Cable Sag Calculator

Cable sag and tension analysis using catenary equations. Enter span, sag, and applied load to get horizontal tension, total cable length, and sag-to-span ratio. Educational use only.

This page documents the scope, inputs, outputs, and computational approach of the Cable Sag Calculator on steelcalculator.app. The interactive calculator runs in your browser; this documentation ensures the page is useful even without JavaScript.

What this tool is for

Computing cable tension, sag, and total length for cables under self-weight or uniform load.
Comparing catenary and parabolic approximations for different sag-to-span ratios.
Understanding the relationship between horizontal tension and sag for guy wires, suspension cables, and transmission lines.

What this tool is not for

It does not handle cables with concentrated point loads at arbitrary locations.
It does not account for cable stretching (elastic elongation), temperature effects, or creep.
It does not design cable end connections, anchorages, or supporting structures.

Key concepts this page covers

catenary equation y = (H/w)(cosh(wx/H) - 1)
parabolic approximation for small sag-to-span ratios
horizontal tension H and maximum tension Tmax
cable length from the hyperbolic integral

Inputs and outputs

Typical inputs: horizontal span, sag (or horizontal tension), cable self-weight per unit length, and any additional uniform load.

Typical outputs: horizontal tension H, maximum tension Tmax (at the supports), total cable length, sag-to-span ratio, and the cable profile (catenary or parabolic coordinates).

Computation approach

For a cable under its own weight, the calculator solves the catenary equation. The relationship between horizontal tension H, sag d, span L, and weight per unit length w is: d = (H/w)(cosh(wL/2H) - 1). This transcendental equation is solved iteratively (Newton-Raphson or bisection) for the unknown variable (H or d). The total cable length is S = 2H/w sinh(wL/2H). For sag-to-span ratios less than 1/8, the parabolic approximation d = wL^2/(8H) gives results within 1% of the catenary.

Frequently Asked Questions

When can I use the parabolic approximation instead of the catenary? The parabolic approximation assumes a uniform load per unit horizontal length (like a suspension bridge where the deck weight dominates). The catenary assumes a uniform load per unit cable length (like a cable under its own weight). For sag-to-span ratios less than about 1/8 (12.5%), the difference between the two is less than 1%, and the simpler parabolic formula is adequate. For larger sag ratios, the catenary gives the more accurate profile.

How does sag affect cable tension? Sag and tension are inversely related: reducing sag increases the horizontal tension (and therefore the maximum tension at the supports). Halving the sag approximately doubles the tension. This is why high-tension cables (transmission lines, guy wires) have small sag, while low-tension cables (decorative chains, safety nets) have large sag. The support structures must be designed for the cable tension, so there is always a tradeoff between cable sag and support cost.

What is the sag-to-span ratio for common applications? Typical sag-to-span ratios include: transmission lines 2-5% (high tension, small sag), suspension bridge main cables 8-12%, guy wires 1-3%, and catenary overhead wires for railways approximately 0.1-0.5%. The appropriate ratio depends on the clearance requirements, the allowable tension in the cable, and the lateral load (wind) that must be resisted.

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

The site operator provides the content "as is" and "as available" without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.