Angular Size Calculator

Frequently Asked Questions

What units should I use?

Use the same unit for the actual size and the distance, such as kilometers and kilometers. The result is an angle, so the units cancel.

Why does the calculator use arctangent?

The arctangent form is exact for any angle, so it stays accurate even for nearby objects that span a wide angle in the sky.

Provided by AllCalculators.io
Free online calculators for everyday. No registration required.

Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

JavaScript is required to use the interactive calculator above. The questions and answers below remain readable without JavaScript.

How This Calculator Works

Angular size is how large an object appears in the sky, measured as the angle it spans from the observer's point of view. A small object up close can look the same size as a huge object far away. The calculator uses the exact trigonometric relation, taking the arctangent of half the actual size over the distance and doubling it, so it stays accurate even for nearby objects that span a wide angle.

Reference Angular Sizes

The full Moon and the Sun both span about half a degree, which is why solar eclipses can be so close to total. A fingertip held at arm's length covers roughly one degree. Stars are so distant that they appear as points, with angular sizes far below what any telescope can resolve.

Tips

Keep the size and distance in matching units.

Use arcseconds for small, distant objects.

Doubling the distance roughly halves the angular size.

Frequently Asked Questions

Related Science Calculators