Main Page | See live article | Alphabetical index 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 (1,296,600), divided by 2&pi. The exact formula is D = 2 d tan(απ/1,296,600) and the above approximation follows from this because tan(x) is approximately equal to x if x is small. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.