Circles to Radians Converter

Enter the angle in circles below to convert it to radians.

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Result in Radians:

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1 cir = 6.283185 rad

Do you want to convert radians to circles?

How to Convert Circles to Radians

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

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

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

radians = circles × 6.283185

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

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

How Many Radians Are in a Circle?

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

1 cir = 6.283185 rad

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

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.

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.

Circle to Radian Conversion Table

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

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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