The radian is the SI angle unit.
Radians to Milliradians Converter — rad to mrad
Convert Radian (rad) to Milliradian (mrad) using the exact conversion factor (1 radian = 1,000 milliradian). See the formula, worked examples, conversion table, history, and common uses.
Radians 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 1 / 0.001.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Radians to Milliradians
Radian 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. Radian is most often used for calculus and trigonometry (derivatives of trig functions are simplest in radians).
Formula
milliradians = radians × 1000
This factor comes from each unit's defined relationship to the category's base unit: 1 radian equals 1 base unit, and 1 milliradian equals 0.001 base units, so dividing one by the other gives the direct radian-to-milliradian factor of 1000.
Simple example
1 rad × 1000 = 1,000 mrad
1 radian = 1,000 milliradians.
Real-world example
90 rad × 1000 = 90,000 mrad
90 radians = 90,000 milliradians.
Conversion table
| Radian (rad) | Milliradian (mrad) |
|---|---|
| 0 rad | 0 mrad |
| 30 rad | 30,000 mrad |
| 45 rad | 45,000 mrad |
| 90 rad | 90,000 mrad |
| 180 rad | 180,000 mrad |
| 360 rad | 360,000 mrad |
Reverse conversion: Milliradian to Radian
1 mrad × 0.001 = 0.001 rad
1 milliradian = 0.001 radians.
radians = milliradians × 0.001
For a page dedicated to this direction, see Milliradian to Radian.
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.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
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 milliradians are in 1 radian?
1 radian equals 1,000 milliradians, using the exact defined conversion factor rather than an estimate.
How do I convert radian to milliradian?
Multiply the radian value by 1000. The converter above does this instantly to whatever precision you set.
How do I convert milliradian back to radian?
Use the reverse factor: 1 milliradian equals 0.001 radians. You can also use the swap control in the converter above to flip the direction instantly.
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.
What is a milliradian?
Milliradian (mrad) is a unit of angle.
Is the radian to milliradian conversion exact?
Yes. Both radian and milliradian are defined by fixed standards rather than physical artifacts, so the factor of 1000 used above is exact to as many digits as you choose to display.
Where is the radian still used today?
Standard angle unit in mathematics, physics, and engineering worldwide.