Revolutions to Radians Converter

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


Result in Radians:

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1 r = 6.283185 rad

Do you want to convert radians to revolutions?

How to Convert Revolutions to Radians

To convert a measurement in revolutions to a measurement in radians, multiply the angle by the following conversion ratio: 6.283185 radians/revolution.

Since one revolution is equal to 6.283185 radians, you can use this simple formula to convert:

radians = revolutions × 6.283185

The angle in radians is equal to the angle in revolutions multiplied by 6.283185.

For example, here's how to convert 5 revolutions to radians using the formula above.
radians = (5 r × 6.283185) = 31.415927 rad

How Many Radians Are in a Revolution?

There are 6.283185 radians in a revolution, which is why we use this value in the formula above.

1 r = 6.283185 rad

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

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.

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.

Revolution to Radian Conversion Table

Table showing various revolution measurements converted to radians.
Revolutions Radians
1 r 6.2832 rad
2 r 12.57 rad
3 r 18.85 rad
4 r 25.13 rad
5 r 31.42 rad
6 r 37.7 rad
7 r 43.98 rad
8 r 50.27 rad
9 r 56.55 rad
10 r 62.83 rad
11 r 69.12 rad
12 r 75.4 rad
13 r 81.68 rad
14 r 87.96 rad
15 r 94.25 rad
16 r 100.53 rad
17 r 106.81 rad
18 r 113.1 rad
19 r 119.38 rad
20 r 125.66 rad
21 r 131.95 rad
22 r 138.23 rad
23 r 144.51 rad
24 r 150.8 rad
25 r 157.08 rad
26 r 163.36 rad
27 r 169.65 rad
28 r 175.93 rad
29 r 182.21 rad
30 r 188.5 rad
31 r 194.78 rad
32 r 201.06 rad
33 r 207.35 rad
34 r 213.63 rad
35 r 219.91 rad
36 r 226.19 rad
37 r 232.48 rad
38 r 238.76 rad
39 r 245.04 rad
40 r 251.33 rad


  1. International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019,

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