Convert Radians to Turns
Please provide values below to convert Radians [r] to Turns [turns].
How to Convert Radians to Turns
1 r = 0.15915494309189535 turns
1 turns = 6.283185307179586 r
Example: convert 10 r to turns: 10 r = 10 × 0.15915494309189535 r = 1.5915494309189535 r
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
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 to Turns Conversion Table
| Radians | Turns |
|---|---|
| 0.01 r | 0.0015915494309189536 turns |
| 0.1 r | 0.015915494309189534 turns |
| 1 r | 0.15915494309189535 turns |
| 2 r | 0.3183098861837907 turns |
| 3 r | 0.477464829275686 turns |
| 5 r | 0.7957747154594768 turns |
| 10 r | 1.5915494309189535 turns |
| 20 r | 3.183098861837907 turns |
| 50 r | 7.957747154594768 turns |
| 100 r | 15.915494309189535 turns |
| 1000 r | 159.15494309189535 turns |