numvana

Cable Sag Calculator

Estimate the sag, support tension, and extra length of a cable strung taut between two equal-height supports, from its span, weight, and horizontal tension.

Maximum sag (at midspan)
0.77 m
Sag as a % of span
1.53%
Tension at each support
2,003.8 N
Actual cable length
50.031 m
Extra length beyond the span
0.031 m

How it works

A cable strung between two supports at the same height sags into a catenary, but when the sag is shallow relative to the span, that curve is extremely well approximated by a parabola — overhead power lines, guy wires, and zip lines are all designed with this shortcut. The standard formula is D = w·L² / (8·H): maximum sag D at midspan, from the cable's weight per unit length w, the span L, and the horizontal tension H.

Weight per length is derived from the cable's mass per length (what a datasheet actually lists) using standard gravity, w = m × 9.80665 m/s². The tension at each support is higher than the horizontal tension alone, since it also has to carry half the cable's weight: T_support = √(H² + (wL/2)²). The cable's true length is slightly more than the span itself, by an amount the parabolic model gives as 8D²/(3L).

This approximation is only valid for shallow sag — this calculator rejects inputs where the sag would exceed 1/8 of the span, the threshold widely cited as where the parabola noticeably diverges from the true catenary curve.

FAQ

Why does this calculator ask for mass per length instead of weight per length directly?

Because that's what cable and wire datasheets actually publish — mass per unit length is a property of the cable itself, independent of gravity. The calculator converts it to weight internally using Earth's standard gravitational acceleration before applying the sag formula.

What happens if I enter a span, weight, and tension combination that sags too much?

The calculator rejects it rather than returning a misleading number. Past roughly 1/8 of the span, real sag is a true catenary — shaped by hyperbolic cosine, not a parabola — and the parabolic shortcut used here starts noticeably overstating how much the cable actually sags. In practice, that combination means the tension is too low (or the span too long) for how heavy the cable is: a taut cable should sag much less than its span.

Related calculators