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math.catenary-curve Calculator
Calculates the shape of a catenary curve (y = a·cosh(x/a)) from end-point height and span, giving sag at midspan and arc length. Power lines, chains, and suspension bridge cables all hang in catenary curves — not parabolas, as often assumed.
Inputs
A
Reference formula or conversion factor shown for context.
X
Reference formula or conversion factor shown for context.
Span
Distance between supports (m). Longer spans experience larger bending moments — structural adequacy must be rechecked.
Load
Applied force or weight (N or kN). Divide into dead load (permanent) and live load (variable — people, wind, etc.).
Results
y at x=
The value at the specified point or condition.
midspan sag
Sample size or count used in the calculation.
cable length
The computed linear length.
catenary constant a
The value at the specified point or condition.
tension at midspan (N)
The tensile force or stress — the pulling force that stretches the material. Must stay below the material's tensile strength.
y = a*cosh(x/a)
Reference formula or conversion factor shown for context.