Mils (NATO) to Radians (mil to rad)

1 mil (NATO) equals 0.0009817477042 radians (rounded).

1 mil (NATO) = 0.0009817477042 radians

How to convert mils (NATO) to radians

To convert mils (NATO) to radians, multiply the number of mils (NATO) by 0.0009817477042. The factor is rounded to 10 significant digits. To go the other way, multiply radians by 1,018.591636 (rounded).

radians = mils (NATO) × 0.0009817477042

Example: 10 mils (NATO) = 0.009817477042 radians.

About these units

Mil (NATO) (mil)

MilitaryCurrent unit

One 6,400th of a full turn (0.05625 degree). The NATO standard for artillery and sighting.

The NATO mil divides the circle into 6,400 parts, so each is 0.05625 degree, or about 0.98 milliradian. NIST lists the angular mil at exactly 0.05625 degree, about 9.817 × 10⁻⁴ radian, which works out to roughly 0.98 meter at a distance of 1 kilometer. A true milliradian is a thousandth of a radian, so a true circle holds about 6,283. The figure 6,400 is a deliberate rounding to a number that divides easily: a quarter turn is exactly 1,600 mils.

The system came from France. Around the start of World War I, French artillery tested millièmes, 6,400 to the circle, in place of decigrades, which put 4,000 in a circle, and then adopted them. The United States later copied French artillery practice, and NATO standardized the unit in the 1950s as it moved to metric measurements. Other forces use different circles, such as the 6,000-mil circle of the Soviet system.

1 mil (NATO) = 0.00015625 turns (exactly).

Sources: NIST Guide to the SI, Appendix B.8 (angle conversion factors); Wikipedia: Angular mil; Wikipedia: Milliradian

Radian (rad)

Metric (SI)Current unit

The SI unit of angle: the angle at the center of a circle subtended by an arc equal in length to the radius. A full turn is 2π radians (about 6.2832).

The radian builds its unit out of the circle itself. Lay a length of string equal to the radius along the circumference, and the angle that arc makes at the center is one radian. The SI Brochure calls it the coherent unit of plane angle, and it also serves as the coherent unit of phase angle, which grows by 2π radians over one period of a repeating wave. The same document notes that you could write rad as m/m, but warns that this is not intrinsic and can mislead, since angle is not the same kind of quantity as an ordinary ratio of lengths. It also records an alternative definition: a right angle equals π/2 radian.

A circle's circumference is 2π times its radius, so a full turn is 2π radians, about 6.2832, which makes one radian roughly 57.3 degrees, or about 0.159 of a turn. The SI Brochure's table of derived units expresses angular velocity in radians per second.

1 radian = 0.1591549431 turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Angle; NIST Guide to the SI, Appendix B.8 (angle conversion factors)

Related conversions

See all angle units.