Convert Turn to Radian

One turn equals 6.283185307 rad. This converter allows you to easily convert between Turn and Radian in real time.

Formula

turn × 6.283185307 = rad

Example: 1 turn = 6.283185307 rad

What is Turn?

The turn represents one complete rotation, equal to 360 degrees, 2 pi radians, or 400 gradians. It is the most intuitive angular unit in everyday language: a "half turn" is 180 degrees, and a "quarter turn" is 90 degrees. In sports, figure skating jumps are described in turns (a triple axel is 3.5 turns), and skateboard tricks use 360 for one full rotation. In engineering, rotational speed in RPM is based on the turn.

What is Radian?

The radian is the SI unit of angle, defined as the angle subtended by an arc equal in length to the radius of the circle. One radian is approximately 57.296 degrees, and a full circle is 2 pi radians. Radians are the standard angular unit in mathematics, physics, and engineering because calculus formulas (such as the derivative of sine being cosine) require radian measure. Programming language math libraries also use radians by default.