Gradians to Radians
A gradian divides a full circle into 400 parts, used in some surveying and engineering contexts, especially in Europe. The radian is the SI unit of angle, defined by an arc length equal to the circle's radius; a full circle is 2π radians. 1 grad equals ≈0.015708 rad, so converting between them is a matter of multiplying by that fixed factor — type any value into the converter below and both sides update instantly as you type.
Both units belong to angle, measured here against angle's base unit (rad) — every other angle unit on this site converts through that same reference point, which is why the table below can also be read as a quick cross-check against nearby values.
Formula
rad = grad × ≈0.015708
grad = rad × ≈63.662
Worked example: 5 grad × ≈0.015708 = ≈0.0785398 rad.
Conversion table
| Gradian (grad) | Radian (rad) |
|---|---|
| 1 grad | ≈0.015708 rad |
| 2 grad | ≈0.0314159 rad |
| 3 grad | ≈0.0471239 rad |
| 5 grad | ≈0.0785398 rad |
| 10 grad | ≈0.15708 rad |
| 20 grad | ≈0.314159 rad |
| 25 grad | ≈0.392699 rad |
| 50 grad | ≈0.785398 rad |
| 100 grad | ≈1.5708 rad |
| 250 grad | ≈3.92699 rad |
| 500 grad | ≈7.85398 rad |
| 1,000 grad | ≈15.708 rad |
Frequently asked
- How many Radians in a gradian?
- 1 grad equals ≈0.015708 rad.
- How do I convert Gradians to Radians?
- Multiply the value in grad by ≈0.015708 to get rad. The converter above does this instantly as you type.
- Is the conversion exact?
- Yes — Gradian and Radian are both defined by a fixed conversion factor to angle's base unit (rad), so the result shown is exact to the precision displayed, not an approximation.