Revolutions to Radians Converter

To convert a measurement in revolutions to radians, multiply the value by 6.283185. The conversion factor comes from the relationship between both units and the radian.

For example, to convert 5 rev to radians: 5 × 6.283185 = 31.415927 rad.

A revolution (also called a turn or full circle) is one complete rotation, equal to 360 degrees or 2π radians. The revolution is the most intuitive angular unit — one full spin. It is the natural way to count rotations in machinery, and forms the basis of rotational-speed units such as revolutions per minute (RPM).

Common uses of revolutions include: Engine and motor speed (RPM); Counting rotations of wheels, gears, and turbines; Vinyl record and hard-drive spin rates; Describing full turns in everyday language.

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).

Here are some common values converted:

1 rev = 6.283185 rad 5 rev = 31.415927 rad 10 rev = 62.831853 rad 50 rev = 314.159265 rad 100 rev = 628.318531 rad