📐 Angle Converter

All angle conversions route through the degree. One full circle is 360°, 2π radians, 400 gradians, or 1 turn. The radian is the SI unit — defined as the angle subtended by an arc equal in length to the radius, which is why π rad = 180°. To convert degrees to radians, multiply by π/180; to go the other way, multiply by 180/π.

Gradians are a metric curiosity — 100 grad = 90°, so 1 grad = 0.9°. They were introduced with the French revolution but never widely adopted outside surveying. Engineers still occasionally use them on some theodolites.

You'll also see minutes and seconds of arc (1° = 60′ = 3600″) — mostly in astronomy and cartography. This tool handles decimal degrees, degrees-minutes-seconds, radians, gradians, and full turns.

Real-world applications

Surveyors use gradians for theodolite readings - a 400-grad circle is more decimal-friendly than 360 degrees. 1 grad = 0.9 degrees, so you can multiply grads by 0.9 to get degrees mentally.

Astronomers use minutes & seconds of arc for precision star positions. Polaris is about 2 degrees north of true north, which is 120 arc-minutes or 7,200 arc-seconds.

Game engines and GPS internally store angles as turns (full revolutions) because modular arithmetic is simpler: adding turns wraps around cleanly at 1.0.