Catenary Curve Calculator

A catenary is the curve formed by a uniform flexible chain or cable hanging freely under its own weight between two supports. Its equation is y = a·cosh(x/a), where a = H/w (horizontal tension divided by weight per unit length). It is similar to but distinct from a parabola.

A parabola describes the shape of a cable under a uniform horizontal load (like a suspension bridge deck). A catenary describes a cable under its own weight only. For small sag-to-span ratios, the two curves are nearly identical, but they diverge for large sag.