How to Convert Turns to Radians
To convert turns to radians, multiply the value by 6.2832.
The Formula
Radians = Turns × 6.2832
Key Fact
1 turn = 6.2832 radians
Tip: To convert radians back to turns, divide by 6.2832.
Turns to Radians
Convert turns (turn) to radians (rad) with formulas, examples, and conversion tables.
turn
rad
1 turn = 6.2832 rad
Full precision:6.2832 rad
Step-by-Step Solution
To convert 1 turns to radians, we multiply by 6.2832 because one turn equals exactly 6.2832 radians.
1 turn = 6.2832 radians
Since each turn contains 6.2832 radians, we multiply our value by this factor:
1 × 6.2832 = 6.2832 radians
So 1 turns = 6.2832 radians.
Quick check: 6.2832 ÷ 6.2832 = 1 turns
Example Conversions
Example 1: 1 turn = 6.2832 rad
1 × 6.2832 = 6.2832
1 × 6.2832 = 6.2832
Example 2: 5 turn = 31.4159 rad
5 × 6.2832 = 31.4159
5 × 6.2832 = 31.4159
Example 3: 10 turn = 62.8318 rad
10 × 6.2832 = 62.8318
10 × 6.2832 = 62.8318
Turns to Radians Table
| Turns | Radians |
|---|---|
| 1 turn | 6.2832 rad |
| 2 turn | 12.5664 rad |
| 5 turn | 31.4159 rad |
| 10 turn | 62.8318 rad |
| 20 turn | 125.664 rad |
| 25 turn | 157.08 rad |
| 50 turn | 314.159 rad |
| 100 turn | 628.318 rad |
| 250 turn | 1570.8 rad |
| 500 turn | 3141.59 rad |
| 1000 turn | 6283.18 rad |
1 Turn in Other Units
| Unit | 1 turn = |
|---|---|
| Turns to Degrees | 360 ° |
| Turns to Radians | 6.2832 rad |
| Turns to Gradians | 400 grad |
| Turns to Arc Minutes | 21599.96 ′ |
| Turns to Arc Seconds | 1295998.96 ″ |
| Turns to Milliradians | 6283.18 mrad |
| Turns to Revolutions | 1 rev |
| Turns to Quadrants | 4 quad |
| Turns to Sextants | 6 sext |