One milliradian is 0.001 radians.
Milliradians to Gradians Converter — mrad to gon
Convert Milliradian (mrad) to Gradian (gon) using the exact conversion factor (1 milliradian = 0.0636619772 gradian). See the formula, worked examples, and conversion table.
Milliradians to Gradians 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 gradian is 1/400 of a turn.
Result = input x 0.001 / 0.01570796327.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Milliradians to Gradians
Milliradian and Gradian 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 gradian is 1/400 of a turn.
Formula
gradians = milliradians × 0.0636619772368
This factor comes from each unit's defined relationship to the category's base unit: 1 milliradian equals 0.001 base units, and 1 gradian equals 0.0157079632679 base units, so dividing one by the other gives the direct milliradian-to-gradian factor of 0.0636619772368.
Simple example
1 mrad × 0.06366197724 = 0.0636619772 gon
1 milliradian = 0.0636619772 gradians.
Real-world example
90 mrad × 0.06366197724 = 5.729577951 gon
90 milliradians = 5.729577951 gradians.
Conversion table
| Milliradian (mrad) | Gradian (gon) |
|---|---|
| 0 mrad | 0 gon |
| 30 mrad | 1.909859317 gon |
| 45 mrad | 2.864788976 gon |
| 90 mrad | 5.729577951 gon |
| 180 mrad | 11.4591559 gon |
| 360 mrad | 22.91831181 gon |
Reverse conversion: Gradian to Milliradian
0.0636619772 gon × 15.70796327 = 0.9999999994 mrad
0.0636619772 gradians = 0.9999999994 milliradians.
milliradians = gradians × 15.7079632679
For a page dedicated to this direction, see Gradian to Milliradian.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
Understanding the Gradian (gon)
A gradian is 1/400 of a turn.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many gradians are in 1 milliradian?
1 milliradian equals 0.0636619772 gradians, using the exact defined conversion factor rather than an estimate.
How do I convert milliradian to gradian?
Multiply the milliradian value by 0.06366197724. The converter above does this instantly to whatever precision you set.
How do I convert gradian back to milliradian?
Use the reverse factor: 1 gradian equals 15.70796327 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 gradian?
Gradian (gon) is a unit of angle.
Is the milliradian to gradian conversion exact?
Yes. Both milliradian and gradian are defined by fixed standards rather than physical artifacts, so the factor of 0.06366197724 used above is exact to as many digits as you choose to display.