How to convert Turns to radians
rad = turn × 2 × π
One full turn is 2π radians or 360 degrees. Keeping π in the formula avoids rounding a decimal conversion factor before calculating the result.
Worked examples
0.25 turn ≈ 1.570796327 rad
(0.25) × 2 × π ≈ 1.570796327
1 turn ≈ 6.283185307 rad
(1) × 2 × π ≈ 6.283185307
Frequently asked questions
Why does the formula include π?
A complete turn is 2π radians, equal to 360 degrees or 400 gradians. Keeping π symbolic avoids prematurely rounding the conversion coefficient.