Enter a value in radians below to convert to another unit of angle.

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A radian is a unit used to measure angle.

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.

### Background and Origin

The radian was designed in 1714 by Roger Cotes, but it wasn’t named and defined in publication until 1873. It was designed as a more natural measure of angle as an alternative to the degree.

### Uses

Radians are the defacto unit for measuring angles in calculus and physics. Radians are more easily expressed in formulae and are a more natural mathematical unit, hence the appeal in these fields.

## How Much 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 radian is equal to 180/π degrees, or about 57.29578°. There are about 6.28318 radians in a circle.

To convert radians to another unit of angle, you need to multiply the value by a conversion factor. A conversion factor is a numerical value used to change the units of a measurement without changing the value.

You can find the conversion factors for radians in the conversion table below.

Then, multiply the angle measurement by the conversion factor to find the equivalent value in the desired unit of measurement.

radians × conversion factor = result

You can also use a calculator, such as one of the converters below, for the conversion.

Common radian values and equivalent imperial and metric angle measurements
1 rad 1,000 mrad 57.29578° 3,438' 206,265" 63.661977g 0.159155 r 0.159155 cir 1,019 mil
2 rad 2,000 mrad 114.591559° 6,875' 412,530" 127.323954g 0.31831 r 0.31831 cir 2,037 mil
3 rad 3,000 mrad 171.887339° 10,313' 618,794" 190.985932g 0.477465 r 0.477465 cir 3,056 mil
4 rad 4,000 mrad 229.183118° 13,751' 825,059" 254.647909g 0.63662 r 0.63662 cir 4,074 mil
5 rad 5,000 mrad 286.478898° 17,189' 1,031,324" 318.309886g 0.795775 r 0.795775 cir 5,093 mil
6 rad 6,000 mrad 343.774677° 20,626' 1,237,589" 381.971863g 0.95493 r 0.95493 cir 6,112 mil
7 rad 7,000 mrad 401.070457° 24,064' 1,443,854" 445.633841g 1.114085 r 1.114085 cir 7,130 mil
8 rad 8,000 mrad 458.366236° 27,502' 1,650,118" 509.295818g 1.27324 r 1.27324 cir 8,149 mil
9 rad 9,000 mrad 515.662016° 30,940' 1,856,383" 572.957795g 1.432394 r 1.432394 cir 9,167 mil
10 rad 10,000 mrad 572.957795° 34,377' 2,062,648" 636.619772g 1.591549 r 1.591549 cir 10,186 mil
11 rad 11,000 mrad 630.253575° 37,815' 2,268,913" 700.28175g 1.750704 r 1.750704 cir 11,205 mil
12 rad 12,000 mrad 687.549354° 41,253' 2,475,178" 763.943727g 1.909859 r 1.909859 cir 12,223 mil
13 rad 13,000 mrad 744.845134° 44,691' 2,681,442" 827.605704g 2.069014 r 2.069014 cir 13,242 mil
14 rad 14,000 mrad 802.140913° 48,128' 2,887,707" 891.267681g 2.228169 r 2.228169 cir 14,260 mil
15 rad 15,000 mrad 859.436693° 51,566' 3,093,972" 954.929659g 2.387324 r 2.387324 cir 15,279 mil
16 rad 16,000 mrad 916.732472° 55,004' 3,300,237" 1,019g 2.546479 r 2.546479 cir 16,297 mil
17 rad 17,000 mrad 974.028252° 58,442' 3,506,502" 1,082g 2.705634 r 2.705634 cir 17,316 mil
18 rad 18,000 mrad 1,031° 61,879' 3,712,767" 1,146g 2.864789 r 2.864789 cir 18,335 mil
19 rad 19,000 mrad 1,089° 65,317' 3,919,031" 1,210g 3.023944 r 3.023944 cir 19,353 mil
20 rad 20,000 mrad 1,146° 68,755' 4,125,296" 1,273g 3.183099 r 3.183099 cir 20,372 mil