Convert Radians to Turns
Radians to turns is the conversion you need when an angle comes out of math or code in radians and you want it as a fraction of a full circle. One radian is approximately 0.159155 turn, since a whole turn is 2 pi radians, so the turn number always comes out much smaller.
Radians to Turns conversion table
| Radians (rad) | Turns (turn) |
|---|---|
| 1 | 0.159155 |
| 2 | 0.31831 |
| 3 | 0.477465 |
| 5 | 0.795775 |
| 10 | 1.591549 |
| 20 | 3.183099 |
| 50 | 7.957747 |
| 100 | 15.915494 |
| 500 | 79.577472 |
| 1,000 | 159.154943 |
The formula
To convert radians to turns, multiply the angle in radians by 0.159155 (which is 1 divided by 2 pi):
turns = radians × 0.159155
A worked example
Say you have pi radians — 3.141592653589793 — and want it in turns:
3.141592653589793 × 0.159155 = 0.5 turn
So pi radians is half a turn, which is half a circle.
Why it's an approximation
The factor 0.159155 is a rounded value. Here's where it comes from: a full circle is one turn and also 2 pi radians, so one radian is 1 divided by 2 pi of a turn. Because pi is irrational and never ends, that division never resolves to a clean number, so any turn figure you write down is rounded. 0.159155 is precise enough for almost anything.
When you'll use it
Turning an angle from math or code, where sin, cos, and tan expect radians, into a plain fraction of a full circle — handy for rotations, gears, and anything measured in revolutions.
Frequently asked questions
How many turns are in a radian?
About 0.159155 turn. It's a rounded figure — a radian equals 1 divided by 2 pi turns, and pi never ends, so 0.159155 is the practical number to use.
What is a turn?
One turn is one full revolution — all the way around a circle. A full circle is 2 pi radians, so one radian is a small slice of a turn, roughly a sixth of the way around.
Is the radians to turns conversion exact?
No. The factor is 1 divided by 2 pi, and pi is irrational, so 0.159155 is rounded for everyday use. More decimal places give you more precision if you need it.