Degree to Mil

The Babylonians used base-60 arithmetic and noticed the year was close to 360 days — convenient because 360 divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, and more. That ridiculous number of factors makes slicing a circle into halves, thirds, quarters, fifths, sixths, and eighths all come out to whole numbers. A base-100 system would only divide cleanly by 2, 4, 5, 10, 20, 25, and 50 — far less flexible for geometry and land surveying.

Navigation requires quick mental arithmetic with headings, bearings, and wind corrections. "Turn right to heading 270" is instantly understood in a cockpit; "turn right to 4.712 radians" would get someone killed. Compass roses, runway numbers (which are headings divided by 10), and nautical charts all assume a 360° circle. The entire global aviation and maritime infrastructure — from VOR stations to AIS transponders — is calibrated in degrees.

The degree symbol is a small raised circle placed immediately after the number with no space (45°, not 45 °). On Windows, hold Alt and type 0176 on the numpad. On Mac, press Option+Shift+8. On phones, long-press the zero key. In HTML, use ° or °. A common mistake is using a superscript letter "o" or the ring-above diacritic — these look similar but are different Unicode characters and can break search or data parsing.

One degree equals 60 arcminutes, and one arcminute equals 60 arcseconds — so 1° = 3,600″. To convert DMS to decimal, divide minutes by 60 and seconds by 3,600, then add them to the degree value. For example, 40°26′46″N becomes 40 + 26/60 + 46/3600 = 40.4461°. Google Maps uses decimal degrees internally but lets you enter either format. At the equator, one degree of longitude spans about 111 km.

Yes — the French Revolutionary government introduced the gradian (grad), dividing a circle into 400 parts to match the metric system. A right angle became exactly 100 grad. They also tried decimal time (10-hour days) and a decimal calendar. The time and calendar experiments died within a few years, but gradians survived and are still used in French and German surveying. Every scientific calculator has a GRAD mode because of this 230-year-old French experiment.

Because mils create a beautifully simple relationship: at 1,000 meters, 1 mil ≈ 1 meter of lateral distance. An artillery spotter who sees a shell land 30 meters left of the target simply radios "right 30" and the gunner adjusts 30 mils. No trigonometry, no calculator, no conversion tables — just a direct, linear approximation that works under fire. Degrees would require multiplying by 17.45 to get the same offset, which is exactly the kind of arithmetic you don't want to do while being shot at.

NATO uses 6,400 mils per circle because it divides evenly by many tactically useful numbers (2, 4, 8, 16, 32, 64). The former Warsaw Pact used 6,000 for simpler decimal arithmetic. Sweden historically used 6,300 (a closer approximation to 2,000π). The mathematically "pure" mil would be 6,283.19… (2,000π), making 1 mil exactly 1 milliradian — but nobody uses that because it doesn't divide evenly by anything. NATO's 6,400 won out as the global standard.

A true milliradian (mrad) is 1/1000 of a radian, giving 6,283.19… per circle. A NATO mil is 1/6400 of a circle, which is about 0.98 milliradians. The difference is roughly 2%, which matters in precision shooting but not in artillery. Long-range rifle scopes are increasingly calibrated in true milliradians (mrad), while military artillery sticks with NATO mils. If a scope says "mil-dot," it almost certainly means milliradians, not NATO mils.

A mil-dot reticle has dots spaced exactly 1 milliradian apart. If you know the size of your target, you can estimate distance: a 1.8-meter-tall person who spans 3 mil-dots is at 1,800/3 = 600 meters. The formula is target size (mm) ÷ size in mils = range (m). Snipers memorize common reference sizes — vehicle widths, door heights, shoulder widths — so they can range targets without a laser rangefinder. It's 18th-century trigonometry dressed up in modern optics.

A military lensatic compass reads 0 to 6400 mils instead of 0 to 360°. North is 0 (or 6400), east is 1600, south is 3200, west is 4800. Grid references and fire missions are called in mils because they plug directly into artillery calculations. To convert a mil bearing to degrees, multiply by 0.05625 (or divide by 17.78). Most soldiers never bother converting — they think in mils natively, the same way a pilot thinks in knots rather than converting to km/h.