Spur Gear API

Spur-gear geometry as an API, computed locally and deterministically for standard full-depth involute teeth. The geometry endpoint takes a module and a number of teeth (and an optional pressure angle, default 20°) and returns the complete tooth geometry: the pitch diameter (module × teeth), the base, tip (outside) and root diameters, the addendum, dedendum, whole and working depth, the circular and base pitch, the diametral pitch and the tooth thickness — all in millimetres. The module can be given directly or derived from a diametral pitch or a circular pitch. The pair endpoint meshes two gears of the same module and returns each gear's pitch and tip diameter, the centre distance (module × (z1 + z2) ÷ 2) and the gear ratio. The module endpoint converts freely between module, diametral pitch and circular pitch, or derives the module from a pitch diameter and tooth count. Everything is computed locally and deterministically, so it is instant and private. Ideal for machine-design and CAD tools, gear and gearbox calculators, maker, robotics and 3D-printing projects, and mechanical-engineering apps. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is spur-gear geometry; for bicycle gear ratios and development use a bike-gear API and for belt-and-pulley drives use a belt-drive API.