Gradians to Radians (grad to rad) Converter
1 gradian (grad) = 0.015708 radians (rad). To convert gradians to radians, multiply by 0.015708: 25 grad × 0.015708 = 0.392699 rad.
Quick facts
- 1 grad = 0.015708 rad
- 1 rad = 63.662 grad
- Formula: rad = grad × 0.015708
- Quick estimate: multiply by about 0.016
How to convert gradians to radians
- Take the value in gradians.
- Multiply it by 0.015708 (the number of radians in one gradian).
- Round the result to the precision you need.
Worked example: 25 grad × 0.015708 = 0.392699 rad.
To convert radians back to gradians, multiply by 63.662, or divide by 0.015708.
Source: BIPM SI Brochure, 9th edition (the radian).
Gradians to Radians conversion table
| Gradians [grad] | Radians [rad] |
|---|---|
| 0.01 grad | 0.0001570796 rad |
| 0.1 grad | 0.0015707963 rad |
| 1 grad | 0.0157079633 rad |
| 2 grad | 0.0314159265 rad |
| 3 grad | 0.0471238898 rad |
| 5 grad | 0.0785398163 rad |
| 10 grad | 0.1570796327 rad |
| 20 grad | 0.3141592654 rad |
| 50 grad | 0.7853981634 rad |
| 100 grad | 1.5707963268 rad |
| 1000 grad | 15.7079632679 rad |
grad to rad chart from 1 to 100
- 1 grad 0.015708 rad
- 2 grad 0.0314159 rad
- 3 grad 0.0471239 rad
- 4 grad 0.0628319 rad
- 5 grad 0.0785398 rad
- 6 grad 0.0942478 rad
- 7 grad 0.109956 rad
- 8 grad 0.125664 rad
- 9 grad 0.141372 rad
- 10 grad 0.15708 rad
- 11 grad 0.172788 rad
- 12 grad 0.188496 rad
- 13 grad 0.204204 rad
- 14 grad 0.219911 rad
- 15 grad 0.235619 rad
- 16 grad 0.251327 rad
- 17 grad 0.267035 rad
- 18 grad 0.282743 rad
- 19 grad 0.298451 rad
- 20 grad 0.314159 rad
- 25 grad 0.392699 rad
- 30 grad 0.471239 rad
- 35 grad 0.549779 rad
- 40 grad 0.628319 rad
- 45 grad 0.706858 rad
- 50 grad 0.785398 rad
- 55 grad 0.863938 rad
- 60 grad 0.942478 rad
- 65 grad 1.02102 rad
- 70 grad 1.09956 rad
- 75 grad 1.1781 rad
- 80 grad 1.25664 rad
- 85 grad 1.33518 rad
- 90 grad 1.41372 rad
- 95 grad 1.49226 rad
- 100 grad 1.5708 rad
Radians to Gradians conversion table
| Radians [rad] | Gradians [grad] |
|---|---|
| 0.01 rad | 0.6366197724 grad |
| 0.1 rad | 6.3661977237 grad |
| 1 rad | 63.6619772368 grad |
| 2 rad | 127.3239544735 grad |
| 3 rad | 190.9859317103 grad |
| 5 rad | 318.3098861838 grad |
| 10 rad | 636.6197723676 grad |
| 20 rad | 1273.2395447352 grad |
| 50 rad | 3183.0988618379 grad |
| 100 rad | 6366.1977236758 grad |
| 1000 rad | 63661.9772367581 grad |
Gradians vs Radians
| Gradian | Radian | |
|---|---|---|
| Symbol | grad | rad |
| Equals | 1 grad = 0.015708 rad | 1 rad = 63.662 grad |
What is a gradian?
One 400th of a full rotation, so a right angle is 100 gradians. Used in some surveying and European engineering contexts.
What is a radian?
The SI unit of angle, where one full rotation equals 2π radians. Used throughout calculus, physics, and engineering.
Frequently asked questions
How many radians are in a gradian?
There are 0.015708 radians in 1 gradian (1 grad = 0.0157079633 rad).
How many gradians are in a radian?
There are 63.662 gradians in 1 radian (1 rad = 63.6619772368 grad).
How do I convert gradians to radians?
Multiply the number of gradians by 0.015708. For example, 10 grad × 0.015708 = 0.15708 rad. To convert back, multiply by 63.662.
What is 10 grad in radians?
10 grad = 0.15708 rad.
What is 100 grad in radians?
100 grad = 1.5708 rad.
Is the conversion exact?
Yes. The factor comes from the official definitions of both units (BIPM SI Brochure, 9th edition (the radian)). Results are shown to up to 10 decimal places; round them to suit your purpose.
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