How to convert gradians to radians
rad = gon × 0.01570796327Multiply the value in gradians by 0.01570796327. To go the other way, multiply by 63.66197724 (or divide by 0.01570796327).
A gradian is smaller than a radian: it takes 63.66197724 gradians to make one radian.
Worked examples
- 1 gradian1 gon × 0.01570796327 = 0.01570796327 rad
- 5 gradians5 gon × 0.01570796327 = 0.07853981634 rad
- 10 gradians10 gon × 0.01570796327 = 0.1570796327 rad
- 20 gradians20 gon × 0.01570796327 = 0.3141592654 rad
- 100 gradians100 gon × 0.01570796327 = 1.570796327 rad
Gradians to radians conversion table
Values are calculated by the conversion engine and rounded to 8 significant figures.
| Gradians (gon) | Radians (rad) |
|---|---|
| 0.1 gon | 0.0015707963 rad |
| 0.25 gon | 0.0039269908 rad |
| 0.5 gon | 0.0078539816 rad |
| 1 gon | 0.015707963 rad |
| 2 gon | 0.031415927 rad |
| 3 gon | 0.04712389 rad |
| 4 gon | 0.062831853 rad |
| 5 gon | 0.078539816 rad |
| 6 gon | 0.09424778 rad |
| 7 gon | 0.10995574 rad |
| 8 gon | 0.12566371 rad |
| 9 gon | 0.14137167 rad |
| 10 gon | 0.15707963 rad |
| Gradians (gon) | Radians (rad) |
|---|---|
| 12 gon | 0.18849556 rad |
| 15 gon | 0.23561945 rad |
| 20 gon | 0.31415927 rad |
| 25 gon | 0.39269908 rad |
| 30 gon | 0.4712389 rad |
| 40 gon | 0.62831853 rad |
| 50 gon | 0.78539816 rad |
| 75 gon | 1.1780972 rad |
| 100 gon | 1.5707963 rad |
| 250 gon | 3.9269908 rad |
| 500 gon | 7.8539816 rad |
| 1,000 gon | 15.707963 rad |
About the units
Gradian (gon)
One 400th of a turn, so a right angle is 100 gon. Used in surveying in some countries. One gradian equals 0.01570796327 radians (rad).
Radian (rad)
The angle subtended by an arc equal in length to the radius; 2π rad make a full turn, so 1 rad ≈ 57.2958°.
Frequently asked questions
How many radians are in one gradian?
There are 0.01570796327 radians in one gradian, and this value is exact by definition.
How do I convert gradians to radians?
Multiply the number of gradians by 0.01570796327. For example, 10 gon × 0.01570796327 = 0.1570796327 rad.
How many gradians are in one radian?
One radian equals 63.66197724 gradians. That is the reverse factor, 1 ÷ 0.01570796327.
What is 10 gradians in radians?
10 gon = 0.1570796327 rad.
Is this gon to rad converter accurate?
Yes. Both units are defined exactly in terms of SI units, so the conversion factor is exact; results are shown to 12 significant figures by default and you can change precision in the converter. Calculations run in your browser using the same tested engine that generated this page.