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Angle
Degrees to Turns
Convert degrees (°) to turns (tr). Type a value below to see the result update instantly. Reference table and formula included.
Calculator
1 ° = 0.002778 tr
Degrees to Turns Conversion Table
Common values, ready to copy:
| degrees | turns |
|---|---|
| 1 ° | 0.002778 tr |
| 2 ° | 0.005556 tr |
| 5 ° | 0.013889 tr |
| 10 ° | 0.027778 tr |
| 25 ° | 0.069444 tr |
| 50 ° | 0.138889 tr |
| 100 ° | 0.277778 tr |
| 1,000 ° | 2.7778 tr |
Formula
turns = degrees × 2.77777778e-3
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
About Degrees and Turns
Degrees (°): 1/360 of a full turn; the 360-degree division comes from ancient Babylonian astronomy and the convenience of 360 being divisible by many small integers. Common uses: Navigation (compass headings), construction (angle cuts), geometry, geography (latitude and longitude), and almost any practical angle measurement.
Turns (tr): A full revolution; the most natural way to describe rotation (one turn = 360° = 2π rad = 400 gon). Common uses: Engineering specifications for rotation (number of turns of a bolt, a screw thread, or a knob), and clear communication when degree confusion is a risk.
How the conversion works
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
The exact relationship is turns = degrees × 2.77777778e-3, which the calculator at the top of this page applies in both directions. Type into either field and the other updates immediately.
When this conversion matters
Converting between degrees and turns comes up wherever angle measurements move between systems — from one country's conventions to another's, from a scientific reference to a practical specification, or from one industry's working unit to another's. The calculator and reference table above cover the everyday range; for unusual values you can type any number into either field.