Convert Circles to Radians

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

Results in Radians:

1 cir = 6.283185 rad

Do you want to convert radians to circles?

How to Convert Circles to Radians

Protractors are often used to measure angle

To convert a circle measurement to a radian measurement, multiply the angle by the conversion ratio. One circle is equal to 6.283185 radians, so use this simple formula to convert:

radians = circles × 6.283185

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

For example, here's how to convert 5 circles to radians using the formula above.

5 cir = (5 × 6.283185) = 31.415927 rad

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

Circles

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 radian is the measurement of angle equal to the start to the end of an arc divided by the radius of the circle or arc. 1 radian is equal to 180/π, 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 exmaple, 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 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.

Circle Measurements and Equivalent Radian Conversions

Common circle values converted to the equivalent radian value
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