The turn
The turn (tr) represents one complete rotation, exactly 360 degrees or 2π radians. It is used for describing full rotations in mechanics, screw threads, and rotational-speed contexts before converting to a rate like RPM.
Turns to Radians Converter
1 tr = 6.28319 rad (turn → radian)
1 tr = 6.28319 rad
1 turn equals 6.28319 radians. To convert turns to radians, multiply the turn value by 6.28319. For quick reference: 1 tr = 6.28319 rad, 5 tr = 31.4159 rad, 10 tr = 62.8319 rad, 100 tr = 628.319 rad.
Formula
Radians = Turns × 6.28319Quick
How to convert turns to radians
Take your value
Start with your value in turns.
Multiply by 6.28319
Multiply the turn value by 6.28319. This is the exact conversion factor from turns to radians.
Read the result
The product is your value in radians. For example, 5 tr × 6.28319 = 31.4159 rad.
Conversion formula
The exact factor from turns to radians is 6.28319.
Radians = Turns × 6.28319
Turns to Radians conversion table
Fifty common reference values, hand-picked for skim utility. Use the calculator above for any value not listed.
| Turns (tr) | Radians (rad) |
|---|---|
| 0.1 tr | 0.62832 rad |
| 0.25 tr | 1.5708 rad |
| 0.5 tr | 3.1416 rad |
| 1 tr | 6.2832 rad |
| 2 tr | 12.566 rad |
| 3 tr | 18.85 rad |
| 4 tr | 25.133 rad |
| 5 tr | 31.416 rad |
| 6 tr | 37.699 rad |
| 7 tr | 43.982 rad |
| 8 tr | 50.265 rad |
| 9 tr | 56.549 rad |
| 10 tr | 62.832 rad |
| 11 tr | 69.115 rad |
| 12 tr | 75.398 rad |
| 13 tr | 81.681 rad |
| 14 tr | 87.965 rad |
| 15 tr | 94.248 rad |
| 16 tr | 100.53 rad |
| 18 tr | 113.1 rad |
| 20 tr | 125.66 rad |
| 22 tr | 138.23 rad |
| 24 tr | 150.8 rad |
| 25 tr | 157.08 rad |
| 28 tr | 175.93 rad |
| 30 tr | 188.5 rad |
| 32 tr | 201.06 rad |
| 36 tr | 226.19 rad |
| 40 tr | 251.33 rad |
| 45 tr | 282.74 rad |
| 48 tr | 301.59 rad |
| 50 tr | 314.16 rad |
| 60 tr | 376.99 rad |
| 70 tr | 439.82 rad |
| 75 tr | 471.24 rad |
| 80 tr | 502.65 rad |
| 90 tr | 565.49 rad |
| 100 tr | 628.32 rad |
| 125 tr | 785.4 rad |
| 150 tr | 942.48 rad |
| 200 tr | 1256.6 rad |
| 250 tr | 1570.8 rad |
| 300 tr | 1885 rad |
| 400 tr | 2513.3 rad |
| 500 tr | 3141.6 rad |
| 600 tr | 3769.9 rad |
| 750 tr | 4712.4 rad |
| 800 tr | 5026.5 rad |
| 900 tr | 5654.9 rad |
| 1000 tr | 6283.2 rad |
Real-world reference
A wheel completing one full rotation has turned 1 turn. A screw might require 3 turns to fully seat. In radians, that gives you: 1 tr = 6.28319 rad, 10 tr = 62.8319 rad, 100 tr = 628.319 rad.
Frequently asked questions
- How many radians are in 1 turn?
- 1 turn equals 6.28319 radians.
- How do I convert turns to radians?
- Multiply the turn value by 6.28319. So x tr × 6.28319 = the equivalent in rad.
- What is 5 turns in radians?
- 5 turns equals 31.4159 radians.
- What is 10 turns in radians?
- 10 turns equals 62.8319 radians.
- What is 100 turns in radians?
- 100 turns equals 628.319 radians.
- How do I convert back from radians to turns?
- Multiply the radian value by 0.159155. For example, 1 rad = 0.159155 tr.
- Is the turn bigger than the radian?
- Yes. 1 turn is larger than 1 radian — specifically 6.28319 times larger.
- Are these conversion factors exact?
- The factor is derived directly from the SI definitions of turn and radian; the displayed value is rounded for readability, and the browser computes using IEEE 754 double-precision arithmetic.
About the turn and the radian
The radian
The radian (rad) is the SI unit of angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One full turn equals exactly 2π radians (≈6.2832 rad). It is the standard unit in mathematics, physics, and engineering calculations.