Gradian to Radian (gon to rad)
Result
0.01570796327 Radian
Formula
rad = gon × 0.01570796327
1 gon = 0.01570796327 rad, and 1 rad = 63.66197724 gon.
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 gon × 0.01570796327 = 0.015707963 rad
- 10 gon × 0.01570796327 = 0.15707963 rad
- 100 gon × 0.01570796327 = 1.5707963 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.
Gradian to Radian table
| Gradian (gon) | Radian (rad) |
|---|---|
| 1 | 0.015707963 |
| 2 | 0.031415927 |
| 5 | 0.078539816 |
| 10 | 0.15707963 |
| 20 | 0.31415927 |
| 50 | 0.78539816 |
| 100 | 1.5707963 |
| 1,000 | 15.707963 |
The units
- Gradian (gon)
- 1 Gradian = 0.9 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