One milliradian is 0.001 radians.
Milliradians to Degrees Converter — mrad to deg
Convert Milliradian (mrad) to Degree (deg) using the exact conversion factor (1 milliradian = 0.0572957795 degree). See the formula, worked examples, conversion table, history, and common uses.
Milliradians to Degrees 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.
A degree is pi/180 radians.
Result = input x 0.001 / 0.01745329252.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Milliradians to Degrees
Milliradian and Degree 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 a degree is pi/180 radians.
Formula
degrees = milliradians × 0.0572957795131
This factor comes from each unit's defined relationship to the category's base unit: 1 milliradian equals 0.001 base units, and 1 degree equals 0.0174532925199 base units, so dividing one by the other gives the direct milliradian-to-degree factor of 0.0572957795131.
Simple example
1 mrad × 0.05729577951 = 0.0572957795 deg
1 milliradian = 0.0572957795 degrees.
Real-world example
90 mrad × 0.05729577951 = 5.156620156 deg
90 milliradians = 5.156620156 degrees.
Conversion table
| Milliradian (mrad) | Degree (deg) |
|---|---|
| 0 mrad | 0 deg |
| 30 mrad | 1.718873385 deg |
| 45 mrad | 2.578310078 deg |
| 90 mrad | 5.156620156 deg |
| 180 mrad | 10.31324031 deg |
| 360 mrad | 20.62648062 deg |
Reverse conversion: Degree to Milliradian
0.0572957795 deg × 17.45329252 = 0.9999999998 mrad
0.0572957795 degrees = 0.9999999998 milliradians.
milliradians = degrees × 17.4532925199
For a page dedicated to this direction, see Degree to Milliradian.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
Understanding the Degree
Degree (deg) measures angle. A degree is 1/360 of a full rotation, a division dating to Babylonian base-60 astronomy. It is classified as a Non-SI unit accepted for use with SI.
Where it's used: Used worldwide for navigation, geography, and everyday angle measurement.
Uses of the Degree today
- Navigation and cartography (latitude/longitude)
- Construction and surveying
- Everyday angle measurement (protractors, sports)
History of the Degree
The 360-degree circle traces to ancient Babylonian astronomy, whose base-60 (sexagesimal) number system made 360 — divisible by many small numbers — a practical choice for dividing a circle. The convention passed through Greek astronomy (Hipparchus, Ptolemy) into common use.
Historical origin. Degree was not the invention of a single named person; it developed through the process described above.
Degree — sources
- NIST Special Publication 811 — Lists the degree among non-SI units accepted for use with SI.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many degrees are in 1 milliradian?
1 milliradian equals 0.0572957795 degrees, using the exact defined conversion factor rather than an estimate.
How do I convert milliradian to degree?
Multiply the milliradian value by 0.05729577951. The converter above does this instantly to whatever precision you set.
How do I convert degree back to milliradian?
Use the reverse factor: 1 degree equals 17.45329252 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 degree?
Degree (deg) measures angle. A degree is 1/360 of a full rotation, a division dating to Babylonian base-60 astronomy. It is classified as a Non-SI unit accepted for use with SI.
Is the milliradian to degree conversion exact?
Yes. Both milliradian and degree are defined by fixed standards rather than physical artifacts, so the factor of 0.05729577951 used above is exact to as many digits as you choose to display.