Convert Radians to Revolutions

Enter the angle in radians below to get the value converted to revolutions.

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1 rad = 0.159155 r

How to Convert Radians to Revolutions

Protractors are often used to measure angle

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:

revolutions = radians × 0.159155

The angle in revolutions is equal to the radians multiplied by 0.159155.

For example, here's how to convert 5 radians to revolutions using the formula above.
5 rad = (5 × 0.159155) = 0.795775 r

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 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 exmaple, 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 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 or cycle. Revolutions can be abbreviated as r, for example 1 revolution can be written as 1 r.

Radian Measurements and Equivalent Revolution Conversions

Common radian values converted to the equivalent revolution value
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

More Radian Angle Conversions

Convert to Milliradians
1 rad is equal to 1,000 milliradians
Convert to Degrees
1 rad is equal to 57.29578 degrees
Convert to Minutes Of Arc
1 rad is equal to 3,437.75 minutes of arc
Convert to Seconds Of Arc
1 rad is equal to 206,264.8 seconds of arc
Convert to Gradians
1 rad is equal to 63.661977 gradians
Convert to Circles
1 rad is equal to 0.159155 circles
Convert to Mils (NATO)
1 rad is equal to 1,018.59 mils (NATO)