Convert Gradians to Radians
One gradian equals 0.015708 radians. Type any value to convert gradians to radians instantly — with a full reference table below.
Convert Gradians to Radians
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How to convert Gradians to Radians
To convert gradians to radians, multiply by 0.015708. One gradian equals 0.015708 rad, and one radian equals 63.66198 grad.
- Take the value in gradians — for example 7.5 grad.
- Multiply by 0.015708 (the number of radians in one gradian).
- 7.5 × 0.015708 = 0.11781 rad.
Quick mental estimate: Divide the number of gradians by 64 (within 0.5% of the exact answer).
Gradians to Radians conversion table
| Gradians | Radians |
|---|---|
| 1 grad | 0.015708 rad |
| 5 grad | 0.0785398 rad |
| 10 grad | 0.15708 rad |
| 15 grad | 0.235619 rad |
| 30 grad | 0.471239 rad |
| 45 grad | 0.706858 rad |
| 60 grad | 0.942478 rad |
| 90 grad | 1.413717 rad |
| 120 grad | 1.884956 rad |
| 180 grad | 2.827433 rad |
| 270 grad | 4.24115 rad |
| 360 grad | 5.654867 rad |
| Radians | Gradians |
|---|---|
| 1 rad | 63.66198 grad |
| 5 rad | 318.3099 grad |
| 10 rad | 636.6198 grad |
| 15 rad | 954.9297 grad |
| 30 rad | 1,909.859 grad |
| 45 rad | 2,864.789 grad |
| 60 rad | 3,819.719 grad |
| 90 rad | 5,729.578 grad |
| 120 rad | 7,639.437 grad |
| 180 rad | 11,459.16 grad |
| 270 rad | 17,188.73 grad |
| 360 rad | 22,918.31 grad |
About converting Gradians to Radians
Gradians (grad) and Radians (rad) are both units of angle. The exact factor is 1 grad = 0.015708 rad, so multiply by 0.015708 to go from gradians to radians (or divide to go back).
The conversion runs entirely in your browser. Need the reverse? Use the Radians to Gradians converter, or the full unit converter for every unit at once.
Real-world angle in gradians and radians
| Example | Gradians | Radians |
|---|---|---|
| A 1:12 wheelchair ramp (ADA) | 5.292934 grad | 0.0831412 rad |
| A 4/12 roof pitch | 20.48328 grad | 0.321751 rad |
| Earth's axial tilt | ≈ 26.04444 grad | ≈ 0.409105 rad |
| A right angle | 100 grad | 1.570796 rad |
| A straight angle | 200 grad | 3.141593 rad |
| A full turn | 400 grad | 6.283185 rad |
“≈” marks typical values; the rest are defined or measured figures.
The units
1/400 of a full turn, so a right angle is 100 grad.
Used for: Surveying in some European countries.
The SI unit of angle: the angle whose arc equals the radius; a full turn is 2π.
Used for: Maths, physics and programming (Math.sin uses radians).
A full turn is 360°, 2π radians or 400 gradians; the radian factor is irrational, so it is shown rounded.