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Angle
Gradians to Radians
Convert gradians (gon) to radians (rad). Type a value below to see the result update instantly. Reference table and formula included.
Calculator
1 gon = 0.015708 rad
Gradians to Radians Conversion Table
Common values, ready to copy:
| gradians | radians |
|---|---|
| 1 gon | 0.015708 rad |
| 2 gon | 0.031416 rad |
| 5 gon | 0.07854 rad |
| 10 gon | 0.15708 rad |
| 25 gon | 0.392699 rad |
| 50 gon | 0.785398 rad |
| 100 gon | 1.5708 rad |
| 1,000 gon | 15.708 rad |
Formula
radians = gradians × 1.57079633e-2
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
About Gradians and Radians
Gradians (gon): 1/400 of a full turn; introduced in revolutionary France as a metric-style angle unit (100 gradians = right angle). Common uses: Surveying in some European countries, some scientific calculators have a 'GRAD' mode, mostly historical interest elsewhere.
Radians (rad): The natural SI unit for angle; one radian is the angle subtended by an arc equal in length to the radius (so a full circle is 2π radians ≈ 6.283). Common uses: Mathematics (calculus, trigonometry derivatives), physics, computer graphics, and any context where the formula simplifies in radians.
How the conversion works
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
The exact relationship is radians = gradians × 1.57079633e-2, which the calculator at the top of this page applies in both directions. Type into either field and the other updates immediately.
When this conversion matters
Converting between gradians and radians comes up wherever angle measurements move between systems — from one country's conventions to another's, from a scientific reference to a practical specification, or from one industry's working unit to another's. The calculator and reference table above cover the everyday range; for unusual values you can type any number into either field.