Convert gradians to radians
Converting gradians to radians is a common angle task, whether you are checking a recipe, a spec sheet, a travel distance or a homework problem. Since 1 gon equals 0.015708 rad, the math is a single multiplication — and this page does it for you instantly, with the formula, a table of common values and answers to the questions people ask most.
Exact factor
How to convert gradians to radians
To convert gradians to radians, multiply the number of gradians by 0.015708. For example, 10 gon × 0.015708 = 0.15708 rad.
rad = gon × 0.015708
- Write down the value in gradians you want to convert.
- Multiply it by 0.015708 (the exact gon→rad factor).
- The result is your value in radians. Check it below with the converter or the table.
Conversion table
Common values of gradians and their equivalents in radians:
| gon | rad |
|---|---|
| 1 | 0.015708 |
| 2 | 0.0314159 |
| 3 | 0.0471239 |
| 4 | 0.0628319 |
| 5 | 0.0785398 |
| 10 | 0.15708 |
| 20 | 0.314159 |
| 25 | 0.392699 |
| 50 | 0.785398 |
| 100 | 1.5708 |
| 250 | 3.92699 |
| 500 | 7.85398 |
About these units
Gradian (gon). A gradian (gon) is 1/400 of a full circle, so a right angle is exactly 100 gradians. It is used in surveying and some European engineering fields for decimal-friendly math.
Radian (rad). A radian is the angle subtended by an arc equal in length to the radius, with π radians in a half circle (about 57.2958°). It is the natural angle unit in mathematics and programming.
Frequently asked questions
How do I convert gradians to radians?
To convert gradians to radians, multiply the number of gradians by 0.015708. For example, 10 gon × 0.015708 = 0.15708 rad. Or skip the math: type the value into the converter at the top of this page and the result updates instantly.
How many radians are in 1 gradian?
1 gon = 0.015708 rad. That is the fixed relationship used by this converter and by international standards.
How many gradians are in 1 radian?
1 rad = 63.662 gon. If you are converting in the opposite direction, use our Radian to Gradian converter for the dedicated table and FAQ.
Is the gradians to radians conversion exact?
Yes. Both units are defined by international agreement, so the factor of 0.015708 is exact. Displayed results are rounded to 6 significant digits only for readability.
What is gradian used for?
A gradian (gon) is 1/400 of a full circle, so a right angle is exactly 100 gradians. It is used in surveying and some European engineering fields for decimal-friendly math.