan(α ÷ 2)). If you know how big something really is, its apparent size tells you how far away it must be.
- 4
Convert the units
One degree is 60 arcminutes (′) and one arcminute is 60 arcseconds (″). The result is also compared with the full Moon, which is about 0.52° across.
Frequently asked questions
How big is the Moon in the sky in degrees?
About 0.5°. It ranges from about 29.4′ at its farthest to 33.5′ at its closest, which is the difference between a micromoon and a supermoon.
Why do the Sun and Moon look the same size?
The Sun is about 400 times wider than the Moon, and also about 400 times farther away, so both cover close to half a degree. That coincidence is what allows total solar eclipses.
What is the smallest angle the human eye can see?
A sharp eye separates details about 1 arcminute apart. Objects smaller than that, such as planets and stars, look like points of light without optical aid.
Is the small-angle formula accurate enough?
For anything in the sky, yes. The simple form α ≈ d ÷ D in radians differs from the exact formula by only about 0.01% even at 2°. This calculator uses the exact version, so it also works for large, close objects.