Milliradian

Palais de Rumine 1

Observed angle, arc length and subtension

Ballistic table for 7.62x51 mm NATO (mrad and moa)

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Milliradian (mrad) sight adjustment

Figure 2- Illustration of a Rifle Showing Line of Sight and Bore Angle

S&B P4 reticle at 25x zoom

Milliradian (mrad) is a measurement unit used for angles, commonly found in the fields of ballistics, optics, and geodesy. It is a SI derived unit that is defined as one-thousandth of a radian, which is the standard unit of angular measure used in many areas of mathematics. The milliradian is particularly useful in applications where precise adjustments or measurements are required, such as aiming devices on firearms, telescopes, and surveying equipment.

Definition

A milliradian is defined as 1/1000th of a radian. Since a radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle, a milliradian is therefore the angle made by an arc that is 1/1000th of that radius. In terms of degrees, one milliradian is approximately equal to 0.0573 degrees.

Usage

Milliradians are widely used in the military, particularly in artillery, tank, and mortar gunnery, where they serve as a unit for angular measurement. The advantage of using milliradians in these contexts is their ability to provide precise adjustments or measurements over long distances. For example, in sniper scopes, adjustments are often made in milliradians to accurately aim at distant targets.

In surveying and engineering, milliradians are used to describe small angles in projects requiring high precision, such as bridge construction or the alignment of large structures. Optics, such as laser systems and telescopic sights, also frequently employ milliradians for the fine tuning of angles.

Conversion

To convert milliradians to degrees, the value in milliradians is multiplied by 180/π. Conversely, to convert degrees to milliradians, the value in degrees is multiplied by π/180 and then by 1000.

Advantages

The use of milliradians offers several advantages in precision applications:

• It allows for easy calculation and conversion between angular size and linear size at a given distance.
• It provides a straightforward method for adjusting sighting devices on firearms.
• It is universally applicable, being based on the radian, which is a fundamental unit of measurement in the International System of Units (SI).

See Also

• Radian
• Degree (angle)
• Angular measurement
• Surveying
• Ballistics

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