#bike

Bicycle wheel-building maths as an API, computed locally and deterministically — the spoke-length and tension numbers a wheelbuilder laces a wheel by. The spoke endpoint runs the classic spoke-length formula from the hub and rim geometry: L = √(R² + r² + f² − 2·R·r·cos θ) − hole ÷ 2, where R is half the effective rim diameter (ERD), r is half the hub flange diameter, f is the centre-to-flange offset and θ = crosses × 720° ÷ spokes — so a 602 mm ERD rim on a 45 mm flange at 35 mm offset, 32 spokes laced 3-cross (a 67.5° crossing angle), needs a 293.9 mm spoke. It handles radial (0-cross) builds and computes the drive and non-drive sides separately from their own offsets, since a dished wheel’s two sides differ. The bracing endpoint gives each side’s bracing angle = atan(offset ÷ (ERD/2)) — the lever that resists side loads — and the resulting tension ratio, because the side with the smaller offset must carry higher tension, which is why a rear wheel’s non-drive spokes (often only about half the drive-side tension) go slack first. Everything is computed locally and deterministically, so it is instant and private. Ideal for bike-shop, wheelbuilding, cycling and bike-fit app developers, spoke-calculator and build-sheet tools, and component-database software. Pure local computation — no key, no third-party service, instant. Millimetres. Live, nothing stored. 2 compute endpoints. For gear inches or gearing use a bicycle-gear API.

api.oanor.com/spokelength-api