Convert Turns to Radians

How to Convert Turns to Radians

1 turns = 6.283185307179586 r

1 r = 0.15915494309189535 turns

Example: convert 10 turns to r: 10 turns = 10 × 6.283185307179586 turns = 62.83185307179586 turns

Turns

Definition: A turn (also known as a revolution or full rotation) is a unit of angular measurement equivalent to 360 degrees or 2π radians. It represents a complete circular movement back to the starting position.

History: The concept of a turn as a unit of measurement has been used throughout history in various mathematical and engineering applications. The idea of a full rotation being equivalent to 360 degrees likely originated from ancient astronomical observations, where the Earth’s orbit around the Sun was divided into 360 parts.

Radians

Definition: A radian (r) is the SI unit of angular measurement. One radian is the angle formed when the arc length of a circle equals the circle's radius, with a full rotation being equal to 2π radians.

History: The radian was first introduced in the 18th century by Roger Cotes but became widely accepted in the 19th century. It was officially defined as the standard unit of angular measurement in SI due to its natural mathematical properties, particularly in trigonometry and calculus.

Turns to Radians Conversion Table

Convert Turns to Other Angle Units

• Turns to Degrees
• Turns to Radians
• Turns to Gradians
• Turns to Grades
• Turns to Gons

Convert Other Angle Units to Radians

• Degrees to Radians
• Turns to Radians
• Gradians to Radians
• Grades to Radians
• Gons to Radians