One milliradian is 0.001 radians.
Milliradians to Circles Converter — mrad to circle
Convert Milliradian (mrad) to Circle (circle) using the exact conversion factor (1 milliradian = 0.0001591549 circle). See the formula, worked examples, and conversion table.
Milliradians to Circles 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 complete circle.
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 Circles
Milliradian and Circle 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 complete circle.
Formula
circles = 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 circle equals 6.28318530718 base units, so dividing one by the other gives the direct milliradian-to-circle factor of 0.000159154943092.
Simple example
1 mrad × 0.0001591549431 = 0.0001591549 circle
1 milliradian = 0.0001591549 circles.
Real-world example
90 mrad × 0.0001591549431 = 0.0143239449 circle
90 milliradians = 0.0143239449 circles.
Conversion table
| Milliradian (mrad) | Circle (circle) |
|---|---|
| 0 mrad | 0 circle |
| 30 mrad | 0.0047746483 circle |
| 45 mrad | 0.0071619724 circle |
| 90 mrad | 0.0143239449 circle |
| 180 mrad | 0.0286478898 circle |
| 360 mrad | 0.0572957795 circle |
Reverse conversion: Circle to Milliradian
0.0001591549 circle × 6283.185307 = 0.9999997292 mrad
0.0001591549 circles = 0.9999997292 milliradians.
milliradians = circles × 6283.18530718
For a page dedicated to this direction, see Circle to Milliradian.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
Understanding the Circle (circle)
One complete circle.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many circles are in 1 milliradian?
1 milliradian equals 0.0001591549 circles, using the exact defined conversion factor rather than an estimate.
How do I convert milliradian to circle?
Multiply the milliradian value by 0.0001591549431. The converter above does this instantly to whatever precision you set.
How do I convert circle back to milliradian?
Use the reverse factor: 1 circle 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 circle?
Circle (circle) is a unit of angle.
Is the milliradian to circle conversion exact?
Yes. Both milliradian and circle 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.