1 grad = 0.015708 rad (gradian → radian)
1 grad = 0.015708 rad
1 gradian equals 0.015708 radians. To convert gradians to radians, multiply the gradian value by 0.015708. For quick reference: 1 grad = 0.015708 rad, 5 grad = 0.0785398 rad, 10 grad = 0.15708 rad, 100 grad = 1.5708 rad.
Radians = Gradians × 0.015708Start with your value in gradians.
Multiply the gradian value by 0.015708. This is the exact conversion factor from gradians to radians.
The product is your value in radians. For example, 5 grad × 0.015708 = 0.0785398 rad.
The exact factor from gradians to radians is 0.015708.
Radians = Gradians × 0.015708
Fifty common reference values, hand-picked for skim utility. Use the calculator above for any value not listed.
| Gradians (grad) | Radians (rad) |
|---|---|
| 0.1 grad | 0.0015708 rad |
| 0.25 grad | 0.003927 rad |
| 0.5 grad | 0.007854 rad |
| 1 grad | 0.015708 rad |
| 2 grad | 0.031416 rad |
| 3 grad | 0.047124 rad |
| 4 grad | 0.062832 rad |
| 5 grad | 0.07854 rad |
| 6 grad | 0.094248 rad |
| 7 grad | 0.10996 rad |
| 8 grad | 0.12566 rad |
| 9 grad | 0.14137 rad |
| 10 grad | 0.15708 rad |
| 11 grad | 0.17279 rad |
| 12 grad | 0.1885 rad |
| 13 grad | 0.2042 rad |
| 14 grad | 0.21991 rad |
| 15 grad | 0.23562 rad |
| 16 grad | 0.25133 rad |
| 18 grad | 0.28274 rad |
| 20 grad | 0.31416 rad |
| 22 grad | 0.34558 rad |
| 24 grad | 0.37699 rad |
| 25 grad | 0.3927 rad |
| 28 grad | 0.43982 rad |
| 30 grad | 0.47124 rad |
| 32 grad | 0.50265 rad |
| 36 grad | 0.56549 rad |
| 40 grad | 0.62832 rad |
| 45 grad | 0.70686 rad |
| 48 grad | 0.75398 rad |
| 50 grad | 0.7854 rad |
| 60 grad | 0.94248 rad |
| 70 grad | 1.0996 rad |
| 75 grad | 1.1781 rad |
| 80 grad | 1.2566 rad |
| 90 grad | 1.4137 rad |
| 100 grad | 1.5708 rad |
| 125 grad | 1.9635 rad |
| 150 grad | 2.3562 rad |
| 200 grad | 3.1416 rad |
| 250 grad | 3.927 rad |
| 300 grad | 4.7124 rad |
| 400 grad | 6.2832 rad |
| 500 grad | 7.854 rad |
| 600 grad | 9.4248 rad |
| 750 grad | 11.781 rad |
| 800 grad | 12.566 rad |
| 900 grad | 14.137 rad |
| 1000 grad | 15.708 rad |
A right angle is exactly 100 gradians. Some European surveying instruments are graduated in gradians. In radians, that gives you: 1 grad = 0.015708 rad, 10 grad = 0.15708 rad, 100 grad = 1.5708 rad.
The gradian (grad), also called the gon, divides a full rotation into 400 equal parts, making a right angle exactly 100 gradians. It was introduced with the metric system for surveying and civil engineering, where its decimal relationship to a right angle simplifies calculations.
The radian (rad) is the SI unit of angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One full turn equals exactly 2π radians (≈6.2832 rad). It is the standard unit in mathematics, physics, and engineering calculations.
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