A catenary calculation is any mathematical operation involving a curve formed by the hyperbolic cosine function. Called a catenary, such curves are the shape that a cable forms when it's supported at its ends and otherwise acted upon only by its own weight.
Though similar in appearance to a parabolic curve, catenary curves are hyperbolic. They are formed naturally any time rope or cable or chain is suspended between two points and allowed to hang free. Inverted catenary curves have long been used in architecture to create arches. The shape is generally regarded as optimal for a freestanding arch of constant thickness.