Protractors are often used to measure angle

Convert Circles to Radians

Convert from circles to radians with this simple formula:
radians = circles × 6.283185
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1 Circle = 6.283185 Radians

Learn How to Convert Circles to Radians Using our Conversion Formula

Converting a circle angle measurement to a radian measurement involves multiplying your angle by the conversion ratio to find the result. A circle is equal to 6.283185 radians, so to convert simply multiply by 6.283185.

For example, 5cir = (5 × 6.283185) = 31.415927rad.

Circles and radians are both units used to measure angle. Learn more about angle and find more angle measurement conversion calculators. A circle is an angle measurement and can be abbreviated as cir, for example 1cir. A radian is an angle measurement and can be abbreviated as rad, for example 1rad.

A radian is the measurement of the angle from the start to the end of an arc equal to the radius of the circle. 1 radian is equal to 180/π, or about 57.29578°. There are about 6.28318 radians in a circle. The radian is the standard SI unit of measurement for an angle.

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

circles and radians are units used to measure angle
Convert Radians to Circles

More Angle Conversions

Convert to Degrees Angle
1cir is equal to 360 degrees
Convert to Grad Angle
1cir is equal to 400 grad
Convert to Revolutions Angle
1cir is equal to 1 revolutions
Convert to Mils Angle
1cir is equal to 6,400 mils

Circle Measurements and Equivalent Radian Conversions

Common circle values converted to the equivalent radian value
Circles Radians Circles Radians Circles Radians
1 6.2832 21 131.95 41 257.61
2 12.57 22 138.23 42 263.89
3 18.85 23 144.51 43 270.18
4 25.13 24 150.8 44 276.46
5 31.42 25 157.08 45 282.74
6 37.7 26 163.36 46 289.03
7 43.98 27 169.65 47 295.31
8 50.27 28 175.93 48 301.59
9 56.55 29 182.21 49 307.88
10 62.83 30 188.5 50 314.16
11 69.12 31 194.78 51 320.44
12 75.4 32 201.06 52 326.73
13 81.68 33 207.35 53 333.01
14 87.96 34 213.63 54 339.29
15 94.25 35 219.91 55 345.58
16 100.53 36 226.19 56 351.86
17 106.81 37 232.48 57 358.14
18 113.1 38 238.76 58 364.42
19 119.38 39 245.04 59 370.71
20 125.66 40 251.33 60 376.99