Radians to Revolutions Converter

Enter the angle in radians below to get the value converted to revolutions. The calculator supports values containing decimals, fractions, and π: (π/2, 1/2π, etc)

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1 rad = 0.159155 r

Do you want to convert revolutions to radians?


How to Convert Radians to Revolutions

To convert a measurement in radians to a measurement in revolutions, multiply the angle by the following conversion ratio: 0.159155 revolutions/radian.

Since one radian is equal to 0.159155 revolutions, you can use this simple formula to convert:

revolutions = radians × 0.159155

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

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

How Many Revolutions Are in a Radian?

There are 0.159155 revolutions in a radian, which is why we use this value in the formula above.

1 rad = 0.159155 r

Radians and revolutions are both units used to measure angle. Keep reading to learn more about each unit of measure.

What Is a Radian?

A radian is the measurement of angle equal to the length of an arc divided by the radius of the circle or arc.[1] 1 radian is equal to 180/π degrees, 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 an angle in 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.

Radians are also considered to be a "unitless" unit. That is, when multiplying or dividing by radians, the result does not include radians as part of the final units.

For example, when determining the length of an arc for a given angle, we use the formula above, rearranged to be s = θr. If θ is in radians and r is in meters, then the units of s will be meters, not radian-meters. If θ were in degrees, however, then s would have units of degree-meters.

Learn more about radians.

What Is a Revolution?

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.

Learn more about revolutions.

Radian to Revolution Conversion Table

Table showing various 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

  1. International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf

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