Radians to Circles Converter

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

SWAP UNITS
Results in Circles:
Loading content.
1 rad = 0.159155 cir

Do you want to convert circles to radians?

How to Convert Radians to Circles

By
Bio image of Joe Sexton

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

Full bio

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

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

circles = radians × 0.159155

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

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

How Many Circles Are in a Radian?

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

1 rad = 0.159155 cir

Radians and circles 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 Circle?

A circle is the equivalent of 1 revolution around a circle, or 360°.

A circle is sometimes also referred to as a revolution. Circles can be abbreviated as cir; for example, 1 circle can be written as 1 cir.

A circle is more commonly used to describe a round, symmetrical shape with no corners or edges than it is to describe plane angle. The shape is described by its radius and circumference.

Learn more about circles.

Radian to Circle Conversion Table

Table showing various radian measurements converted to circles.
Radians Circles
1 rad 0.159155 cir
2 rad 0.31831 cir
3 rad 0.477465 cir
4 rad 0.63662 cir
5 rad 0.795775 cir
6 rad 0.95493 cir
7 rad 1.1141 cir
8 rad 1.2732 cir
9 rad 1.4324 cir
10 rad 1.5915 cir
11 rad 1.7507 cir
12 rad 1.9099 cir
13 rad 2.069 cir
14 rad 2.2282 cir
15 rad 2.3873 cir
16 rad 2.5465 cir
17 rad 2.7056 cir
18 rad 2.8648 cir
19 rad 3.0239 cir
20 rad 3.1831 cir
21 rad 3.3423 cir
22 rad 3.5014 cir
23 rad 3.6606 cir
24 rad 3.8197 cir
25 rad 3.9789 cir
26 rad 4.138 cir
27 rad 4.2972 cir
28 rad 4.4563 cir
29 rad 4.6155 cir
30 rad 4.7746 cir
31 rad 4.9338 cir
32 rad 5.093 cir
33 rad 5.2521 cir
34 rad 5.4113 cir
35 rad 5.5704 cir
36 rad 5.7296 cir
37 rad 5.8887 cir
38 rad 6.0479 cir
39 rad 6.207 cir
40 rad 6.3662 cir

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

More Radian & Circle Conversions