Radians Conversion
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.
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] 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 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 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
| 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 |
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