One milliradian is 0.001 radians.
Milliradians to Radians Converter — mrad to rad
Convert Milliradian (mrad) to Radian (rad) using the exact conversion factor (1 milliradian = 0.001 radian). See the formula, worked examples, conversion table, history, and common uses.
Milliradians to Radians 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.
The radian is the SI angle unit.
Result = input x 0.001 / 1.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Milliradians to Radians
Milliradian and Radian 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 the radian is the SI angle unit.
Formula
radians = milliradians × 0.001
This factor comes from each unit's defined relationship to the category's base unit: 1 milliradian equals 0.001 base units, and 1 radian equals 1 base unit, so dividing one by the other gives the direct milliradian-to-radian factor of 0.001.
Simple example
1 mrad × 0.001 = 0.001 rad
1 milliradian = 0.001 radians.
Real-world example
90 mrad × 0.001 = 0.09 rad
90 milliradians = 0.09 radians.
Conversion table
| Milliradian (mrad) | Radian (rad) |
|---|---|
| 0 mrad | 0 rad |
| 30 mrad | 0.03 rad |
| 45 mrad | 0.045 rad |
| 90 mrad | 0.09 rad |
| 180 mrad | 0.18 rad |
| 360 mrad | 0.36 rad |
Reverse conversion: Radian to Milliradian
0.001 rad × 1000 = 1 mrad
0.001 radians = 1 milliradian.
milliradians = radians × 1000
For a page dedicated to this direction, see Radian to Milliradian.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
Understanding the Radian
Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.
Where it's used: Standard angle unit in mathematics, physics, and engineering worldwide.
Uses of the Radian today
- Calculus and trigonometry (derivatives of trig functions are simplest in radians)
- Physics and engineering (angular velocity, rotational mechanics)
- Computer graphics and robotics
History of the Radian
The radian was developed in the 1870s, with the term itself coined by James Thomson (brother of Lord Kelvin) around 1873, formalizing a ratio-based angle measure that mathematicians had used implicitly for calculus since Newton and Leibniz.
It was adopted as the SI derived unit of angle because it makes many physics and calculus formulas simpler than using degrees.
Historical origin. Radian was not the invention of a single named person; it developed through the process described above.
Radian — sources
- BIPM SI Brochure — Coherent derived units — Defines the radian as the SI unit of plane angle.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many radians are in 1 milliradian?
1 milliradian equals 0.001 radians, using the exact defined conversion factor rather than an estimate.
How do I convert milliradian to radian?
Multiply the milliradian value by 0.001. The converter above does this instantly to whatever precision you set.
How do I convert radian back to milliradian?
Use the reverse factor: 1 radian equals 1,000 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 radian?
Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.
Is the milliradian to radian conversion exact?
Yes. Both milliradian and radian are defined by fixed standards rather than physical artifacts, so the factor of 0.001 used above is exact to as many digits as you choose to display.