Degree to Revolution

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.

RPM (revolutions per minute) counts how many full 360° rotations an object completes each minute. It dominates because it maps directly to what you can see and feel — a wheel either goes around or it doesn't. Degrees per second would produce absurdly large numbers: an engine at 3,000 RPM is spinning at 18,000 degrees per second, which is meaningless to a mechanic. RPM is intuitive, and that's why every tachometer, drill spec sheet, and turntable rating uses it.

Earth completes one revolution on its axis every 23 hours 56 minutes (a sidereal day). At the equator, that's a surface speed of about 1,670 km/h. If it suddenly stopped, everything not bolted to bedrock would continue moving eastward at that speed — winds would scour the surface, oceans would slosh into continental-scale tsunamis, and the atmosphere would take years to settle. Thankfully, Earth is decelerating by only about 2.3 milliseconds per century due to tidal friction with the Moon.

A vinyl record plays at 33⅓ or 45 RPM. A washing machine spin cycle hits 1,000–1,400 RPM. A car engine idles at 600–900 RPM and redlines at 6,000–9,000 RPM (F1 cars reached 20,000 RPM before regulations capped them). A dentist's drill spins at 250,000–400,000 RPM. Hard drive platters rotate at 5,400 or 7,200 RPM. A jet engine's high-pressure turbine reaches 10,000–15,000 RPM. The fastest man-made spinning object — a nanorotor in a lab — reached 300 billion RPM in 2018.

In strict usage, "revolution" is orbital (Earth revolves around the Sun) while "rotation" is axial (Earth rotates on its axis). But colloquially the two words get swapped constantly, even by scientists. The key distinction: an orbit traces a path around an external point, while a spin is about an internal axis. The Moon is tidally locked, meaning its rotation period equals its revolution period — which is why we always see the same face.

Conservation of angular momentum. When a skater pulls their arms inward, they reduce their moment of inertia (the rotational equivalent of mass). Since angular momentum (L = Iω) must stay constant, decreasing I forces ω (angular velocity in revolutions per second) to increase. A skater can go from 2 revolutions per second with arms out to 5–7 revolutions per second with arms tucked. It's the same physics that makes neutron stars spin at hundreds of revolutions per second after a massive star collapses.