A gradian is 1/400 of a turn.
Gradians to Radians Converter — gon to rad
Convert Gradian (gon) to Radian (rad) using the exact conversion factor (1 gradian = 0.0157079633 radian). See the formula, worked examples, conversion table, history, and common uses.
Gradians to Radians converter
Converter
Angle Converter
Convert radians, degrees, gradians, turns, arcminutes, arcseconds, and milliradians.
Context values
Some unit families need one extra value for a physically accurate result.
The radian is the SI angle unit.
Result = input x 0.01570796327 / 1.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Gradians to Radians
Gradian and Radian are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Specifically: A gradian is 1/400 of a turn, and the radian is the SI angle unit.
Formula
radians = gradians × 0.0157079632679
This factor comes from each unit's defined relationship to the category's base unit: 1 gradian equals 0.0157079632679 base units, and 1 radian equals 1 base unit, so dividing one by the other gives the direct gradian-to-radian factor of 0.0157079632679.
Simple example
1 gon × 0.01570796327 = 0.0157079633 rad
1 gradian = 0.0157079633 radians.
Real-world example
90 gon × 0.01570796327 = 1.413716694 rad
90 gradians = 1.413716694 radians.
Conversion table
| Gradian (gon) | Radian (rad) |
|---|---|
| 0 gon | 0 rad |
| 30 gon | 0.471238898 rad |
| 45 gon | 0.7068583471 rad |
| 90 gon | 1.413716694 rad |
| 180 gon | 2.827433388 rad |
| 360 gon | 5.654866776 rad |
Reverse conversion: Radian to Gradian
0.0157079633 rad × 63.66197724 = 1.000000002 gon
0.0157079633 radians = 1.000000002 gradians.
gradians = radians × 63.6619772368
For a page dedicated to this direction, see Radian to Gradian.
Understanding the Gradian (gon)
A gradian is 1/400 of a turn.
Understanding the Radian
Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.
Where it's used: Standard angle unit in mathematics, physics, and engineering worldwide.
Uses of the Radian today
- Calculus and trigonometry (derivatives of trig functions are simplest in radians)
- Physics and engineering (angular velocity, rotational mechanics)
- Computer graphics and robotics
History of the Radian
The radian was developed in the 1870s, with the term itself coined by James Thomson (brother of Lord Kelvin) around 1873, formalizing a ratio-based angle measure that mathematicians had used implicitly for calculus since Newton and Leibniz.
It was adopted as the SI derived unit of angle because it makes many physics and calculus formulas simpler than using degrees.
Historical origin. Radian was not the invention of a single named person; it developed through the process described above.
Radian — sources
- BIPM SI Brochure — Coherent derived units — Defines the radian as the SI unit of plane angle.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many radians are in 1 gradian?
1 gradian equals 0.0157079633 radians, using the exact defined conversion factor rather than an estimate.
How do I convert gradian to radian?
Multiply the gradian value by 0.01570796327. The converter above does this instantly to whatever precision you set.
How do I convert radian back to gradian?
Use the reverse factor: 1 radian equals 63.66197724 gradians. You can also use the swap control in the converter above to flip the direction instantly.
What is a gradian?
Gradian (gon) is a unit of angle.
What is a radian?
Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.
Is the gradian to radian conversion exact?
Yes. Both gradian and radian are defined by fixed standards rather than physical artifacts, so the factor of 0.01570796327 used above is exact to as many digits as you choose to display.