Catenary Sag Calculator

Calculator Inputs

Use one force unit and one length unit consistently. Enter the distributed load per horizontal length.

Example Data Table

Formula Used

This calculator assumes level supports and a cable carrying uniform load per horizontal length.

• a = H / w
• Exact sag, f = a[cosh(L / 2a) - 1]
• Approximate sag, f_p = wL² / 8H
• Cable length, S = 2a sinh(L / 2a)
• Support tension, T_s = H cosh(L / 2a)
• Vertical reaction, V = H sinh(L / 2a)

L is span length, H is horizontal tension, and w is uniform load per horizontal length.

How to Use This Calculator

1. Enter the horizontal span between the two support points.
2. Enter the horizontal tension at the cable lowest point.
3. Enter the distributed load per horizontal length using matching units.
4. Optionally enter an allowable sag for a quick pass check.
5. Select graph points and decimal precision for the profile output.
6. Press the calculate button to show results above the form.
7. Review the graph, summary values, and selected profile coordinates.
8. Use the export buttons to save the results as CSV or PDF.

About Catenary Sag in Construction

Catenary sag matters when contractors hang temporary lines, suspended utilities, lighting runs, and supported cables across open spans. The curve affects clearance, anchorage forces, and material quantities. Exact catenary analysis is more reliable than simple approximations when spans grow longer or sag becomes noticeable.

This page helps estimate sag, support tension, cable length, and profile shape from a consistent set of inputs. The plotted curve and coordinate table make field review easier when layout teams need checkpoints along the span. The allowable sag field also helps compare design intent with the calculated drop.

FAQs

1. What is catenary sag?

Catenary sag is the vertical drop between the support line and the cable’s lowest point. It comes from the cable shape formed under its own distributed load and horizontal tension.

2. Why compare exact and approximate sag?

The approximate equation is quick for shallow curves. The exact catenary equation is better when sag is larger, spans are longer, or field tolerances demand more dependable values.

3. Which load should I enter?

Enter the total distributed load per horizontal length. That often includes cable self-weight and any regularly distributed added load expressed in the same force and length units.

4. Can I use feet and pounds?

Yes. Choose the length and force units you want, then keep all related entries consistent. The calculator treats units as labels, so mixed units should not be combined.

5. Why does sag reduce when horizontal tension increases?

Greater horizontal tension resists curvature more strongly, so the cable flattens and the lowest point rises. That reduces sag for the same span and distributed load.

6. Does this version handle unequal support elevations?

No. This version assumes both supports are level. For unequal support heights, the lowest point shifts horizontally and the calculation needs an adjusted catenary solution.

7. What does support tension represent?

Support tension is the cable force magnitude at each support for a level span. It combines the horizontal component with the vertical reaction caused by the distributed load.

8. How should I use the graph?

Use the graph to see the cable profile along the span and spot the deepest point quickly. The coordinate table and CSV export help convert that shape into field checkpoints.