One milliradian is 0.001 radians.
Milliradians to Turns Converter — mrad to turn
Convert Milliradian (mrad) to Turn (turn) using the exact conversion factor (1 milliradian = 0.0001591549 turn). See the formula, worked examples, and conversion table.
Milliradians to Turns 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 full revolution.
Result = input x 0.001 / 6.283185307.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Milliradians to Turns
Milliradian and Turn 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 milliradian is 0.001 radians, and one full revolution.
Formula
turns = milliradians × 0.000159154943092
This factor comes from each unit's defined relationship to the category's base unit: 1 milliradian equals 0.001 base units, and 1 turn equals 6.28318530718 base units, so dividing one by the other gives the direct milliradian-to-turn factor of 0.000159154943092.
Simple example
1 mrad × 0.0001591549431 = 0.0001591549 turn
1 milliradian = 0.0001591549 turns.
Real-world example
90 mrad × 0.0001591549431 = 0.0143239449 turn
90 milliradians = 0.0143239449 turns.
Conversion table
| Milliradian (mrad) | Turn (turn) |
|---|---|
| 0 mrad | 0 turn |
| 30 mrad | 0.0047746483 turn |
| 45 mrad | 0.0071619724 turn |
| 90 mrad | 0.0143239449 turn |
| 180 mrad | 0.0286478898 turn |
| 360 mrad | 0.0572957795 turn |
Reverse conversion: Turn to Milliradian
0.0001591549 turn × 6283.185307 = 0.9999997292 mrad
0.0001591549 turns = 0.9999997292 milliradians.
milliradians = turns × 6283.18530718
For a page dedicated to this direction, see Turn to Milliradian.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
Understanding the Turn (turn)
One full revolution.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many turns are in 1 milliradian?
1 milliradian equals 0.0001591549 turns, using the exact defined conversion factor rather than an estimate.
How do I convert milliradian to turn?
Multiply the milliradian value by 0.0001591549431. The converter above does this instantly to whatever precision you set.
How do I convert turn back to milliradian?
Use the reverse factor: 1 turn equals 6,283.185307 milliradians. You can also use the swap control in the converter above to flip the direction instantly.
What is a milliradian?
Milliradian (mrad) is a unit of angle.
What is a turn?
Turn (turn) is a unit of angle.
Is the milliradian to turn conversion exact?
Yes. Both milliradian and turn are defined by fixed standards rather than physical artifacts, so the factor of 0.0001591549431 used above is exact to as many digits as you choose to display.