Catenary Cable Sag Calculator
Enter span and cable weight per metre then solve for sag from tension, or find the tension needed for a given sag. Cable length and SVG catenary curve included. Nothing uploaded.
Cable Parameters
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Learn more: catenary curves and cable sag
What is catenary sag
When a cable or chain is suspended between two points under its own weight, it forms a curve called a catenary. Catenary sag is the vertical distance between the two support points and the lowest point of the cable. Sag increases as tension decreases or cable weight increases. Understanding sag is critical for overhead wire clearance checks, rigging design, sailing rig pre-tensioning, and structural analysis.
Calculating cable sag from tension
Using the catenary equation: a = T_h / w (where T_h is horizontal tension in N and w is cable weight per metre in N/m). Sag = a x (cosh(L/2a) - 1) where L is the span. For shallow sags (less than 10% of span), the parabola approximation sag = wL²/(8T_h) is accurate to within 1%. The calculator uses the exact catenary equation for all sag ratios.
Catenary vs parabola
A catenary is the true shape of a cable hanging under its own weight; a parabola is the shape when the load is uniformly distributed horizontally (like a suspension bridge). For sag:span ratios below 1:10, the two shapes are nearly identical. The catenary equation is more accurate for cables with significant sag, rigging lines, power transmission lines, and suspension bridges. This calculator uses the true catenary curve.
Cable length and support tension
The cable length is always longer than the span due to the sag. As you increase sag, cable length increases - a nearly straight cable (low sag) is only slightly longer than the span; a heavily sagging cable (high sag) requires significantly more length. Tension at the supports (the load-bearing force) is greater than the horizontal tension because it must support both the horizontal tension and the cable weight. The calculator shows both tension components.
FAQ
What is catenary sag?
When a cable or chain is suspended between two points under its own weight, it forms a curve called a catenary. Catenary sag is the vertical distance between the two support points and the lowest point of the cable. Sag increases as tension decreases or cable weight increases.
How do I calculate cable sag from tension?
Catenary parameter a = T_h / w. Sag = a x (cosh(L/2a) - 1). For shallow sag (<10% span): approximation sag ≈ wL²/(8T_h) is accurate within 1%. The calculator uses the exact catenary equation.
Catenary vs. parabola - which to use?
Catenary is the correct shape for a cable under self-weight. Parabola applies when load is uniformly distributed horizontally. For sag:span below 1:10, both give nearly identical results. This calculator uses the true catenary.