Last updated: 2026-06-16

What Angular Size Means

Angular size is how big something looks, measured as an angle rather than a length. A distant mountain and a nearby pebble can subtend the same angle at your eye. In astronomy this is often the only "size" we can measure directly, because we see objects projected on the sky without knowing their distance in advance.

For the small angles that dominate astronomy, the angular size is simply the object's physical size divided by its distance:

$\theta = \frac{D}{d}$

with $\theta$ in radians. To express the result in more familiar units, multiply by 57.3 for degrees, by 3,438 for arcminutes, or by 206,265 for arcseconds.

Worked Example

How large does the Moon appear? Its diameter is 3,474 km and its average distance is 384,400 km:

$\theta = \frac{3{,}474}{384{,}400} = 0.00904\ \text{rad} \approx 0.52^\circ$

That is just over half a degree — about the width of a pea held at arm's length, or roughly the size of a fingernail at the end of an outstretched arm.

The Eclipse Coincidence

The Sun's diameter is about 400 times the Moon's, yet the Sun is also about 400 times farther away. Because angular size depends only on the ratio of size to distance, the two almost exactly cancel: both the Sun and the Moon span close to 0.5° in our sky. This is why the Moon can just barely cover the Sun during a total solar eclipse — a coincidence unique to this moment in the Earth–Moon system's history, since the Moon is slowly drifting away.

The Small-Angle Approximation

The relation $\theta = D/d$ is an approximation that treats the object's width as a straight chord rather than a curved arc. The exact expression is $\theta = 2\arctan\!\left(\tfrac{D}{2d}\right)$. For any object more than a few times farther away than it is wide — which covers essentially everything in the sky — the two agree to far better than one percent, so the simple division is all that is needed in practice.