Convert Degrees to Turns
Degrees to turns is the conversion you need when you want to think about angles as fractions of one full spin. A turn is a single complete revolution — all the way around — so one degree is about 0.002777777777777778 of a turn, and the number comes out very small.
Degrees to Turns conversion table
| Degrees (°) | Turns (turn) |
|---|---|
| 1 | 0.002778 |
| 2 | 0.005556 |
| 3 | 0.008333 |
| 5 | 0.013889 |
| 10 | 0.027778 |
| 20 | 0.055556 |
| 50 | 0.138889 |
| 100 | 0.277778 |
| 500 | 1.388889 |
| 1,000 | 2.777778 |
The formula
To convert degrees to turns, multiply the number of degrees by 0.002777777777777778 (which is 1/360):
turns = degrees × 0.002777777777777778
A worked example
Say you have 90 degrees — a right angle — and want it in turns:
90 × 0.002777777777777778 = 0.25 turn
So 90 degrees is exactly 0.25 turn, or a quarter of the way around.
Why it's an approximation
The clean number is on the other side: one full turn is exactly 360 degrees. Flip that to go from degrees to turns and you divide by 360, which gives 0.00277… — a decimal that repeats forever and never settles. So the multiply factor, 0.002777777777777778, is rounded off at some point. Round angles still come out tidy — 90 degrees is exactly a quarter turn, 180 is half, 360 is a whole one — because those divide evenly; it's only the general factor that has to be trimmed.
When you'll use it
Describing rotations as whole or fractional spins — half a turn, three-quarters of a turn — in mechanics, animation, and games, and any time "one full revolution" is a more natural unit than 360 degrees.
Frequently asked questions
How many turns are in a degree?
About 0.002777777777777778 of a turn. The clean fact runs the other way: one full turn is exactly 360 degrees, so a degree is 1/360 of a turn — a repeating decimal that never quite ends.
What is 90 degrees in turns?
Exactly 0.25 turn — a quarter turn. A full turn is 360 degrees, so 90 degrees is a quarter of the way around.
Is the degrees to turns conversion exact?
The reverse is: one turn is exactly 360 degrees. Going from degrees to turns you divide by 360, which gives a repeating decimal (0.00277…), so the factor is rounded even though round angles like 90 degrees still land on clean fractions.