Radian to Turn (rad to turn)
Result
0.1591549431 Turn
Formula
turn = rad × 0.1591549431
1 rad = 0.1591549431 turn, and 1 turn = 6.283185307 rad.
A full turn is 360°, 2π radians or 400 gradians, so 1 rad = 180/π ° (about 57.29578°) and 1 gradian = 0.9°.
Worked examples
- 1 rad × 0.1591549431 = 0.15915494 turn
- 10 rad × 0.1591549431 = 1.5915494 turn
- 100 rad × 0.1591549431 = 15.915494 turn
Common mistakes
- Calculators and spreadsheet trigonometry functions usually expect radians: sin(30) in radian mode is −0.988, not 0.5.
- Compass bearings run clockwise from north; mathematical angles run anticlockwise from the positive x-axis.
Radian to Turn table
| Radian (rad) | Turn (turn) |
|---|---|
| 1 | 0.15915494 |
| 2 | 0.31830989 |
| 5 | 0.79577472 |
| 10 | 1.5915494 |
| 20 | 3.1830989 |
| 50 | 7.9577472 |
| 100 | 15.915494 |
| 1,000 | 159.15494 |
The units
- Radian (rad)
- 1 Radian = 57.29577951 Degree.
- Turn (turn)
- 1 Turn = 360 Degree.
Sources for these factors
- The International System of Units (SI Brochure), 9th edition — BIPM
- Guide for the Use of the International System of Units (SP 811), Appendix B: conversion factors — NIST
Last reviewed against these sources. An automated check recomputes every factor from its definition on each build. How we check accuracy