Radians to Revolutions Conversion (rad to r)

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)

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.

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

Radians to Revolutions Converter

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Result in Revolutions:

How to Convert Radians to Revolutions

How Many Revolutions Are in a Radian?

What Is a Radian?

What Is a Revolution?

Radian to Revolution Conversion Table

References

More Radian & Revolution Conversions