Radian to Gradian Converter (rad to grad)
1 radian equals 63.661977 gradians (1 rad = 63.661977 grad) — multiply the number of radians by 63.661977 to convert. The exact factor is 200/π, because a full circle is 2π radians and 400 gradians (a gradian is 1/400 of a turn).
The formula
To convert radians to gradians, multiply by 200/π:
grad = rad × 63.661977
For example, 1.5708 rad × 63.661977 ≈ 100 grad (a right angle is 100 gradians). To reverse it, divide gradians by 63.661977 (or multiply by 0.01570796).
Conversion table
| Radians (rad) | Gradians (grad) |
|---|---|
| 1 | 63.661977 |
| 2 | 127.323954 |
| 5 | 318.309885 |
| 10 | 636.61977 |
| 25 | 1,591.549425 |
| 50 | 3,183.09885 |
| 100 | 6,366.1977 |
| 500 | 31,830.9885 |
| 1000 | 63,661.977 |
How to convert online
- Type your radian value into the first box.
- Read the gradian result instantly in the second box.
- Or enter gradians to convert back to radians — it works both ways.
Use the Radian to Gradian Converter — free and instant in your browser.
Where this conversion is used
Gradians (also called gons) are standard in surveying and some civil-engineering and continental European contexts, where a right angle is a clean 100 units. Converting from radians lets calculation results from trig functions be expressed in the units used on survey instruments and plans.
FAQ
How many gradians are in a radian?
One radian equals 63.661977 gradians. For example, 10 rad = 636.61977 grad.
What is the formula to convert radians to gradians?
Multiply the radian value by 200/π (about 63.661977): grad = rad × 63.661977.
How do I convert gradians back to radians?
Divide by 63.661977 (multiply by π/200, about 0.01570796). So 100 grad = π/2 radians ≈ 1.5708 rad.
Is the conversion exact?
The exact factor is 200/π, an irrational number; 63.661977 is its rounded value and is precise for practical use.
Related converters
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