Convert Radians to Revolutions (rad to rev)
1 radian (rad) = 0.1591549431 revolutions (rev). 1 rev = 6.283185307 rad. Example: 15 rad = 15 × 0.1591549431 = 2.387324146 rev.
Also searched as radians to rev, radians in rev, radians into revolutions, rad to rev, rad in revolutions, rad into revolution, radian to revolution, rad to revolutions converter and how many revolutions in a radian.
1 rad = 0.1591549431 rev
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk radian to revolution converter to paste a column from Excel.
How to Convert Radian to Revolution
- 1 rad = 0.1591549431 rev
- 1 rev = 6.283185307 rad
- Example: convert 15 rad to rev: 15 rad = 15 × 0.1591549431 rev = 2.387324146 rev
Formula
rev = rad × 0.1591549430919
or rev = rad ÷ 6.28318530718
Derivation from SI units:
- The SI unit of plane angle: the angle subtended at the centre of a circle by an arc equal in length to the radius (1 rad = 1 m/m).
- 1 revolution = 2π rad = 360°.
Both units are defined exactly, so the factor is exact. Radian definition: radian; Revolution definition: revolution.
Worked examples
- A reading of 2 rad converts to 0.3183098862 rev.
2 rad × 0.1591549431 = 0.3183098862 rev - A value of 4 rad is 0.6366197724 rev.
4 rad × 0.1591549431 = 0.6366197724 rev
Radian to Revolution conversion table
| Radians (rad) | Revolutions (rev) |
|---|---|
| 0.5 rad | 0.07957747155 rev |
| 1 rad | 0.1591549431 rev |
| 1.5 rad | 0.2387324146 rev |
| 2 rad | 0.3183098862 rev |
| 3 rad | 0.4774648293 rev |
| 3.14159 rad | 0.4999995777 rev |
| 4 rad | 0.6366197724 rev |
| 5 rad | 0.7957747155 rev |
| 6 rad | 0.9549296586 rev |
| 6.28318 rad | 0.9999991553 rev |
Where it's used
Radians are used for trigonometry and calculus (derivatives of sin and cos assume radians), while revolutions appear in rotating machinery (rpm). Both measure plane angle, so the conversion is a fixed factor.
Radian to other angle units
| Conversion | 1 rad equals |
|---|---|
| radian to revolution | 0.1591549431 rev |
| radian to degree | 57.29577951 ° |
| radian to gradian | 63.66197724 gon |
| radian to minute of arc | 3437.746771 ′ |
| radian to second of arc | 206264.8062 ″ |
Frequently asked questions
How many revolutions are in 1 radian?
1 rad = 0.1591549431 rev.
How do I convert radians to revolutions?
Multiply the value in rad by 0.1591549431, or divide it by 6.283185307. For example, 15 rad × 0.1591549431 = 2.387324146 rev.
Is the rad to rev conversion exact?
Yes. Both units are defined exactly, so the ratio is exact; its decimal form does not terminate and is shown here to 10 significant figures (more with the precision selector).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures , Table 4 (radian) and Table 8 (non-SI units accepted for use with the SI).
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Convert Radians to Revolutions (rad to rev). Retrieved October 25, 2026, from https://scientificconverters.com/angle/radians-to-revolutions/
IEEE
Scientific Converters, "Convert Radians to Revolutions (rad to rev)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/radians-to-revolutions/