How to convert gradians to milliradians
To convert a measurement in gradians to milliradians, multiply the value by 15.707963. The conversion factor comes from the relationship between both units and the radian.
For example, to convert 5 gon to milliradians: 5 × 15.707963 = 78.539816 mrad.
What is a gradian?
A gradian (also called gon or grade) is a unit of plane angle equal to 1/400 of a full turn, so a right angle is exactly 100 gradians. Introduced in France around the time of the French Revolution as part of the push to decimalize all measurement, the gradian divides the quarter circle into a tidy 100 units. It survives mainly in surveying and some European civil engineering.
Common uses of gradians include: Land surveying and geodesy in parts of Europe; Civil engineering slope and grade calculations; Some scientific calculators (GRAD mode); Cadastral (property boundary) measurement.
What is a milliradian?
A milliradian is one thousandth of a radian. At a distance of 1,000 units it subtends almost exactly 1 unit, which makes it convenient for range and angle estimation. The milliradian became widely used in the military for artillery and rifle sighting because of its clean relationship between angle and distance. Riflescopes commonly use 'mil' adjustments and reticles based on it.
Common uses of milliradians include: Rifle and artillery sighting (mil-dot reticles); Range estimation from known target size; Laser divergence and beam-spread specifications; Precision optics and alignment.
Gradians to milliradians worked examples
Here are some common values converted:
1 gon = 15.707963 mrad 5 gon = 78.539816 mrad 10 gon = 157.079633 mrad 50 gon = 785.398163 mrad 100 gon = 1,570.7963 mrad
Frequently asked questions
How many milliradians are in one gradian?
One gradian (gon) equals 15.707963 milliradians (mrad). Multiply any value in gradians by 15.707963 to convert to milliradians.
How do I convert gradians to milliradians?
Multiply the value in gradians by 15.707963. For example, 5 gon × 15.707963 = 78.539816 mrad.
How do I convert milliradians to gradians?
Multiply the value in milliradians by 0.063661977237, or divide by 15.707963. Use the swap button on the converter above to reverse the direction.
Is the gradian to milliradian conversion exact?
Angle conversions are exact. Degrees, gradians and revolutions are defined as exact fractions of a full turn (2π radians).
What is the formula for gradians to milliradians?
The formula is: mrad = gon × 15.707963. This comes from the definition of both units relative to the radian.