Radians to Gradians (rad to grad)

1 radian equals 63.66197724 gradians (rounded).

How to convert radians to gradians

To convert radians to gradians, multiply the number of radians by 63.66197724. The factor is rounded to 10 significant digits. To go the other way, multiply gradians by 0.01570796327 (rounded).

gradians = radians × 63.66197724

Example: 10 radians = 636.6197724 gradians.

About these units

Radian (rad)

Metric (SI)Current unit

The SI unit of angle: the angle at the center of a circle subtended by an arc equal in length to the radius. A full turn is 2π radians (about 6.2832).

The radian builds its unit out of the circle itself. Lay a length of string equal to the radius along the circumference, and the angle that arc makes at the center is one radian. The SI Brochure calls it the coherent unit of plane angle, and it also serves as the coherent unit of phase angle, which grows by 2π radians over one period of a repeating wave. The same document notes that you could write rad as m/m, but warns that this is not intrinsic and can mislead, since angle is not the same kind of quantity as an ordinary ratio of lengths. It also records an alternative definition: a right angle equals π/2 radian.

A circle's circumference is 2π times its radius, so a full turn is 2π radians, about 6.2832, which makes one radian roughly 57.3 degrees, or about 0.159 of a turn. The SI Brochure's table of derived units expresses angular velocity in radians per second.

1 radian = 0.1591549431 turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Angle; NIST Guide to the SI, Appendix B.8 (angle conversion factors)

Gradian (grad)

General & non-SICurrent unit

One 400th of a full turn, so a right angle is exactly 100 gradians. Used in surveying in parts of Europe, also called the gon.

The gradian came out of the French Revolution as part of the push to make measurement rational. It was first called the grade, and it divides the right angle into 100 parts, so a full turn is 400 grads and one grad is 0.9 degree. In northern Europe the word grad already meant an ordinary degree, which caused confusion, so the name gon was adopted, first regionally and later internationally. Gon is the symbol given in ISO 31-1, Annex B.

The link to the meter explains the appeal. The meter was originally set at one ten-millionth of a quarter of Earth's meridian, so one gon of arc along the surface spans about 100 kilometers and one centigon about 1 kilometer. Surveyors, mainly in Europe, still use it, along with some mining and geology work, and it is legally recognized in the European Union and Switzerland. It is not part of the SI, and the SI Brochure does not mention it. Many scientific calculators of the 1970s through the 1990s offered a gon mode, though some recent models have dropped it.

1 gradian = 0.0025 turns (exactly).

Sources: Wikipedia: Gradian; NIST Guide to the SI, Appendix B.8 (angle conversion factors); MDN Web Docs: CSS <angle>

Related conversions

See all angle units.