Cable Sag Calculator
Sag, end tension and developed length of a cable or wire strung between two supports at the same height.
Results
What this tool does
A cable pulled tight between two poles can never be straight: the tighter you pull it the closer it comes, but the tension climbs far faster than the sag falls. Halving the sag doubles the tension, which is why overhead lines are strung with a deliberate droop and why a washing line that looks perfectly taut is quietly loading its posts with several times the weight of the washing.
Formula
deflection = w L² / (8 H) (parabolic approximation)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
wl | Load per metre | N/m |
sp | Span | m |
ht | Horizontal tension | N |
SG | Sag | m |
TT | Tension at the supports | N |
LL | One-way cable length | m |
EX | Extra length over the span | mm |
Worked example
- Load per metre10 N/m
- Span100 m
- Horizontal tension5000 N
- Sag2.500 m
- Tension at the supports5025.0 N
- One-way cable length100.1667 m
- Extra length over the span166.7 mm
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
Frequently asked questions
Is this the same as a catenary?
Not quite. A cable hanging under its own weight forms a true catenary, a cosh curve. The parabola used here is what you get if the load is spread evenly along the horizontal instead, and the two agree closely as long as the sag is less than about a tenth of the span — which covers most overhead lines, guy wires and washing lines. At larger sags the catenary is noticeably deeper.