Gradian to Radian (grad to rad) Converter
1 gradian equals 0.01570796 radians (rad) — multiply the number of gradians by 0.01570796 to convert. That factor is π/200, because a full circle is 400 gradians and also 2π radians.
The formula
To convert gradians to radians, multiply by 0.01570796 (π/200):
radians = gradians × 0.01570796
For example, 100 grad × 0.01570796 = 1.5707963 rad (π/2). To reverse it, divide radians by 0.01570796 (or multiply by 63.661977).
Conversion table
| Gradians (grad) | Radians (rad) |
|---|---|
| 1 | 0.01570796 |
| 2 | 0.03141593 |
| 5 | 0.07853982 |
| 10 | 0.15707963 |
| 25 | 0.39269908 |
| 50 | 0.78539816 |
| 100 | 1.57079633 |
| 200 | 3.14159265 |
| 400 | 6.28318531 |
How to convert online
These irrational values are best left to the tool:
- Enter your gradian value in the first box.
- Read the radian result instantly in the second box.
- Or type a radian value to convert back to gradians — it works both ways.
Use the Gradian to Radian Converter — free and instant in your browser.
Where this conversion is used
Radians are the native angle unit in trigonometry, calculus and most programming math libraries, while gradians appear in surveying instruments. Converting grad to rad lets you feed surveyed angles into code, spreadsheets or physics formulas that expect radians.
FAQ
How many radians are in a gradian?
One gradian equals about 0.01570796 radians (exactly π/200). Ten gradians is roughly 0.15707963 rad.
What is the formula to convert gradians to radians?
Multiply gradians by π/200 ≈ 0.01570796: radians = grad × 0.01570796.
How do I convert radians back to gradians?
Divide radians by 0.01570796, or multiply by 63.661977 (200/π). So π/2 rad = 100 gradians.
Is the conversion exact?
The relationship is exact (π/200), but because π is irrational the decimal 0.01570796 is a rounded approximation of it.
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