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.
Angular Size (degrees)
0.5178 °
Angular Size (degrees) vs Physical Diameter
Formule
## 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.
Exemple Résolu
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.
Questions Fréquentes
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.