Rope Length for a Span Calculator
Enter the span between two supports and the midspan sag to estimate the actual length of cable needed to cross that gap.
Rope length
A little sag adds up over a long span
The extra length a sagging cable needs grows with the square of the sag and shrinks as the span gets longer, which is why the same absolute sag matters much more on a short span than a long one. For a typical, well-tensioned ropeway cable the extra length is a small fraction of the total — often well under one percent — but it’s a real number worth accounting for when estimating cable stock or checking a manufacturer’s cut length.
The tool uses the same shallow-sag geometry as the Cable Span Sag Calculator, so the two work well together: find the expected sag first, then use it here to estimate the cable length across that span.
Frequently Asked Questions
Why is a sagging cable longer than the span it crosses?
A cable that hangs in a curve between two points always travels a little further than the straight-line distance between them — the same way a slack clothesline is longer than the distance between its two poles. The more it sags, the more extra length it needs. This calculator estimates that extra length from the span and the midspan sag.
What formula does this use?
It uses the standard parabolic arc-length series for a shallow-sag curve: extra length ≈ 8d²/(3L) − 32d⁴/(5L³), where d is the midspan sag and L is the span. The first term alone is the classic engineering rule of thumb for a taut cable; the second term sharpens the estimate as sag grows relative to span.
How accurate is this for a real ropeway cable?
Very close for a shallow sag — roughly under 20% of the span, which covers most taut ropeway track cables and haul ropes. Beyond that, the true shape is a catenary rather than a parabola and this series approximation drifts further from reality, which is why the tool flags a deep-sag result as less reliable.
How does this relate to the Cable Span Sag Calculator?
The sag calculator on this site starts from a span, cable weight, and tension and works out how much a cable sags. This tool runs the geometry the other way: starting from a span and a sag figure — measured, assumed, or taken from the sag calculator's result — it works out how much cable length that sag actually adds.
Educational estimate using a shallow-sag approximation — not a cut-length specification. Procurement lengths for a real cable should come from the manufacturer or the project’s certified engineering drawings.