## Milliradians

**Abbreviation/Symbol:**

mrad

mils

**Worldwide use:**

Milliradians, also known as mils, are a unit of measurement commonly used in various fields worldwide.

Milliradians are a versatile unit of measurement that find applications in military operations, surveying, and navigation highlights their importance in achieving accuracy and precision in measurements and calculations.

**Definition:**

A Radian is the angle made by taking the radius of a circle and wrapping it along the circle's edge. Therefore 1 Radian is equal to (180/π) degrees. A milliradian is 1/1000 of this value

Milliradians, often abbreviated as mrad or mil, are a unit of angular measurement. The term "milliradian" is derived from the Latin word "mille," meaning thousand, and "radius," referring to the radius of a circle. In simple terms, a milliradian is equal to one-thousandth of a radian.

**Origin:**

The origin of the milliradian can be traced back to the early 20th century when it was first introduced by the Swedish engineer and inventor Carl Gustav Jungner. Jungner developed the concept of the milliradian as a way to simplify and standardize angular measurements in military optics and artillery. Since then, the milliradian has become widely adopted by military organizations around the world and is now a common unit of measurement in various fields, including ballistics, surveying, and navigation.

**Common references:**

One finger width at an arms length is approximately 30 mils wide

A fist at arms length is approx. 150 mils

A spread out hand is approx. 300 mils.

**Usage context:**

A milliradian is a useful unit of measurement because it allows for precise and consistent angular calculations. It is often used to measure small angles, especially in situations where accuracy is crucial. For example, in the field of optics, milliradians are used to measure the field of view of a telescope or binoculars. In ballistics, milliradians are used to calculate bullet drop and windage adjustments, ensuring accurate long-range shooting. In surveying, milliradians are used to measure horizontal and vertical angles, aiding in the precise mapping of land and construction projects.

The milliradian is a unit of measurement commonly used in military and firearms applications.

**Conversion of milliradians:**

To convert milliradians to other units of angular measurement, such as degrees or radians, a simple conversion factor is used. One milliradian is equal to approximately 0.0573 degrees or 0.001 radians. Conversely, to convert degrees or radians to milliradians, one can multiply the value by approximately 17.453 or 1000, respectively.

**About NATO milliradians:**

NATO milliradians (NATO mils) are a unit of angular measurement commonly used in military and artillery applications. They are derived from the radian, which is the standard unit for measuring angles in the International System of Units (SI). A radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

NATO mils are a more practical and convenient unit for military purposes, as they allow for easier estimation and calculation of angles in the field. One NATO mil is equal to 1/6400th of a circle, or approximately 0.05625 degrees. This means that a full circle is divided into 6400 NATO mils.

NATO mils are particularly useful in artillery and target acquisition, as they provide a simple and accurate way to measure angles and distances. They are often used to determine the direction and elevation of artillery fire, as well as to calculate the range to a target. NATO mils are also employed in land navigation and map reading, allowing military personnel to quickly and accurately determine their position and plan their movements. Overall, NATO mils provide a practical and efficient means of angular measurement in military operations.

**About USSR milliradians:**

The USSR milliradian, also known as the Soviet milliradian, is a unit of measurement used in the former Soviet Union for angular measurements. It is derived from the radian, which is the standard unit for measuring angles in the International System of Units (SI). The milliradian is roughly equal to one thousandth of a radian, making it a smaller unit of measurement.

The USSR milliradian was widely used in various fields, including military and engineering applications. It provided a convenient way to measure small angles with high precision. In military applications, the milliradian was used for artillery targeting and range estimation. It allowed for accurate calculations of bullet trajectory and helped improve the accuracy of artillery fire. In engineering, the milliradian was used for surveying and mapping, providing a precise way to measure angles and distances.

Although the USSR milliradian is no longer in common use since the dissolution of the Soviet Union, it still holds historical significance. It serves as a reminder of the unique measurement systems that were developed in different regions of the world. Today, the radian and its decimal multiples, such as the milliradian, are widely used in various fields, including mathematics, physics, and engineering, providing a standardized way to measure angles and facilitate accurate calculations.

There are 6,300 USSR milliradians to a full circle.

**About US WW2 Milliradians:**

During World War II, milliradians (mils) and radians played a crucial role in various military operations. Milliradians are a unit of angular measurement commonly used in artillery and long-range shooting. They are derived from the concept of a radian, which is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. A milliradian is equal to one-thousandth of a radian, making it a more precise unit for measuring small angles.

In the context of World War II, milliradians were used extensively by artillery units to calculate the elevation and azimuth angles required to accurately hit targets at long distances. Artillery gunners would use specialized instruments, such as the M2A2 aiming circle, to measure the angle between the target and the gun. By converting this angle into milliradians, gunners could then adjust the elevation and direction of the gun to ensure accurate fire. This was particularly important in situations where targets were located far away or obscured by terrain, as milliradians allowed for precise adjustments to be made, increasing the chances of hitting the target successfully.

There are 4,000 US WW2 milliradians in a full circle.

**About UK Milliradians:**

The milliradian (mrad) is a unit of measurement commonly used in the United Kingdom to express angles and distances. It is derived from the radian, which is the standard unit for measuring angles in the International System of Units (SI). The milliradian is equal to one thousandth of a radian, making it a smaller and more precise unit of measurement.

In the UK, milliradians are often used in various fields such as surveying, engineering, and ballistics. They are particularly useful for measuring small angles and distances with high accuracy. For example, in surveying, milliradians are used to measure the slope of the land or the inclination of a surface. In engineering, milliradians are used to calculate the angular displacement of mechanical components or the field of view of optical instruments.

The advantage of using milliradians over degrees or other units is their ability to provide more precise measurements. Since a milliradian is a smaller unit, it allows for finer adjustments and more accurate calculations. Additionally, milliradians are often used in conjunction with metric units, which makes them compatible with the SI system and facilitates conversions between different units of measurement. Overall, the use of milliradians in the UK ensures greater precision and consistency in various applications that require accurate angular and distance measurements.