In 1 turns there are 6.283185 radians. Meanwhile in 1 radians there are 0.159155 turns. Keep reading to learn more about each unit of measure and how they are calculated. Or just use the Radians to Turns calculator above to convert any number.
* Values rounded to 6 decimal places for readability
A turn is one full rotation around a circle. In radians, one full rotation equals 2π radians. That gives a direct conversion between turns to radians:
Quick examples
Tip: If an angle is written with no unit, it often means radians (for example, 3 usually means 3 radians).
A turn is a full rotation around a point. One complete circle equals 1 turn. People also call it a full turn or full rotation.
A radian is a unit used to measure angles. It’s based on a circle’s radius. Radians are common in math, physics, and engineering.
There are (2\pi) radians in 1 turn. That equals about (6.283185) radians.
Use this conversion formula: [ \text{radians} = \text{turns} \times 2\pi ]
A full circle has a circumference of (2\pi r). In radians, a full rotation measures the arc length in units of the radius (r). So ((2\pi r) / r = 2\pi) radians.
Multiply the fraction by (2\pi).
Examples:
Here are some common conversions:
You can’t remove (\pi) in the exact form because (\pi) is part of the definition. If you need a decimal, use ( \pi \approx 3.14159265 ) and compute: [ \text{radians} \approx \text{turns} \times 6.283185307 ]
Use the formula: [ 0.75 \times 2\pi = 1.5\pi \approx 4.712389 ] So (0.75) turns equals ( \tfrac{3\pi}{2} ) radians, about (4.712389) rad.
Yes. A negative turn means rotating in the opposite direction. The conversion stays the same: [ \text{radians} = \text{turns} \times 2\pi ] Example: (-0.5) turn (= -\pi) radians.
Yes. In most math and science settings, 1 turn equals 1 revolution. Both mean one full rotation (360° or (2\pi) radians).
Turns, degrees, and radians all measure angles.
Radians work best in formulas for trig, calculus, waves, and rotation. Many math rules assume angles are in radians, not turns or degrees.
It depends on your use.
Compare it to key points:
The Calculate Box tool to convert turns to radians uses the open source script Convert.js to convert units of measurement. To use this tool, simply type a turns value in the box and have it instantly converted to radians.