Convert Radians to Gradians
One radian equals 63.66198 gradians. Type any value to convert radians to gradians instantly — with a full reference table below.
Convert Radians to Gradians
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How to convert Radians to Gradians
To convert radians to gradians, multiply by 63.66198. One radian equals 63.66198 grad, and one gradian equals 0.015708 rad.
- Take the value in radians — for example 7.5 rad.
- Multiply by 63.66198 (the number of gradians in one radian).
- 7.5 × 63.66198 = 477.4648 grad.
Quick mental estimate: Multiply the number of radians by 64 (within 0.5% of the exact answer).
Radians to Gradians conversion table
| 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 |
| 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 |
About converting Radians to Gradians
Radians (rad) and Gradians (grad) are both units of angle. The exact factor is 1 rad = 63.66198 grad, so multiply by 63.66198 to go from radians to gradians (or divide to go back).
The conversion runs entirely in your browser. Need the reverse? Use the Gradians to Radians converter, or the full unit converter for every unit at once.
Real-world angle in radians and gradians
| Example | Radians | Gradians |
|---|---|---|
| A 1:12 wheelchair ramp (ADA) | 0.0831412 rad | 5.292934 grad |
| A 4/12 roof pitch | 0.321751 rad | 20.48328 grad |
| Earth's axial tilt | ≈ 0.409105 rad | ≈ 26.04444 grad |
| A right angle | 1.570796 rad | 100 grad |
| A straight angle | 3.141593 rad | 200 grad |
| A full turn | 6.283185 rad | 400 grad |
“≈” marks typical values; the rest are defined or measured figures.
The units
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).
1/400 of a full turn, so a right angle is 100 grad.
Used for: Surveying in some European countries.
A full turn is 360°, 2π radians or 400 gradians; the radian factor is irrational, so it is shown rounded.