What is the formula to convert an angle measure in degrees to one between 0 and 360 degrees?

Question

I know that I can find an equivalent angular measure to $460^\circ$ that's at least $0^\circ$ and less than $360^\circ$ by repeatedly subtracting $360^\circ$ till it's smaller than $360^\circ$, which comes out to be $100^\circ$.

But is there a general formula to do this? Or is there a formula for this "subtract till smaller than $360^\circ$" in math?

I have tried using modulo but that doesn't make sense … in fact I didn't know what I was doing at the end.

I think I used to know, but now I don't.

If $\theta$ is your angle, use $\theta-360 \lfloor \frac{\theta}{360} \rfloor$. — copper.hat, Sep 16 '13 at 17:08
i found out that beside the first comment there is another way too... θ-360(Floor(360/θ)) — Muhammad Umer, Sep 16 '13 at 17:27
@MuhammadUmer copper.hat's equation is precisely what you wrote. Those funny square brackets is the floor function. — EuYu, Sep 16 '13 at 17:32
oh i i didn't know that.. those brackets are floor.. Thanks. — Muhammad Umer, Sep 16 '13 at 18:16
why!? i dont see how this relates to question. As it is pretty basic stuff. But anyways, i was doing something in javascript in which i need to calculate the correct angle. To show. — Muhammad Umer, Sep 16 '13 at 18:17

score 6 · Answer 1 · answered Feb 18 '15 at 13:27

6

use ((n mod 360) + 360) mod 360 if n can be a negative angle.

answered Feb 18 '15 at 13:27

aau

61

1

or abs(n mod 360) – gatzkerob Sep 27 '16 at 01:05
abs(n mod 360) gives you 1 for -1. If you need to get 359 instead, use the @aau's solution ((n mod 360) + 360) mod 360 – Michal Fapso Oct 31 '21 at 19:45

score 5 · Accepted Answer · edited Aug 06 '19 at 14:23

5

$n$ mod $360$ where $n$ is your angle.

In most programming languages, mod is the % operator.

edited Aug 06 '19 at 14:23

answered Sep 16 '13 at 20:05

Jemmy

1,411

What is the formula to convert an angle measure in degrees to one between 0 and 360 degrees?

2 Answers2