Convert turn to radian
Enter the value to convert from turn to radian.
How to Convert Turn to Radian
Converting turn to radian is straightforward using our conversion calculator.
Conversion Formula
rad = tr × 3.1415927Reverse conversion: Convert radian to turn
Comparison: Turn vs Radian
When to Use Each Unit
Turn: Used for describing rotational speed, mechanical rotations, and complete angular motions in engineering.
Radian: Primary unit in mathematics, physics, engineering calculations, and scientific applications requiring precise angular measurement.
Common Conversion Values
- 1 turn = 360°
- 1 turn = 2π rad
- 1 turn = 400 gon
- 0.5 turn = 180°
About Turn
Definition: The turn (symbol: tr) represents one complete rotation or revolution, equal to 360 degrees or 2π radians.
History: Natural unit representing complete rotational motion, used in mechanical systems and rotational applications.
Current Use: Used for describing rotational speed, mechanical rotations, and complete angular motions in engineering.
Examples: Motor rotations: RPM (revolutions per minute), mechanical systems: gear ratios, astronomy: planetary rotations
About Radian
Definition: The radian (symbol: rad) is the SI unit of angular measurement where one radian equals the angle subtending an arc equal to the radius.
History: Introduced in 1714 by mathematician Roger Cotes. Became standard in mathematics for its natural relationship to circular functions.
Current Use: Primary unit in mathematics, physics, engineering calculations, and scientific applications requiring precise angular measurement.
Examples: Calculus: trigonometric functions, physics: angular velocity, engineering: rotational mechanics, robotics: joint angles