The radian is the SI angle unit.
Radians to Gradians Converter — rad to gon
Convert Radian (rad) to Gradian (gon) using the exact conversion factor (1 radian = 63.66197724 gradian). See the formula, worked examples, conversion table, history, and common uses.
Radians to Gradians 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.
A gradian is 1/400 of a turn.
Result = input x 1 / 0.01570796327.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Radians to Gradians
Radian and Gradian 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. Radian is most often used for calculus and trigonometry (derivatives of trig functions are simplest in radians).
Formula
gradians = radians × 63.6619772368
This factor comes from each unit's defined relationship to the category's base unit: 1 radian equals 1 base unit, and 1 gradian equals 0.0157079632679 base units, so dividing one by the other gives the direct radian-to-gradian factor of 63.6619772368.
Simple example
1 rad × 63.66197724 = 63.66197724 gon
1 radian = 63.66197724 gradians.
Real-world example
90 rad × 63.66197724 = 5,729.577951 gon
90 radians = 5,729.577951 gradians.
Conversion table
| Radian (rad) | Gradian (gon) |
|---|---|
| 0 rad | 0 gon |
| 30 rad | 1,909.859317 gon |
| 45 rad | 2,864.788976 gon |
| 90 rad | 5,729.577951 gon |
| 180 rad | 11,459.1559 gon |
| 360 rad | 22,918.31181 gon |
Reverse conversion: Gradian to Radian
63.66197724 gon × 0.01570796327 = 1 rad
63.66197724 gradians = 1 radians.
radians = gradians × 0.0157079632679
For a page dedicated to this direction, see Gradian to Radian.
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.
Understanding the Gradian (gon)
A gradian is 1/400 of a turn.
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 gradians are in 1 radian?
1 radian equals 63.66197724 gradians, using the exact defined conversion factor rather than an estimate.
How do I convert radian to gradian?
Multiply the radian value by 63.66197724. The converter above does this instantly to whatever precision you set.
How do I convert gradian back to radian?
Use the reverse factor: 1 gradian equals 0.0157079633 radians. You can also use the swap control in the converter above to flip the direction instantly.
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.
What is a gradian?
Gradian (gon) is a unit of angle.
Is the radian to gradian conversion exact?
Yes. Both radian and gradian are defined by fixed standards rather than physical artifacts, so the factor of 63.66197724 used above is exact to as many digits as you choose to display.
Where is the radian still used today?
Standard angle unit in mathematics, physics, and engineering worldwide.