Angular Size Calculator

Angular size describes how big an object appears to an observer, rather than how big it actually is — the Moon and the Sun look almost the same size in Earth's sky despite the Sun being vastly larger, simply because it's also vastly farther away.

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Instant Result
Angular Size (degrees) -
Angular Size (arcminutes) -
Angular Size (arcseconds) -
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What Is a Angular Size Calculator?

Angular size describes how big an object appears to an observer, rather than how big it actually is — the Moon and the Sun look almost the same size in Earth's sky despite the Sun being vastly larger, simply because it's also vastly farther away. This calculator finds angular size from true size and distance (using the small-angle approximation).

How to Use This Angular Size Calculator

  1. Enter the object's true (linear) size, in kilometers.
  2. Enter its distance from the observer, in kilometers (same unit as size).
  3. Click Calculate to get the angular size in degrees, arcminutes, and arcseconds.

Formula

Worked Example

The Moon has a diameter of about 3,474 km and is about 384,400 km away. Angular Size = 3474/384400 ≈ 0.00904 rad ≈ 0.518° ≈ 31.1 arcminutes — matching the Moon's familiar apparent size in our sky.

Frequently Asked Questions

What is angular size?

It's how large an object appears from a given distance, measured as an angle (usually in degrees or arcminutes) rather than physical size.

How is it calculated?

Angular size ≈ 2 × arctan(object size ÷ (2 × distance)), which works well for objects that are small compared to their distance.

Why does the Moon look the same size as the Sun in an eclipse?

Despite being vastly different in actual size, their angular sizes from Earth are nearly identical because the Sun is both much larger and much farther away.

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