Convert Radians to Revolutions

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

Results in Revolutions:

1 rad = 0.159155 r

Do you want to convert revolutions to radians?

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