Cable Span Sag Calculator
Enter a span, the cable’s weight per meter, and the horizontal tension to estimate midspan sag, the tension at the supports, and the cable’s length across the span.
Sag & cable length
These numbers are for learning, not for building
Every figure on this page is illustrative physics, not a design. It shows how span, weight, tension and slope trade off; it cannot tell you that any real cable, rope, anchor or drive is strong enough.
- Never use these figures for a zip line, a rope course, a slackline, a hoist, a winch, or any lifting. A backyard span is where a wrong number hurts someone.
- The models leave out wind, ice and temperature, the weight of riders or cargo, dynamic and shock loads from starting, stopping and bouncing, wear, anchor strength, and any safety factor.
- Any cable system that carries people or loads must be designed by a qualified engineer to the applicable standard (for passenger ropeways, EN 12929 in Europe or ANSI B77.1 in the US) and inspected on the schedule that standard sets.
How towers, tension, and sag fit together
Every aerial ropeway — a gondola, a chairlift, or a full aerial tramway — carries at least one cable strung between towers under tension. Pull it tighter and it sags less but pulls harder on the towers; let it sag more and the towers see less load but the cable needs more clearance above the terrain below. This calculator applies the catenary, the curve a uniform cable actually takes under its own weight, to show that trade-off with real numbers.
The same curve also gives the tool’s support-tension figure: because a real span carries weight along its whole length, the towers feel more force than the flat, midspan tension alone.
Frequently Asked Questions
What is cable sag and why does it matter?
Sag is how far a suspended cable dips below a straight line between its two supports. Every real cable sags at least a little under its own weight — more tension pulls it straighter (less sag), while a heavier cable or a longer span sags more for the same tension. Ropeway and transmission-line engineers size the sag and tension together so the cable clears towers, terrain, and other lines with margin at every temperature and load condition.
Why does this use the catenary and not the parabola?
A cable hanging under its own weight follows a catenary: y = a·cosh(x/a), with a = T/w, where T is the horizontal tension and w the weight per unit length. For a level span L the midspan sag is a·(cosh(L/2a) − 1). The popular parabolic shortcut, sag ≈ w·L²/(8·T), is close on a taut span but always a little low, and on a long, slack span it understates both the sag and the tension at the supports (by about 11% for the support tension on a 450 m span of a 1 kg/m cable at 2,000 N). This tool uses the catenary and rounds sag and tension up, so the figure is never below the physics.
Why is the tension at the supports higher than the horizontal tension?
The horizontal tension you enter is the pull along the flattest part of the cable, at midspan. At the towers the cable also has to support the weight hanging below that point, adding a vertical component. On a catenary the tension at the support is T·cosh(L/2a), which works out to exactly T + w × sag: always more than the horizontal value, and more so on longer or heavier spans.
Does this replace a certified ropeway engineering calculation?
No. This tool is an educational approximation for understanding how span, weight, and tension trade off — it ignores temperature effects, ice/wind loading, carried and dynamic loads, cable stretch, uneven supports, and safety factors. Never use it for a zip line, a rope course, a hoist, or any lifting. Real aerial tramway and gondola cables are designed and certified under ropeway safety standards (such as EN 12929 or equivalent national codes) by a qualified engineer, not estimated with a simple formula.
Educational estimate only, using the catenary for level supports — not a certified engineering calculation. Real ropeway cable design accounts for temperature, ice and wind loading, and safety factors, and must be performed by a qualified engineer under the applicable ropeway safety code.