Angle / ° → turn
Convert Degrees to Turns
Convert plane angles in radians, degrees, turns, and survey grads. Convert Degrees (°) to Turns (turn). Find the formula, worked examples, unit definitions, and practical guidance below.
How to convert degrees to turns
A full turn is 2π radians, 360 degrees, or 400 gradians. Decimal degrees are not degrees-minutes-seconds notation. Angular minutes and seconds are not time units.
Use x for the value in °, b for the intermediate value in rad, and y for the result in turn.
turn = ° × 0.017453292519943295 ÷ 6.283185307179586
Worked examples
10 ° ≈ 0.0277777777778 turn
Step 1: (10 × 0.0174532925199) ≈ 0.174532925199 rad.
Step 2: 0.174532925199 ÷ 6.28318530718 ≈ 0.0277777777778 turn.20 ° ≈ 0.0555555555556 turn
Step 1: (20 × 0.0174532925199) ≈ 0.349065850399 rad.
Step 2: 0.349065850399 ÷ 6.28318530718 ≈ 0.0555555555556 turn.
Results are rounded to 12 significant digits. Converting units does not increase the precision of the original measurement. Very large or small values outside JavaScript’s finite numeric range are rejected.
About Degrees
Degrees (°) measures angle under the conventions above. The base value in rad is (x × 0.0174532925199), where x is the numerical value in °. Factors shown here are rounded for display; calculations use the stored factor.
About Turns
Turns (turn) measures angle under the conventions above. The base value in rad is (x × 6.28318530718), where x is the numerical value in turn. Factors shown here are rounded for display; calculations use the stored factor.
Definitions and sources
Carry the same physical assumptions into subsequent physics calculations.
Degrees to turns reference table
| Degrees (°) | Turns (turn) |
|---|---|
| 1 | 0.00277777777778 |
| 5 | 0.0138888888889 |
| 10 | 0.0277777777778 |
| 25 | 0.0694444444444 |
| 50 | 0.138888888889 |
| 100 | 0.277777777778 |
| 1000 | 2.77777777778 |
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