Circles to Radians Conversion (cir to rad)

Circles to Radians Converter

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

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Result in Radians:

1 cir = 6.283185 rad

How to Convert Circles to Radians

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

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

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