Turn to Radian Converter
Quick answer
To convert Turns to Radians, multiply by 6.2831853072 (or divide by 0.1591549431). Therefore, 1 Turn (tr) equals 6.28318531 Radians (rad).
Formula: rad = tr × 6.2831853072. Worked example: 10 tr = 62.831853 rad.
Convert Turn (tr) to Radian (rad) online with our free unit converter. In angle, 1 tr = 6.283185 rad. Explore step-by-step conversion steps, mathematical formulas, and quick conversion reference tables below.
Worked example: converting Turn to Radian
- Step 1 — start with the formula. rad = tr × 6.2831853072
- Step 2 — substitute your figure. 10 tr × 6.2831853072
- Step 3 — read the result. 10 tr = 62.831853 rad
- Step 4 — check it in reverse. tr = rad × 0.1591549431 returns 10 tr, which matches the figure you started with.
Angle Converter
14 units available
1 tr = 6.283185 rad
Formula:
rad = tr × 6.2831853072With your value: 1 tr = 6.28318531 rad
Other Turn to Radian conversions
Turn to Radian Conversion Table
| Turn (tr) | Radian (rad) |
|---|---|
| 0.5 | 3.141593 |
| 1 | 6.283185 |
| 2 | 12.566371 |
| 5 | 31.415927 |
| 10 | 62.831853 |
| 15 | 94.24778 |
| 20 | 125.663706 |
| 25 | 157.079633 |
| 50 | 314.159265 |
| 100 | 628.318531 |
| 250 | 1,570.796327 |
| 500 | 3,141.592654 |
| 1000 | 6,283.185307 |
Radian to Turn Conversion Table
| Radian (rad) | Turn (tr) |
|---|---|
| 0.5 | 0.079577 |
| 1 | 0.159155 |
| 2 | 0.31831 |
| 5 | 0.795775 |
| 10 | 1.591549 |
| 15 | 2.387324 |
| 20 | 3.183099 |
| 25 | 3.978874 |
| 50 | 7.957747 |
| 100 | 15.915494 |
| 250 | 39.788736 |
| 500 | 79.577472 |
| 1000 | 159.154943 |
Where these values come from
Every factor on this page is traced to the document that defines it. See the full provenance dataset or our methodology.
Turn (tr)
Angle
The radian is the coherent SI unit of plane angle; the degree is exactly π/180 rad and is accepted for use with the SI.
Source: Units accepted for use with the SI, SI Brochure Table 8
Bureau International des Poids et Mesures · Reviewed 2026-07-01
Radian (rad)
Angle
The radian is the coherent SI unit of plane angle; the degree is exactly π/180 rad and is accepted for use with the SI.
Source: Units accepted for use with the SI, SI Brochure Table 8
Bureau International des Poids et Mesures · Reviewed 2026-07-01
How to Convert Turn to Radian
To convert from Turn (tr) to Radian (rad), multiply the value by 6.2831853072.
Formula: rad = tr × 6.2831853072
Reverse: tr = rad × 0.1591549431
Step-by-Step Example
- Start with your value in Turn. For example: 5 tr
- Multiply by the conversion factor: 5 x 6.2831853072
- The result is: 31.415927 rad
Turn and Radian Relationship
This calculation facilitates standardized conversion between recognized units of angle. Since 1 Turn equals approximately 6.2832 Radians, the Turn represents a larger unit interval than the Radian. Understanding the relationship between Turn and Radian is essential for accurate calculations in physics, engineering, commerce, and daily applications.
About Turn
The Turn (symbol: tr) is a recognized unit in the Standard measurement framework, utilized within angle applications for precision and standardized data representation.
Common uses of Turn: angle calculations, engineering and science, education.
About Radian
The radian is the SI unit of angular measurement. One radian equals approximately 57.296 degrees.
Fun Fact: A full circle contains exactly 2π radians.
Common uses of Radian: mathematics, physics, engineering.
Frequently Asked Questions
- How many Radians are in 1 Turn?
- There are exactly 6.2831853072 Radians in 1 Turn. This means the conversion factor from Turn to Radian is 6.2831853072.
- What is the formula to convert Turn to Radian?
- The formula to convert Turn to Radian is: rad = tr × 6.2831853072. For example, to convert 10 Turns to Radians, you would multiply 10 by 6.2831853072.
- What is a Turn?
- The Turn (symbol: tr) is a recognized unit in the Standard measurement framework, utilized within angle applications for precision and standardized data representation.
- What is a Radian?
- The radian is the SI unit of angular measurement. One radian equals approximately 57.296 degrees.
- What are the common uses of Turn?
- The Turn is commonly used in angle calculations, engineering and science, education.
Related Angle Conversions
Cite this page
UnitConvertLab. (2026). Turn to Radian converter. UnitConvertLab. Retrieved from https://unitconvertlab.com/convert/turn-to-radian