One full revolution.
Turns to Milliradians Converter — turn to mrad
Convert Turn (turn) to Milliradian (mrad) using the exact conversion factor (1 turn = 6,283.185307 milliradian). See the formula, worked examples, and conversion table.
Turns to Milliradians converter
Converter
Angle Converter
Convert radians, degrees, gradians, turns, arcminutes, arcseconds, and milliradians.
Context values
Some unit families need one extra value for a physically accurate result.
One milliradian is 0.001 radians.
Result = input x 6.283185307 / 0.001.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Turns to Milliradians
Turn and Milliradian are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Specifically: One full revolution, and one milliradian is 0.001 radians.
Formula
milliradians = turns × 6283.18530718
This factor comes from each unit's defined relationship to the category's base unit: 1 turn equals 6.28318530718 base units, and 1 milliradian equals 0.001 base units, so dividing one by the other gives the direct turn-to-milliradian factor of 6283.18530718.
Simple example
1 turn × 6283.185307 = 6,283.185307 mrad
1 turn = 6,283.185307 milliradians.
Real-world example
90 turn × 6283.185307 = 565,486.6776 mrad
90 turns = 565,486.6776 milliradians.
Conversion table
| Turn (turn) | Milliradian (mrad) |
|---|---|
| 0 turn | 0 mrad |
| 30 turn | 188,495.5592 mrad |
| 45 turn | 282,743.3388 mrad |
| 90 turn | 565,486.6776 mrad |
| 180 turn | 1,130,973.355 mrad |
| 360 turn | 2,261,946.711 mrad |
Reverse conversion: Milliradian to Turn
1 mrad × 0.0001591549431 = 0.0001591549 turn
1 milliradian = 0.0001591549 turns.
turns = milliradians × 0.000159154943092
For a page dedicated to this direction, see Milliradian to Turn.
Understanding the Turn (turn)
One full revolution.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many milliradians are in 1 turn?
1 turn equals 6,283.185307 milliradians, using the exact defined conversion factor rather than an estimate.
How do I convert turn to milliradian?
Multiply the turn value by 6283.185307. The converter above does this instantly to whatever precision you set.
How do I convert milliradian back to turn?
Use the reverse factor: 1 milliradian equals 0.0001591549 turns. You can also use the swap control in the converter above to flip the direction instantly.
What is a turn?
Turn (turn) is a unit of angle.
What is a milliradian?
Milliradian (mrad) is a unit of angle.
Is the turn to milliradian conversion exact?
Yes. Both turn and milliradian are defined by fixed standards rather than physical artifacts, so the factor of 6283.185307 used above is exact to as many digits as you choose to display.