A gradian is 1/400 of a turn.
Gradians to Milliradians Converter — gon to mrad
Convert Gradian (gon) to Milliradian (mrad) using the exact conversion factor (1 gradian = 15.70796327 milliradian). See the formula, worked examples, and conversion table.
Gradians 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 0.01570796327 / 0.001.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Gradians to Milliradians
Gradian 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. Specifically: A gradian is 1/400 of a turn, and one milliradian is 0.001 radians.
Formula
milliradians = gradians × 15.7079632679
This factor comes from each unit's defined relationship to the category's base unit: 1 gradian equals 0.0157079632679 base units, and 1 milliradian equals 0.001 base units, so dividing one by the other gives the direct gradian-to-milliradian factor of 15.7079632679.
Simple example
1 gon × 15.70796327 = 15.70796327 mrad
1 gradian = 15.70796327 milliradians.
Real-world example
90 gon × 15.70796327 = 1,413.716694 mrad
90 gradians = 1,413.716694 milliradians.
Conversion table
| Gradian (gon) | Milliradian (mrad) |
|---|---|
| 0 gon | 0 mrad |
| 30 gon | 471.238898 mrad |
| 45 gon | 706.8583471 mrad |
| 90 gon | 1,413.716694 mrad |
| 180 gon | 2,827.433388 mrad |
| 360 gon | 5,654.866776 mrad |
Reverse conversion: Milliradian to Gradian
15.70796327 mrad × 0.06366197724 = 1 gon
15.70796327 milliradians = 1 gradians.
gradians = milliradians × 0.0636619772368
For a page dedicated to this direction, see Milliradian to Gradian.
Understanding the Gradian (gon)
A gradian is 1/400 of a turn.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many milliradians are in 1 gradian?
1 gradian equals 15.70796327 milliradians, using the exact defined conversion factor rather than an estimate.
How do I convert gradian to milliradian?
Multiply the gradian value by 15.70796327. The converter above does this instantly to whatever precision you set.
How do I convert milliradian back to gradian?
Use the reverse factor: 1 milliradian equals 0.0636619772 gradians. You can also use the swap control in the converter above to flip the direction instantly.
What is a gradian?
Gradian (gon) is a unit of angle.
What is a milliradian?
Milliradian (mrad) is a unit of angle.
Is the gradian to milliradian conversion exact?
Yes. Both gradian and milliradian are defined by fixed standards rather than physical artifacts, so the factor of 15.70796327 used above is exact to as many digits as you choose to display.