Angle / turn → °
Convert Turns to Degrees
Convert plane angles in radians, degrees, turns, and survey grads. Convert Turns (turn) to Degrees (°). Find the formula, worked examples, unit definitions, and practical guidance below.
How to convert turns to degrees
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 turn, b for the intermediate value in rad, and y for the result in °.
° = turn × 6.283185307179586 ÷ 0.017453292519943295
Worked examples
10 turn ≈ 3600 °
Step 1: (10 × 6.28318530718) ≈ 62.8318530718 rad.
Step 2: 62.8318530718 ÷ 0.0174532925199 ≈ 3600 °.20 turn ≈ 7200 °
Step 1: (20 × 6.28318530718) ≈ 125.663706144 rad.
Step 2: 125.663706144 ÷ 0.0174532925199 ≈ 7200 °.
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 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.
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.
Definitions and sources
Carry the same physical assumptions into subsequent physics calculations.
Turns to degrees reference table
| Turns (turn) | Degrees (°) |
|---|---|
| 1 | 360 |
| 5 | 1800 |
| 10 | 3600 |
| 25 | 9000 |
| 50 | 18000 |
| 100 | 36000 |
| 1000 | 360000 |
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