Degree to Revolution Converter
Angle · unit-converter
Convert Degree to Revolution with a fixed input and output unit, step-by-step formula line, and reference tables. All calculations bridge through radians with fixed definitions (360° per turn, 400 grad per turn, 60′ per degree, 60″ per minute, plus practical units like MOA, urad, and NATO 6400 mils per turn).
About Degree
Degrees divide a circle into 360 parts. Common in everyday angles, maps, and many engineering drawings.
About Revolution
One revolution (turn) is a full circle: 2π radians or 360°. Used in rotation rates, motors, and astronomy (e.g. revolutions per minute).
How to convert degrees to revolutions
1 degree equals 0.002777777777777778 revolution in this tool (via radian):
1 deg = (0.017453292519943295 rad ÷ 6.283185307179586 rad) turn = 0.002777777777777778 turn
Each degree carries 0.017453292519943295 rad and each revolution 6.283185307179586 rad, so one deg equals 0.017453292519943295 ÷ 6.283185307179586 turn.
Let θ(deg) be the angle in Degree (deg), and θ(turn) in Revolution (turn). Then:
θ(turn) = θ(deg) × (0.017453292519943295 / 6.283185307179586)
Equivalently, divide by how many deg fit into one turn (rad per turn divided by rad per deg):
θ(turn) = θ(deg) ÷ 360
Examples
Example #1: Convert 1 deg to revolution
1 deg = 1 deg × (0.017453292519943295/6.283185307179586) turn = 0.0027777778 turn
1 deg = 1 deg ÷ 360 = 0.0027777778 turn
1 deg × (0.017453292519943295/6.283185307179586) = 0.002778 turn
Example #2: Convert 10 deg to revolution
10 deg = 10 deg × (0.017453292519943295/6.283185307179586) turn = 0.0277777778 turn
10 deg = 10 deg ÷ 360 = 0.0277777778 turn
10 deg × (0.017453292519943295/6.283185307179586) = 0.027778 turn
Summary
To convert Degree to Revolution, multiply the value in deg by (0.017453292519943295 rad per deg) / (6.283185307179586 rad per turn). Equivalently: value_turn = value_deg × (0.017453292519943295 / 6.283185307179586). Numerically, 1 deg equals 0.002777777777777778 turn.
Relationship context
Both Degree and Revolution are converted by fixed multiples of the radian. Multiplying by (rad per deg) ÷ (rad per turn) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Degree (deg) | Revolution (turn) |
|---|---|
| 0.1 | 0.0002777778 |
| 1 | 0.0027777778 |
| 2 | 0.0055555556 |
| 3 | 0.0083333333 |
| 4 | 0.0111111111 |
| 5 | 0.0138888889 |
| 6 | 0.0166666667 |
| 7 | 0.0194444444 |
| 8 | 0.0222222222 |
| 9 | 0.025 |
| Degree (deg) | Revolution (turn) |
|---|---|
| 10 | 0.0277777778 |
| 20 | 0.0555555556 |
| 30 | 0.0833333333 |
| 40 | 0.1111111111 |
| 50 | 0.1388888889 |
| 60 | 0.1666666667 |
| 70 | 0.1944444444 |
| 80 | 0.2222222222 |
| 90 | 0.25 |
| 100 | 0.2777777778 |