Angular Size Calculator
Calculate the angular size of any celestial object from its diameter and distance using θ = 2 arctan(D/2d), in degrees, arcminutes, and arcseconds.
Reviewed October 7, 2026 Runs in your browser — inputs are never stored
Presets
Formula
θ = 2 × arctan(D ÷ 2d) · output in degrees, arcminutes, arcseconds, radians
This tool provides educational conversions of astronomical distances only. It is not a navigation, mission-planning, or ephemeris service. For professional or spacecraft work, use official IAU, NASA, or observatory data products.
About the Angular Size Calculator
The angular size calculator finds how large an object appears in the sky from its real diameter and its distance. Angular size is measured in degrees, arcminutes or arcseconds and explains everyday observations: the Sun and the Moon look almost exactly the same size because the Sun is about 400 times wider and also about 400 times farther away, which is why total solar eclipses are possible.
How to use it
- 1Enter the object's physical diameter.
- 2Enter the distance to the object (same length unit).
- 3Press Calculate to get the angular size in degrees, arcminutes, arcseconds, and radians.
Worked example
the Moon (diameter 3,474.8 km, distance 384,400 km) has an angular size of about 0.518° (31 arcminutes) — close to the Sun's 0.533°, which is why total solar eclipses are possible.
How it works
The angular size formula
The angular diameter of an object of physical diameter D at distance d is θ = 2 × arctan(D ÷ 2d). For small angles this simplifies to θ ≈ D/d in radians.
Reference angular sizes (from Earth)
- Moon: ≈ 0.518° (31.1 arcmin)
- Sun: ≈ 0.533° (32.0 arcmin)
- Jupiter: ≈ 0.01° (varies with distance)
- Andromeda Galaxy: ≈ 3.17° (wider than the Moon, but faint)
Who it is for
Astronomers, telescope users, and students measuring how large objects appear in the sky.
Why it helps
Angular size tells you how big an object appears from Earth — essential for telescope resolution, eclipse prediction, and comparing apparent sizes.
Common use cases
- Determining how large the Moon or Sun appears in degrees
- Sizing planets and galaxies for telescope observation
- Predicting solar eclipse coverage angles
- Teaching small-angle approximations in astronomy
Tips for better results
- Use the same unit for diameter and distance — the ratio is what matters.
- For small angles, θ ≈ D/d in radians (small-angle approximation).
- 1 degree = 60 arcminutes = 3,600 arcseconds.
- The Moon and Sun appear almost the same size from Earth — a remarkable coincidence.
Common mistakes to avoid
- Using different units for diameter and distance.
- Forgetting the factor of 2 in 2 × arctan(D/2d).
- Confusing angular size with physical size — a huge distant galaxy can look tiny.
Frequently asked questions
A:Angular size is how large an object appears in the sky, measured as an angle. It depends on the object's physical size and its distance from the observer: θ = 2 arctan(D/2d).
A:The Sun is about 400× wider than the Moon but also about 400× farther away, so both subtend roughly 0.5° — which is why total solar eclipses occur.
A:For small angles, arctan(x) ≈ x, so θ ≈ D/d in radians. This is accurate for most astronomical objects and simplifies hand calculations.
A:Yes. It runs in your browser on CalcWisee with no sign-up required.
Reviewed for accuracy · Last updated October 7, 2026
The astronomical unit is taken as exactly 149,597,870,700 metres per the IAU 2012 definition. Related light-time and light-year factors use the defined speed of light and the IAU Julian year where applicable.
CalcWisee Editorial Team
Calculator development and formula review
CalcWisee is an independent site founded by Ayman. Every calculator is built from a published formula or official definition, tested against hand-worked examples before it goes live, and corrected promptly when a reader reports an issue to ayman@calcwisee.com.
Expertise: Financial mathematics, Health and fitness formulas, Applied mathematics, Unit conversion standards
References & sources
