Revolutions to Radians Converter
Convert revolutions (turns) (rev) to radians (rad), with the formula, a conversion table and exact factors.
Change the values and press Calculate to work out your own figures.
Enter an angle, choose its unit and the unit you want. The answer is exact until it is shown, and the same value appears in every other unit.
Show the working
- 1 rev = 6.28318530718 rad
- 1 × 6.28318530718 = 6.28318530718 rad
How to convert revolutions to radians
1 rev = 6.28318530718 rad, so multiply by 6.28318530718 to go from revolutions (turns) to radians. Going the other way, 1 rad = 0.159154943092 rev.
rad = rev × 6.28318530718 rev = rad × 0.159154943092
Worked example:
1 rev = 6.28318530718 rad 5 × 6.28318530718 = 31.4159265359 rad
Revolutions to radians table
| Revolutions | Radians |
|---|---|
| 1 rev | 6.28318530718 rad |
| 2 rev | 12.5663706144 rad |
| 3 rev | 18.8495559215 rad |
| 4 rev | 25.1327412287 rad |
| 5 rev | 31.4159265359 rad |
| 6 rev | 37.6991118431 rad |
| 7 rev | 43.9822971503 rad |
| 8 rev | 50.2654824574 rad |
| 9 rev | 56.5486677646 rad |
| 10 rev | 62.8318530718 rad |
| 15 rev | 94.2477796077 rad |
| 20 rev | 125.663706144 rad |
| 25 rev | 157.079632679 rad |
| 30 rev | 188.495559215 rad |
| 40 rev | 251.327412287 rad |
| 50 rev | 314.159265359 rad |
| 75 rev | 471.238898038 rad |
| 100 rev | 628.318530718 rad |
| 250 rev | 1,570.79632679 rad |
| 500 rev | 3,141.59265359 rad |
| 1000 rev | 6,283.18530718 rad |
About the units
- Revolutions (rev)
- Revolutions (turns), a specialised unit. Involves π, which no fraction equals exactly; this converter uses π to 50 significant digits, far beyond the 12 digits shown. Definition: NIST SP 811 Appendix B.8, factors for units listed alphabetically.
- Radians (rad)
- Radians, a metric unit. Definition: BIPM SI Brochure, 9th edition (SI units, prefixes and units accepted for use with the SI).