Gradian to Milliradian Converter
Convert gradian to milliradian instantly. 1 gradian = 15.707963 milliradian.
Gradian to Milliradian Table
| Gradian | Milliradian |
|---|---|
| 1 grad | 15.707963 mrad |
| 5 grad | 78.539816 mrad |
| 10 grad | 157.079633 mrad |
| 30 grad | 471.238898 mrad |
| 45 grad | 706.858347 mrad |
| 90 grad | 1413.716694 mrad |
| 180 grad | 2827.433389 mrad |
| 360 grad | 5654.866778 mrad |
Related Conversions
Quick Answer
Formula: Milliradian = Gradian × 15.71
Multiply any gradian value by 15.71 to get milliradian.
Reverse: Gradian = Milliradian × 0.06366
Worked Examples
Gradian to Milliradian Conversion Table
Common gradian values — factor: 1 grad = 15.71 mrad
| Gradian (grad) | Milliradian (mrad) | Context |
|---|---|---|
| 1 grad | 15.71 mrad | 1 grad |
| 5 grad | 78.54 mrad | 5 grad |
| 10 grad | 157.1 mrad | 10 grad |
| 25 grad | 392.7 mrad | 22.5° |
| 50 grad | 785.4 mrad | 45° |
| 100 grad | 1571 mrad | 90° right angle |
| 150 grad | 2356 mrad | 135° |
| 200 grad | 3142 mrad | 180° half circle |
| 250 grad | 3927 mrad | 225° |
| 300 grad | 4712 mrad | 270° |
| 400 grad | 6283 mrad | 360° full circle |
| 800 grad | 1.257e+04 mrad | Two circles |
| 1200 grad | 1.885e+04 mrad | Three circles |
| 2000 grad | 3.142e+04 mrad | Five circles |
| 4000 grad | 6.283e+04 mrad | Ten circles |
Mental Math Tricks
1 grad = 15.71 mrad. Memorize for instant estimates.
Right angle: 90° = 1571 mrad.
Multiply result by 0.06366 to recover the original grad value.
Who Uses This Conversion?
Uses gradians for land surveying in France, Sweden, and other European countries.
Applies gradians in road gradient calculations where 100 grad = right angle is convenient.
Works with national coordinate systems in countries that standardized on gradians.
Uses gradians in French topographic mapping traditions.
Applies gradians for dip and strike measurements in some European mining standards.
Uses gradians in some European military targeting and range calculation systems.
Related Conversions
Frequently Asked Questions
About Gradian and Milliradian
Gradian (grad)
The gradian (also called gon or grade) divides a full circle into 400 equal parts, so a right angle equals exactly 100 gradians. It was introduced during the French Revolution as part of the decimal metric system reform in the 1790s.
Gradians are used primarily in surveying, civil engineering, and some European geodetic systems. The advantage: since a right angle = 100 grad, slope percentages and bearing calculations involve simple arithmetic.
Interesting fact: France briefly mandated decimal angles (gradians) in the 1790s alongside the metric system, but the gradian never achieved the same global adoption as the meter and kilogram.
Milliradian (mrad)
The milliradian (mrad) is 1/1000 of a radian, approximately 0.0573°. It was adopted by military organizations in the early 20th century for artillery range calculations and is now standard in precision shooting and optics.
The milliradian has a practical property: at 1,000 meters distance, 1 mrad corresponds to approximately 1 meter of lateral displacement. This 'mil-dot' relationship makes range estimation and scope adjustment intuitive for military and hunting applications.
Interesting fact: NATO and many militaries use a slightly rounded version — the NATO mil — where a full circle is defined as 6,400 mils (instead of the mathematically exact 6,283.19 mrad). This makes angular calculations easier in the field.
About Gradian to Milliradian Conversion
Converting gradian to milliradian is essential in mathematics, physics, engineering, and surveying. Degrees are used in everyday contexts and navigation; radians are the standard in calculus and physics; gradians are common in European surveying. Having accurate conversions ensures correct results across disciplines.
Key reference: a right angle (90°) = 1571 mrad. A full circle (360°) = 6283 mrad. Reverse: 1 mrad = 0.06366 grad. Exact factor: 1 grad = 15.71 mrad.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.