Angle Units: Degrees, Radians, and Gradians

Three ways to measure the same rotation

A full circle can be described as 360 degrees, roughly 6.28 radians, or 400 gradians — three completely different numbering systems for the exact same physical rotation, chosen for different reasons by different fields.

Degrees: the everyday default

Degrees split a circle into 360 parts, a convention traced back to ancient Babylonian astronomy. It's intuitive enough that navigation, everyday geometry, and casual use all default to it.

Radians: the mathematical default

A radian is defined by the geometry of the circle itself — the angle where the arc length equals the radius — which makes it the natural unit for calculus, trigonometry, and physics formulas. Most programming languages' math libraries expect radians, not degrees, which trips up beginners constantly.

Gradians: the rare one

Gradians split a circle into 400 parts, designed to make right angles a clean 100 gradians. They show up occasionally in surveying and some European engineering contexts, but are rare enough that most people never encounter them outside specialized software.

Where this actually matters

Any time you're writing code involving trigonometric functions (sin, cos, tan), double-check whether the function expects degrees or radians — it's one of the most common silent bugs in graphics and game programming.