Why does the Moon appear the same size as the Sun?

The Sun is about 400 times the Moon's diameter and about 400 times farther away, so their angular sizes nearly match (≈0.5°).

When does the small-angle formula fail?

For objects subtending more than a few degrees. Use 2 arctan(d/2D) for the exact result.

What is the angular size of Jupiter from Earth?

At closest approach, about 50 arcseconds. At most, it appears as a tiny disc in binoculars.

Free Angular Size Calculator

Compute the angular size of an object from its physical diameter and distance: theta = 2 arctan(d / (2D)), approximated as theta = d / D (radians) for small angles.

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Physical Diameter

Distance to Object

Angular Size (degrees)

0.5178 °

Angular Size (radians)0.009037 rad

Angular Size (arcmin)31.07 '

Angular Size (arcsec)1,864.11 "

Angular Size (degrees) vs Physical Diameter

View formula & how it works →

Angular Size

The angular size (angular diameter) of an object as seen from a given distance.

Small-Angle Approximation

θ ≈ d / D (radians)

where d = physical diameter, D = distance. Multiply by 180/π for degrees, then by 60 for arcminutes or 3600 for arcseconds.

Example Calculation

The Moon: diameter 3 474 km, distance 384 400 km.

01θ = 3474 / 384400 = 0.009038 rad
02Degrees: 0.009038 × 57.296 = 0.5178°
03Arcminutes: 0.5178 × 60 = 31.07'
04The Moon is about half a degree across.

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