Mils (NATO) to Degrees (mil to °)

1 mil (NATO) equals 0.05625 degrees exactly.

How to convert mils (NATO) to degrees

To convert mils (NATO) to degrees, multiply the number of mils (NATO) by 0.05625. This factor is exact. To go the other way, multiply degrees by 17.77777778 (rounded).

degrees = mils (NATO) × 0.05625

Example: 10 mils (NATO) = 0.5625 degrees.

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

Degree (°)

General & non-SICurrent unit

One 360th of a full turn. The everyday unit of angle, inherited from the ancient Babylonians' base-60 counting.

Dividing the circle into 360 parts traces back to the astronomers of ancient Babylon, who counted in base 60. Why 360 in particular is still debated. One explanation points to Persian and Babylonian calendars, which used a year of about 360 days, so the Sun seemed to advance roughly one degree each day. Another says the Babylonians started from the angle of an equilateral triangle and split it into 60 pieces, and a third credits early chord-based trigonometry, where a chord equal to the radius made a natural base. Greek astronomers such as Aristarchus and Hipparchus were among the first to use Babylonian astronomical knowledge systematically.

The number also divides well. 360 has 24 divisors and splits evenly by every whole number from 1 to 10 except 7, which suits a world cut into 24 time zones of 15 degrees of longitude each. Each degree breaks into 60 arcminutes, and each of those into 60 arcseconds. The SI Brochure lists the degree among the widely used non-SI units, equal to π/180 radian, about 0.01745. For scale, the Moon and the Sun each look about half a degree wide, and a little finger held at arm's length covers roughly one degree of sky.

1 degree = 0.002777777778 turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Degree (angle); Wikipedia: Angular diameter

Related conversions

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