Vinyl Record API

Vinyl-record geometry maths as an API, computed locally and deterministically — the playing-time, groove-length and groove-speed numbers a cutting engineer, pressing plant or audio hobbyist works a record out with. The playing-time endpoint gives a side's maximum time = the number of groove turns ÷ the turntable speed, where the turns = the recorded band's radial width ÷ the groove pitch (the spacing between adjacent grooves): a 12-inch LP with ~85 mm of band at a 100 µm pitch holds about 850 turns, so at 33⅓ rpm that is roughly 25 minutes a side — a tighter pitch fits more time but cuts groove amplitude and so loudness and bass, the classic time-versus-level trade. The groove-length endpoint unrolls the spiral: length ≈ turns × the mean circumference (π × the average of the outer and inner diameters), on the order of 400–500 metres for an LP side, the whole of which the stylus traces once. The groove-speed endpoint gives the linear speed under the stylus = 2π × rpm/60 × radius, so the outer grooves of an LP pass at about 50 cm/s but the inner ones only ~20 cm/s — the cause of inner-groove distortion and why engineers place quieter tracks last. Everything is computed locally and deterministically, so it is instant and private. Ideal for record-cutting and mastering tools, hi-fi and collector apps, and audio-engineering calculators. Pure local computation — no key, no third-party service, instant. 3 compute endpoints. For musical note and tempo maths use a music API.