Radians to Revolutions Conversion

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

Results in Revolutions:

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] 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

Radian measurements converted to revolutions
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

Radian measurements converted to revolutions

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

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