Radians Conversion

Protractors are often used to measure angle

The radian is a unit used to measure angle. Use one of the conversion calculators below to convert to another unit of measure, or read on to learn more about radians.

Radian Conversion Calculators

Choose a unit of angle to convert to.

Convert radians to milliradians
1 radian is equal to 1,000 milliradians
Convert radians to degrees
1 radian is equal to 57.29578 degrees
Convert radians to minutes of arc
1 radian is equal to 3,438 minutes of arc
Convert radians to seconds of arc
1 radian is equal to 206,265 seconds of arc
Convert radians to gradians
1 radian is equal to 63.661977 gradians
Convert radians to revolutions
1 radian is equal to 0.159155 revolutions
Convert radians to circles
1 radian is equal to 0.159155 circles
Convert radians to mils (NATO)
1 radian is equal to 1,019 mils (NATO)

Radian Definition and Usage

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.

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.

Radians Measurement Conversion Table

Common radian values and equivalent imperial and metric angle measurements
radians milliradians degrees minutes of arc seconds of arc gradians revolutions circles mils (NATO)
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