Convert Gradians to Radians
Gradians to radians is the conversion you need when an angle arrives in gradians — the surveyor's unit — but your math or code expects radians. One gradian is approximately 0.015707963267948967 radians, because the factor is π divided by 200 and π never lands on a clean decimal.
Gradians to Radians conversion table
| Gradians (grad) | Radians (rad) |
|---|---|
| 1 | 0.015708 |
| 2 | 0.031416 |
| 3 | 0.047124 |
| 5 | 0.07854 |
| 10 | 0.15708 |
| 20 | 0.314159 |
| 50 | 0.785398 |
| 100 | 1.570796 |
| 500 | 7.853982 |
| 1,000 | 15.707963 |
The formula
To convert gradians to radians, multiply the number of gradians by 0.015707963267948967 (which is π/200):
radians = gradians × 0.015707963267948967
A worked example
Say you have 200 gradians and want it in radians:
200 × 0.015707963267948967 = 3.141592653589793 rad
So 200 gradians is about 3.141592653589793 radians — which is π, half a full circle.
Why it's an approximation
The factor 0.015707963267948967 is a rounded value. Here's where it comes from: a full circle is 400 gradians and also 2π radians, so one gradian is 2π/400, which is π/200. Because π is irrational — its digits never repeat or end — the decimal has to be cut off somewhere, so the result stays approximate no matter how many places you keep. Remember that a gradian and a radian are different units; the "grad" button on a calculator is the gradian.
When you'll use it
Feeding survey or European engineering angles, which often come in gradians, into trigonometry, physics formulas, or code, where the math almost always expects radians.
Frequently asked questions
How many radians are in a gradian?
About 0.015707963267948967 radians. The exact value is π/200, and because π is irrational the decimal goes on forever — this is a practical, rounded figure.
Why isn't the gradians to radians factor a clean number?
Because it involves π. A full circle is 400 gradians and also 2π radians, so one gradian is 2π/400, which simplifies to π/200. Since π can't be written exactly as a decimal, the number always ends up rounded.
Is a gradian the same as a radian?
No — this is the classic mix-up. A gradian divides a full circle into 400 parts (a right angle into 100), while a radian is tied to the circle's radius, with 2π radians in a full circle. A calculator's 'grad' mode means gradians, not radians.