Radians to Gradians Converter

To convert a measurement in radians to gradians, multiply the value by 63.661977. The conversion factor comes from the relationship between both units and the radian.

For example, to convert 5 rad to gradians: 5 × 63.661977 = 318.309886 gon.

A radian is the SI unit of plane angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. A full turn equals 2π radians. The concept dates to the 18th century, but the term 'radian' was coined by James Thomson in 1873. It is the natural unit of angle in mathematics and physics because it makes calculus formulas for trigonometric functions clean and dimensionless.

Common uses of radians include: Calculus, physics, and engineering calculations; Angular velocity and rotational motion (rad/s); Computer graphics and game math libraries; Signal processing and wave phase (2π per cycle).

A gradian (also called gon or grade) is a unit of plane angle equal to 1/400 of a full turn, so a right angle is exactly 100 gradians. Introduced in France around the time of the French Revolution as part of the push to decimalize all measurement, the gradian divides the quarter circle into a tidy 100 units. It survives mainly in surveying and some European civil engineering.

Common uses of gradians include: Land surveying and geodesy in parts of Europe; Civil engineering slope and grade calculations; Some scientific calculators (GRAD mode); Cadastral (property boundary) measurement.

Here are some common values converted:

1 rad = 63.661977 gon 5 rad = 318.309886 gon 10 rad = 636.619772 gon 50 rad = 3,183.0989 gon 100 rad = 6,366.1977 gon