In 1 radians there are 0.159155 turns. Meanwhile in 1 turns there are 6.283185 radians. Keep reading to learn more about each unit of measure and how they are calculated. Or just use the Turns to Radians calculator above to convert any number.
* Values rounded to 6 decimal places for readability
To convert radians to turns, use the fact that one full turn equals 2π radians. A turn means one complete rotation around a circle.
Formula (radians to turns):
Steps:
Quick examples:
This radians to turns conversion works because a full circle has a total angle of 2π radians, which matches 1 turn.
A turn is one full rotation around a circle. It equals 360 degrees. In radians, one full turn equals (2\pi) radians.
Use this simple formula:
[ \text{turns} = \frac{\text{radians}}{2\pi} ]
Divide the radian value by (2\pi) to get turns.
The conversion factor from radians to turns is:
[ 1 \text{ radian} = \frac{1}{2\pi} \text{ turns} \approx 0.1591549 \text{ turns} ]
This means a little under one-sixth of a full turn.
(2\pi) radians equals 1 turn.
[ \frac{2\pi}{2\pi} = 1 ]
This is the key reference point for radian to turn conversions.
(\pi) radians equals 0.5 turns (half a turn).
[ \frac{\pi}{2\pi} = \frac{1}{2} ]
Half a turn also equals 180 degrees.
(\frac{\pi}{2}) radians equals 0.25 turns (a quarter turn).
[ \frac{\frac{\pi}{2}}{2\pi} = \frac{1}{4} ]
A quarter turn also equals 90 degrees.
Multiply turns by (2\pi):
[ \text{radians} = \text{turns} \times 2\pi ]
Example: 0.75 turns equals (0.75 \times 2\pi = \frac{3\pi}{2}) radians.
Yes. A turn and a revolution both mean one full rotation. You may also see “cycle” used in some fields. They all represent the same angle amount.
Yes. Negative turns mean rotation in the opposite direction. For example:
[ -,\pi \text{ radians} = \frac{-\pi}{2\pi} = -0.5 \text{ turns} ]
These values come up often:
Turns make full-rotation thinking simple. Many people find “0.25 turns” easier to picture than “(\frac{\pi}{2}) radians.” Turns also match rotation counts in motors, wheels, and gears.
No. The angle stays the same. Only the unit changes. Radians and turns are just two different ways to describe the same rotation amount.
They measure the same thing in different units:
Choose the unit that fits your work and makes the value easy to read.
The Calculate Box tool to convert radians to turns uses the open source script Convert.js to convert units of measurement. To use this tool, simply type a radians value in the box and have it instantly converted to turns.