Angular Size Calculator

Angular Size Formula

The angular size (or angular diameter) is the angle an object subtends at the observer's eye. It depends on the object's physical size and its distance from the observer.

Where θ is the angular size, d is the physical diameter, and D is the distance to the object.

Small Angle Approximation

When the angular size is small (less than a few degrees), the formula simplifies to:

This approximation is accurate to within 1% for angles up to about 10° and is widely used in astronomy.

Inverse Calculations

The formula can be rearranged to find physical size or distance:

Common Examples

• Moon — ~31.1 arcminutes (~0.52°), roughly the size of a fingertip at arm's length
• Sun — ~31.6 arcminutes, nearly the same angular size as the Moon (hence solar eclipses)
• Jupiter — ~30–50 arcseconds depending on opposition
• Andromeda Galaxy (M31) — ~3°, about 6 times the Moon's diameter
• International Space Station — ~1 arcminute at zenith pass

Applications

• Astronomy — Determining telescope magnification needed to resolve objects
• Photography — Choosing lens focal length to frame a subject
• Surveying — Measuring distant object sizes from angular measurements
• Navigation — Estimating distances by known object sizes

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