Convert Revolutions to Radians (rev to rad)
1 revolution (rev) = 6.283185307 radians (rad). 1 rad = 0.1591549431 rev. Example: 15 rev = 15 × 6.283185307 = 94.24777961 rad.
Also searched as revolutions to rad, revolutions in rad, revolutions into radians, rev to rad, rev in radians, rev into radian, revolution to radian, rev to radians converter and how many radians in a revolution.
1 rev = 6.283185307 rad
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk revolution to radian converter to paste a column from Excel.
How to Convert Revolution to Radian
- 1 rev = 6.283185307 rad
- 1 rad = 0.1591549431 rev
- Example: convert 15 rev to rad: 15 rev = 15 × 6.283185307 rad = 94.24777961 rad
Formula
rad = rev × 6.28318530718
Derivation from SI units:
- 1 revolution = 2π rad = 360°.
- 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).
Both units are defined exactly, so the factor is exact. Revolution definition: revolution; Radian definition: radian.
Worked examples
- A reading of 1 rev converts to 6.283185307 rad.
1 rev × 6.283185307 = 6.283185307 rad - A value of 3 rev is 18.84955592 rad.
3 rev × 6.283185307 = 18.84955592 rad
Revolution to Radian conversion table
| Revolutions (rev) | Radians (rad) |
|---|---|
| 0.25 rev | 1.570796327 rad |
| 0.5 rev | 3.141592654 rad |
| 0.75 rev | 4.71238898 rad |
| 1 rev | 6.283185307 rad |
| 1.5 rev | 9.424777961 rad |
| 2 rev | 12.56637061 rad |
| 3 rev | 18.84955592 rad |
| 5 rev | 31.41592654 rad |
| 10 rev | 62.83185307 rad |
| 100 rev | 628.3185307 rad |
Where it's used
Revolutions are used for rotating machinery (rpm), while radians appear in trigonometry and calculus (derivatives of sin and cos assume radians). Both measure plane angle, so the conversion is a fixed factor.
Revolution to other angle units
| Conversion | 1 rev equals |
|---|---|
| revolution to radian | 6.283185307 rad |
| revolution to degree | 360 ° |
| revolution to gradian | 400 gon |
| revolution to minute of arc | 21600 ′ |
| revolution to second of arc | 1296000 ″ |
Frequently asked questions
How many radians are in 1 revolution?
1 rev = 6.283185307 rad.
How do I convert revolutions to radians?
Multiply the value in rev by 6.283185307. For example, 15 rev × 6.283185307 = 94.24777961 rad.
Is the rev to rad 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 Revolutions to Radians (rev to rad). Retrieved October 25, 2026, from https://scientificconverters.com/angle/revolutions-to-radians/
IEEE
Scientific Converters, "Convert Revolutions to Radians (rev to rad)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/revolutions-to-radians/