milliradians

Milliradian, abbreviated mrad or MRAD, is a unit of angular measurement equal to one thousandth of a radian. A radian is the angle subtended at the center of a circle by an arc whose length equals the circle’s radius, and 1 radian equals 1000 milliradians. The milliradian is widely used in optics, firearms, ballistic calculations, surveying, and targeting systems because, for small angles, linear size on a distant object scales approximately linearly with distance.

In practice, the relation between angle and linear size is s = D × θ, where D is the distance to the target and θ is in radians. Therefore, at distance D, 1 mrad subtends about D/1000 meters. For example, 1 mrad at 100 meters is about 0.1 meters (10 cm); at 1000 meters it is about 1 meter.

There is also a related measurement called the NATO mil, defined as 1/6400 of a circle, approximately 0.05625 degrees. In that system, 1 NATO mil ≈ 0.982 mrad, so 1 mrad ≈ 1.02 NATO mil. This difference means that “mil” and “MRAD” are sometimes used interchangeably in casual discussion but are not identical.

MRAD-based reticles are common in modern riflescopes and ballistic calculators, enabling straightforward holdovers and windage estimates. Conversions are commonly cited as 1 MRAD ≈ 3.437 MOA. However, users should ensure consistent units and be aware of the specific mil definition used by their equipment.