# Get Rotation in degrees (0-360) from a rotated angle?

I have a rectangle that is facing up. ($0^\circ$)

I'm getting a number bettween $-1000$ to $1000$ or even more, and this number is the angle that is rotating the rectangle.

How can I know the degrees it is facing now?

• Rotating by $360^\circ$ is equivalent to not rotating at all, so just keep adding or subtracting multiples of it until you get something in $[0,360]$. (More specifically, $x\to x-360\lfloor x/360\rfloor$, where $\lfloor\cdot\rfloor$ is the floor function.) Also... he? – anon Aug 28 '11 at 9:05
• Cool it works :) but why didn't you put it as answer ? lol – Danpe Aug 28 '11 at 9:14
• Also, if your programming language (I assume you're doing this in a computer program) has an fmod function or something equivalent, $x \mapsto \operatorname{fmod}(x, 360)$ is probably easier than $x \mapsto x - 360 \cdot \lfloor x/360 \rfloor$. – Ilmari Karonen Aug 28 '11 at 12:08

## 2 Answers

This question was answered in a comment:

Rotating by $360^{\circ}$ is equivalent to not rotating at all, so just keep adding or subtracting multiples of it until you get something in $[0,360]$. (More specifically, $x\mapsto x−360⌊x/360⌋$, where $⌊\cdot⌋$ is the floor function.) – anon Aug 28 '11 at 9:05

If the angle $\alpha\in\mathbb{Z}$, you may also use the remainder of $\alpha$ when divided by 360. Implementing this on a computer, you then could use the modulo operation which is quite efficient (compared to a division, a floor and a multiplication) and in most languages shorter to type (e.g. alpha%360 in C++)