## Small Angle Formula

For a planet or other object that will appear like a disk when viewed from some other object, its angular diameter or size can be estimated from this formula:

```

angular diameter                         diameter
in degrees        =   (57.3 degrees) x  ----------
distance

```
where 57.3 degrees is from (360 degrees) / (2 x pi), and the rest of the formula uses the actual diameter of the object divided by its distance away. Note that this can also be written in units of arc-seconds, that is, 1 degree = 3600 arc-seconds, so
```

angular diameter                           diameter
in arc-seconds  = (206265 arc-seconds) x  ----------
distance

```
Both formulas only work for small angles. If you use this formula and get a big angle (more than about 10 degrees), it will not be accurate and would need to be calculated by more precise geometric means.

Make sure the diameter and distance are both in the same units, so that their units cancel.

Last update: February 4, 1998.
email to --> wysin@phys.ksu.edu