Authoritative definitions of the International System of Units and SI prefixes.
Dedicated unit pair
Turns to Radians
Convert turn to rad instantly, then review the formula, assumptions, and rounding guidance.
AngleInstant result
Decimals
Formula result = input × 6.283185307179586 ÷ 1. 1 turn = 6.2832 rad
Common examples
One value, several units
Radians6.2832 rad
Degrees360 °
Gradians400 gon
Arcminutes21,600 ′
Arcseconds1,296,000 ″
Conversion table
| turn | rad |
|---|---|
| 1 turn | 6.2832 rad |
| 2 turn | 12.5664 rad |
| 5 turn | 31.4159 rad |
| 10 turn | 62.8319 rad |
| 25 turn | 157.0796 rad |
| 50 turn | 314.1593 rad |
| 100 turn | 628.3185 rad |
Conversion chart
1 turn6.2832 rad
5 turn31.4159 rad
10 turn62.8319 rad
25 turn157.0796 rad
50 turn314.1593 rad
Worked example
A full turn is 360 degrees or 2π radians.
Unit definition
Turns (turn) One turns equals 6.28318530718 radian.
Unit history
Turns is represented here using its modern SI definition or an internationally accepted relationship to an SI base unit.
Step by step
1. Parse the value, including fractions.
2. Convert turn to radian.
3. Convert the base value to rad and apply your display precision.
Understand the result before using it
Turns to Radians converts a value measured in Turns (turn) into the equivalent value in Radians (rad). The numerical value changes because the size and definition of the selected unit changes; the underlying quantity does not.
Calculated result
The conversion follows the displayed unit relationship. Display rounding can hide additional digits, and measured inputs cannot become more accurate merely by changing units.
Formula, assumptions, and example
Formula
result = input × 6.283185307179586 ÷ 1
Assumptions
- Turns and Radians represent the same angle quantity.
- The input is expressed in turn; the output is expressed in rad.
- The unit definitions and conventional relationship shown on this page apply.
Worked example
1 turn = 6.28318530718 rad. For another value, apply the same relationship and round only to the precision your source measurement supports.
When to use it
Good uses
- Read a turn measurement in a document that expects rad.
- Compare a turns value with a value reported in radians.
- Check the turn-to-rad arithmetic before copying the result into another calculation.
Limitations
Common mistakes to avoid
- Do not confuse turn with another unit that has a similar name or symbol.
- Round the output to a precision justified by the original measurement.
- Verify safety-critical, regulated, laboratory, and contractual conversions against the controlling standard.
Sources and further reading
These references explain the underlying standards or provide authoritative context. Your own contract, institution, clinician, product documentation, local code, or governing standard may be the controlling source.
Guidance on unit names, symbols, conversions, and numerical presentation.
Questions about this calculation
How do I convert Turns to Radians?
result = input × 6.283185307179586 ÷ 1 Using the displayed relationship, 1 turn equals 6.28318530718 rad.
How many Radians are in one Turns?
One Turns is 6.28318530718 Radians. The displayed digits may be rounded.
Can I reverse the turn to rad conversion?
Yes. Swap the source and target units in the converter. The reverse relationship converts rad back to turn.
Is the Turns to Radians result exact?
The conversion follows the displayed unit relationship. Display rounding can hide additional digits, and measured inputs cannot become more accurate merely by changing units.