The small-angle formula is a mathematical approximation, used in astronomy. It relates the linear size (D) of an object to its angular size (α) and its distance from the observer (d) and is a valid approximation if α is small.
The approximate formula is:
- D = α d / 206,265
Here, α has to be measured in arcseconds.
The number 206,265 is approximately equal to the number of arcseconds in a circle (1,296,000), divided by 2π.
The exact formula is
- D = 2 d tan(απ/1,296,000)
and the above approximation follows from this because tan(x) is approximately equal to x if x is small.