Angle / gon → rad
Convert Gradians to Radians
Convert plane angles in radians, degrees, turns, and survey grads. Convert Gradians (gon) to Radians (rad). Find the formula, worked examples, unit definitions, and practical guidance below.
Reverse: Radians to Gradians →
How to convert gradians to radians
A full turn is 2π radians, 360 degrees, or 400 gradians. Decimal degrees are not degrees-minutes-seconds notation. Angular minutes and seconds are not time units.
Use x for the value in gon, b for the intermediate value in rad, and y for the result in rad.
rad = gon × 0.015707963267948967
Worked examples
10 gon ≈ 0.157079632679 rad
Step 1: (10 × 0.0157079632679) ≈ 0.157079632679 rad.
Step 2: 0.157079632679 ÷ 1 ≈ 0.157079632679 rad.20 gon ≈ 0.314159265359 rad
Step 1: (20 × 0.0157079632679) ≈ 0.314159265359 rad.
Step 2: 0.314159265359 ÷ 1 ≈ 0.314159265359 rad.
Results are rounded to 12 significant digits. Converting units does not increase the precision of the original measurement. Very large or small values outside JavaScript’s finite numeric range are rejected.
About Gradians
Gradians (gon) measures angle under the conventions above. The base value in rad is (x × 0.0157079632679), where x is the numerical value in gon. Factors shown here are rounded for display; calculations use the stored factor.
About Radians
Radians (rad) measures angle under the conventions above. The base value in rad is (x × 1), where x is the numerical value in rad. Factors shown here are rounded for display; calculations use the stored factor.
Definitions and sources
Carry the same physical assumptions into subsequent physics calculations.
Gradians to radians reference table
| Gradians (gon) | Radians (rad) |
|---|---|
| 1 | 0.0157079632679 |
| 5 | 0.0785398163397 |
| 10 | 0.157079632679 |
| 25 | 0.392699081699 |
| 50 | 0.785398163397 |
| 100 | 1.57079632679 |
| 1000 | 15.7079632679 |
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