📏Angular Diameter Calculator
δ = 2·arctan(d/2D) — the relationship between true size, distance, and apparent size.
Free Angular Diameter Calculator
Why do the Moon and the Sun look almost exactly the same size in our sky, even though one is 400 times smaller? Our free angular diameter calculator answers questions like this using δ = 2·arctan(d/2D) — the formula relating an object's true size, its distance, and how big it appears. Enter any two of true diameter, distance, and angular size, and the calculator solves for the third instantly.
Try the built-in presets for the Moon, the Sun, and Jupiter to see real numbers, with results shown in degrees, arcminutes, or arcseconds depending on scale. It's the same math behind why solar eclipses are possible and how astronomers measure the apparent size of distant stars and planets.
No sign-up, no downloads, no limits — just clear answers whenever you're curious.
About the Angular Diameter Calculator
Features
Solve for any variable
Enter any two of diameter, distance, and angular size to find the third.
Unit flexibility
Diameter and distance in km, miles, AU, or light-years.
Presets
The Moon, the Sun, Jupiter, and a distant-star example with real values.
Auto-scaling units
Results shown in degrees, arcminutes, or arcseconds depending on scale.
Frequently Asked Questions
What is angular diameter?
The apparent angular size an object appears to have from a given distance, as opposed to its true physical size.
How does this calculator work?
Enter any two of true diameter, distance, and angular diameter, and it solves for the third using δ = 2·arctan(d/2D).
Is it free?
Completely free, no sign-up, downloads, or limits.
Why do the Moon and Sun appear the same size?
The Sun is about 400 times wider than the Moon but also about 400 times farther away, giving both an angular diameter of roughly 0.5°.
What units is angular diameter shown in?
Degrees, arcminutes, or arcseconds, chosen automatically based on scale.
Can I use this for distant stars?
Yes, results for very small angles are shown in arcseconds, the standard unit for stellar angular sizes.
What units can I use for true diameter and distance?
Kilometers, miles, astronomical units, or light-years.
What happens with an invalid distance?
Zero or negative distance is rejected with a clear message.
Is my data stored?
No; everything runs in your browser and isn't stored or sent anywhere.
Does it work on mobile?
Yes, fully responsive on all screen sizes.