Radians to Revolutions Conversion
Enter the angle in radians below to get the value converted to revolutions.
How to Convert Radians to Revolutions
To convert a radian measurement to a revolution measurement, multiply the angle by the conversion ratio. One radian is equal to 0.159155 revolutions, so use this simple formula to convert:
The angle in revolutions is equal to the radians multiplied by 0.159155.
Radians and revolutions are both units used to measure angle. Keep reading to learn more about each unit of measure.
Radians
A radian is the measurement of angle equal to the start to the end of an arc divided by the radius of the circle or arc.[1] 1 radian is equal to 180/π, or about 57.29578°. There are about 6.28318 radians in a circle.
The radian is the SI derived unit for angle in the metric system. Radians can be abbreviated as rad, and are also sometimes abbreviated as c, r, or R. For example, 1 radian can be written as 1 rad, 1 c, 1 r, or 1 R.
Radians are often expressed using their definition. The formula to find radians is θ = s/r, where the angle in radians θ is equal to the arc length s divided by the radius r. Thus, radians may also be expressed as the formula of arc length over the radius.
Revolutions
A revolution, or turn, is equal to 1 rotation around a circle, or 360°. Revolutions are commonly used to measure the speed of rotation, for example when measuring the revolutions per minute (RPM) of a vehicle's engine.
A revolution is sometimes also referred to as a turn, cycle, or complete rotation. Revolutions can be abbreviated as r, and are also sometimes abbreviated as rev or cyc. For example, 1 revolution can be written as 1 r, 1 rev, or 1 cyc.
Radian to Revolution Conversion Table
| Radians | Revolutions |
|---|---|
| 1 rad | 0.159155 r |
| 2 rad | 0.31831 r |
| 3 rad | 0.477465 r |
| 4 rad | 0.63662 r |
| 5 rad | 0.795775 r |
| 6 rad | 0.95493 r |
| 7 rad | 1.1141 r |
| 8 rad | 1.2732 r |
| 9 rad | 1.4324 r |
| 10 rad | 1.5915 r |
| 11 rad | 1.7507 r |
| 12 rad | 1.9099 r |
| 13 rad | 2.069 r |
| 14 rad | 2.2282 r |
| 15 rad | 2.3873 r |
| 16 rad | 2.5465 r |
| 17 rad | 2.7056 r |
| 18 rad | 2.8648 r |
| 19 rad | 3.0239 r |
| 20 rad | 3.1831 r |
| 21 rad | 3.3423 r |
| 22 rad | 3.5014 r |
| 23 rad | 3.6606 r |
| 24 rad | 3.8197 r |
| 25 rad | 3.9789 r |
| 26 rad | 4.138 r |
| 27 rad | 4.2972 r |
| 28 rad | 4.4563 r |
| 29 rad | 4.6155 r |
| 30 rad | 4.7746 r |
| 31 rad | 4.9338 r |
| 32 rad | 5.093 r |
| 33 rad | 5.2521 r |
| 34 rad | 5.4113 r |
| 35 rad | 5.5704 r |
| 36 rad | 5.7296 r |
| 37 rad | 5.8887 r |
| 38 rad | 6.0479 r |
| 39 rad | 6.207 r |
| 40 rad | 6.3662 r |
References
- International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf
