Turn to Radian (turn to rad)
Result
6.283185307 Radian
Formula
rad = turn × 6.283185307
1 turn = 6.283185307 rad, and 1 rad = 0.1591549431 turn.
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 turn × 6.283185307 = 6.2831853 rad
- 10 turn × 6.283185307 = 62.831853 rad
- 100 turn × 6.283185307 = 628.31853 rad
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.
Turn to Radian table
| Turn (turn) | Radian (rad) |
|---|---|
| 1 | 6.2831853 |
| 2 | 12.566371 |
| 5 | 31.415927 |
| 10 | 62.831853 |
| 20 | 125.66371 |
| 50 | 314.15927 |
| 100 | 628.31853 |
| 1,000 | 6,283.1853 |
The units
- Turn (turn)
- 1 Turn = 360 Degree.
- Radian (rad)
- 1 Radian = 57.29577951 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