Mil to Sextant

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.

A sextant uses two mirrors to superimpose the image of a celestial body onto the horizon. The navigator looks through the eyepiece and sees the horizon directly through a half-silvered mirror, while a second mirror on a movable arm reflects the Sun or star down into the same field of view. You swing the arm until the star appears to sit exactly on the horizon, then read the angle off the graduated arc. The double-reflection design means the arc only needs to span 60° (one sextant) to measure angles up to 120°.

The name refers to the arc of the instrument, not its measurement range. A sextant's arc is one-sixth of a circle (60°), but thanks to the double-reflection principle — where the angle of reflection doubles the arc angle — it can actually measure angles up to 120°. Similarly, an octant (one-eighth of a circle, 45° arc) measures up to 90°. The naming convention describes the physical shape of the tool, not its capability.

Yes, and navies worldwide still require it. The US Naval Academy reintroduced mandatory celestial navigation in 2015 after a decade-long hiatus, citing concerns about GPS vulnerability to jamming, spoofing, and satellite failure. A skilled celestial navigator with a sextant, an accurate clock, and a nautical almanac can determine position to within about 1–2 nautical miles — good enough to make port safely. Several solo round-the-world sailors carry sextants as backup specifically because they have no electronics to fail.

The sextant itself couldn't solve longitude — that required an accurate clock (John Harrison's marine chronometer, completed in 1761). But the sextant was the other half of the solution. A navigator used it to measure the Sun's altitude at local noon to find the exact time of solar noon at their position. Comparing this to Greenwich time on the chronometer gave the time difference, and since Earth rotates 15° per hour, that time difference directly yielded longitude. Sextant + chronometer = position anywhere on Earth.

Sixty degrees is the interior angle of an equilateral triangle — the simplest regular polygon after the square. Honeycomb cells are hexagons (six 120° angles, each the supplement of 60°) because hexagonal packing is the most efficient way to tile a plane. Carbon atoms in graphene and diamond form 60° and 109.5° angles respectively. The 60° angle appears everywhere in nature because it's the geometric consequence of close-packing equal-sized spheres or circles.