Radian to Revolution Converter
Angle · unit-converter
Convert Radian 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 Radian
The radian is the SI unit of plane angle. One radian is the angle subtended by an arc equal to the radius; 2π rad = one full circle.
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 radians to revolutions
1 radian equals 0.15915494309189535 revolution in this tool (via radian):
1 rad = (1 rad ÷ 6.283185307179586 rad) turn = 0.15915494309189535 turn
Each radian carries 1 rad and each revolution 6.283185307179586 rad, so one rad equals 1 ÷ 6.283185307179586 turn.
Let θ(rad) be the angle in Radian (rad), and θ(turn) in Revolution (turn). Then:
θ(turn) = θ(rad) × (1 / 6.283185307179586)
Equivalently, divide by how many rad fit into one turn (rad per turn divided by rad per rad):
θ(turn) = θ(rad) ÷ 6.283185307179586
Examples
Example #1: Convert 1 rad to revolution
1 rad = 1 rad × (1/6.283185307179586) turn = 0.1591549431 turn
1 rad = 1 rad ÷ 6.283185307179586 = 0.1591549431 turn
1 rad × (1/6.283185307179586) = 0.159155 turn
Example #2: Convert 10 rad to revolution
10 rad = 10 rad × (1/6.283185307179586) turn = 1.5915494309 turn
10 rad = 10 rad ÷ 6.283185307179586 = 1.5915494309 turn
10 rad × (1/6.283185307179586) = 1.591549 turn
Summary
To convert Radian to Revolution, multiply the value in rad by (1 rad per rad) / (6.283185307179586 rad per turn). Equivalently: value_turn = value_rad × (1 / 6.283185307179586). Numerically, 1 rad equals 0.15915494309189535 turn.
Relationship context
Both Radian and Revolution are converted by fixed multiples of the radian. Multiplying by (rad per rad) ÷ (rad per turn) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Radian (rad) | Revolution (turn) |
|---|---|
| 0.1 | 0.0159154943 |
| 1 | 0.1591549431 |
| 2 | 0.3183098862 |
| 3 | 0.4774648293 |
| 4 | 0.6366197724 |
| 5 | 0.7957747155 |
| 6 | 0.9549296586 |
| 7 | 1.1140846016 |
| 8 | 1.2732395447 |
| 9 | 1.4323944878 |
| Radian (rad) | Revolution (turn) |
|---|---|
| 10 | 1.5915494309 |
| 20 | 3.1830988618 |
| 30 | 4.7746482928 |
| 40 | 6.3661977237 |
| 50 | 7.9577471546 |
| 60 | 9.5492965855 |
| 70 | 11.1408460164 |
| 80 | 12.7323954474 |
| 90 | 14.3239448783 |
| 100 | 15.9154943092 |