A degree is pi/180 radians.
Degrees to Milliradians Converter — deg to mrad
Convert Degree (deg) to Milliradian (mrad) using the exact conversion factor (1 degree = 17.45329252 milliradian). See the formula, worked examples, conversion table, history, and common uses.
Degrees 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 0.01745329252 / 0.001.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Degrees to Milliradians
Degree 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. Degree is most often used for navigation and cartography (latitude/longitude).
Formula
milliradians = degrees × 17.4532925199
This factor comes from each unit's defined relationship to the category's base unit: 1 degree equals 0.0174532925199 base units, and 1 milliradian equals 0.001 base units, so dividing one by the other gives the direct degree-to-milliradian factor of 17.4532925199.
Simple example
1 deg × 17.45329252 = 17.45329252 mrad
1 degree = 17.45329252 milliradians.
Real-world example
90 deg × 17.45329252 = 1,570.796327 mrad
90 degrees = 1,570.796327 milliradians.
Conversion table
| Degree (deg) | Milliradian (mrad) |
|---|---|
| 0 deg | 0 mrad |
| 30 deg | 523.5987756 mrad |
| 45 deg | 785.3981634 mrad |
| 90 deg | 1,570.796327 mrad |
| 180 deg | 3,141.592654 mrad |
| 360 deg | 6,283.185307 mrad |
Reverse conversion: Milliradian to Degree
17.45329252 mrad × 0.05729577951 = 1 deg
17.45329252 milliradians = 1 degrees.
degrees = milliradians × 0.0572957795131
For a page dedicated to this direction, see Milliradian to Degree.
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.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
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 milliradians are in 1 degree?
1 degree equals 17.45329252 milliradians, using the exact defined conversion factor rather than an estimate.
How do I convert degree to milliradian?
Multiply the degree value by 17.45329252. The converter above does this instantly to whatever precision you set.
How do I convert milliradian back to degree?
Use the reverse factor: 1 milliradian equals 0.0572957795 degrees. You can also use the swap control in the converter above to flip the direction instantly.
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.
What is a milliradian?
Milliradian (mrad) is a unit of angle.
Is the degree to milliradian conversion exact?
Yes. Both degree and milliradian are defined by fixed standards rather than physical artifacts, so the factor of 17.45329252 used above is exact to as many digits as you choose to display.
Where is the degree still used today?
Used worldwide for navigation, geography, and everyday angle measurement.