Revolution to Degree Converter
Angle · unit-converter
Convert Revolution to Degree 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 Degree
Degrees divide a circle into 360 parts. Common in everyday angles, maps, and many engineering drawings.
How to convert revolutions to degrees
1 revolution equals 360 degree in this tool (via radian):
1 turn = (6.283185307179586 rad ÷ 0.017453292519943295 rad) deg = 360 deg
Each revolution carries 6.283185307179586 rad and each degree 0.017453292519943295 rad, so one turn equals 6.283185307179586 ÷ 0.017453292519943295 deg.
Let θ(turn) be the angle in Revolution (turn), and θ(deg) in Degree (deg). Then:
θ(deg) = θ(turn) × (6.283185307179586 / 0.017453292519943295)
Equivalently, divide by how many turn fit into one deg (rad per deg divided by rad per turn):
θ(deg) = θ(turn) ÷ 0.002777777777777778
Examples
Example #1: Convert 1 turn to degree
1 turn = 1 turn × (6.283185307179586/0.017453292519943295) deg = 360 deg
1 turn = 1 turn ÷ 0.002777777777777778 = 360 deg
1 turn × (6.283185307179586/0.017453292519943295) = 360.000000 deg
Example #2: Convert 10 turn to degree
10 turn = 10 turn × (6.283185307179586/0.017453292519943295) deg = 3600 deg
10 turn = 10 turn ÷ 0.002777777777777778 = 3600 deg
10 turn × (6.283185307179586/0.017453292519943295) = 3,600.000000 deg
Summary
To convert Revolution to Degree, multiply the value in turn by (6.283185307179586 rad per turn) / (0.017453292519943295 rad per deg). Equivalently: value_deg = value_turn × (6.283185307179586 / 0.017453292519943295). Numerically, 1 turn equals 360 deg.
Relationship context
Both Revolution and Degree are converted by fixed multiples of the radian. Multiplying by (rad per turn) ÷ (rad per deg) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Revolution (turn) | Degree (deg) |
|---|---|
| 0.1 | 36 |
| 1 | 360 |
| 2 | 720 |
| 3 | 1,080 |
| 4 | 1,440 |
| 5 | 1,800 |
| 6 | 2,160 |
| 7 | 2,520 |
| 8 | 2,880 |
| 9 | 3,240 |
| Revolution (turn) | Degree (deg) |
|---|---|
| 10 | 3,600 |
| 20 | 7,200 |
| 30 | 10,800 |
| 40 | 14,400 |
| 50 | 18,000 |
| 60 | 21,600 |
| 70 | 25,200 |
| 80 | 28,800 |
| 90 | 32,400 |
| 100 | 36,000 |