Revolution to Radian Converter
Angle · unit-converter
Convert Revolution to Radian 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 Revolution
One revolution (turn) is a full circle: 2π radians or 360°. Used in rotation rates, motors, and astronomy (e.g. revolutions per minute).
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.
How to convert revolutions to radians
1 revolution equals 6.283185307179586 radian in this tool (via radian):
1 turn = (6.283185307179586 rad ÷ 1 rad) rad = 6.283185307179586 rad
Each revolution carries 6.283185307179586 rad and each radian 1 rad, so one turn equals 6.283185307179586 ÷ 1 rad.
Let θ(turn) be the angle in Revolution (turn), and θ(rad) in Radian (rad). Then:
θ(rad) = θ(turn) × (6.283185307179586 / 1)
Equivalently, divide by how many turn fit into one rad (rad per rad divided by rad per turn):
θ(rad) = θ(turn) ÷ 0.15915494309189535
Examples
Example #1: Convert 1 turn to radian
1 turn = 1 turn × (6.283185307179586/1) rad = 6.2831853072 rad
1 turn = 1 turn ÷ 0.15915494309189535 = 6.2831853072 rad
1 turn × (6.283185307179586/1) = 6.283185 rad
Example #2: Convert 10 turn to radian
10 turn = 10 turn × (6.283185307179586/1) rad = 62.8318530718 rad
10 turn = 10 turn ÷ 0.15915494309189535 = 62.8318530718 rad
10 turn × (6.283185307179586/1) = 62.831853 rad
Summary
To convert Revolution to Radian, multiply the value in turn by (6.283185307179586 rad per turn) / (1 rad per rad). Equivalently: value_rad = value_turn × (6.283185307179586 / 1). Numerically, 1 turn equals 6.283185307179586 rad.
Relationship context
Both Revolution and Radian are converted by fixed multiples of the radian. Multiplying by (rad per turn) ÷ (rad per rad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Revolution (turn) | Radian (rad) |
|---|---|
| 0.1 | 0.6283185307 |
| 1 | 6.2831853072 |
| 2 | 12.5663706144 |
| 3 | 18.8495559215 |
| 4 | 25.1327412287 |
| 5 | 31.4159265359 |
| 6 | 37.6991118431 |
| 7 | 43.9822971503 |
| 8 | 50.2654824574 |
| 9 | 56.5486677646 |
| Revolution (turn) | Radian (rad) |
|---|---|
| 10 | 62.8318530718 |
| 20 | 125.663706144 |
| 30 | 188.495559215 |
| 40 | 251.327412287 |
| 50 | 314.159265359 |
| 60 | 376.991118431 |
| 70 | 439.822971503 |
| 80 | 502.654824574 |
| 90 | 565.486677646 |
| 100 | 628.318530718 |