#sag

Catenary (hanging-cable) maths as an API, computed locally and deterministically. The sag endpoint solves the exact catenary for a cable hung between two level supports: from the span, the weight per unit length and either the horizontal tension or the sag, it returns the catenary parameter a = H/w, the sag a·(cosh(L/2a) − 1), the cable length 2a·sinh(L/2a), the minimum tension (the horizontal tension at the lowest point) and the maximum tension at the supports (H·cosh(L/2a)), plus the slack over the straight span. The parabolic endpoint gives the shallow-sag parabolic approximation — sag = w·L²/(8·H) — that is standard for overhead utility lines, and converts between sag and tension either way. The length endpoint returns the cable length for a given span and sag, with the parabolic value alongside for comparison. Forces and lengths are unit-agnostic but must be consistent (for example newtons, newtons per metre and metres). Everything is computed locally and deterministically, so it is instant and private. Ideal for power-line and transmission tools, zip-line and rigging apps, suspension and surveying calculators, and physics and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is hanging-cable catenary maths; for rigging working load limits use a rigging API and for beam deflection use a beam API.

api.oanor.com/catenary-api