SAG Calculator: Cable & Power Line Sag Calculator Tool

What Is Cable Sag?

Sag is the vertical distance between a straight line joining two supports and the lowest point of a cable strung between them. It happens because the cable's own weight pulls it downward while the supports hold its ends. A sag calculator finds this distance from three inputs: the span between supports, the cable's weight per unit length, and the horizontal tension pulling on it. Engineers use it for power lines, suspension bridges, ropeways, and telecommunication cables.

Sag Formula

For a cable that hangs in a shallow curve, the sag can be estimated with the parabolic sag formula:

$\text{Sag} = \frac{w \times g \times L^2}{8T}$

Where:

• $w$ = mass per unit length of the cable, in kilograms per meter (kg/m)
• $g$ = standard gravity, 9.80665 m/s², which converts that mass into a downward force
• $L$ = span length between supports, in meters (m)
• $T$ = horizontal tension in the cable, in newtons (N)
• Sag = maximum vertical deflection, in meters (m)

The term $w \times g$ turns the cable's mass per length into a weight per length (a force, measured in newtons per meter). This step matters because tension is a force. Mixing a mass-based weight with a force-based tension without the gravity term gives an answer that is too small, by a factor of about 9.8.

This formula comes from approximating the cable's true shape, a curve called a catenary, as a parabola. The approximation holds well when the sag is small compared with the span, roughly under 10% of the span length. Longer, more slack cables need the full catenary equation instead.

How to Calculate Cable Sag

1. Measure the span: the straight horizontal distance between the two supports, in meters.
2. Find the weight per unit length of the cable, in kilograms per meter. For a power line, this includes the conductor and any attached hardware.
3. Find the horizontal tension in the cable, in newtons.
4. Multiply the weight per unit length by 9.80665, then by the span squared.
5. Divide that result by 8 times the tension.

Worked Example: Overhead Power Line

A medium-voltage power line has these values:

• Span: 300 m
• Conductor weight: 1.2 kg/m
• Horizontal tension: 15,000 N

$\text{Sag} = \frac{1.2 \times 9.80665 \times 300^2}{8 \times 15{,}000} = \frac{1{,}059{,}118.2}{120{,}000} \approx 8.83 \text{ m}$

The conductor hangs about 8.83 m below the straight line connecting the two towers at its lowest point.

Worked Example: Ski Lift Cable

A ski lift cable, carrying the weight of its chairs, has these values:

• Span: 200 m
• Cable weight: 8 kg/m
• Horizontal tension: 100,000 N

$\text{Sag} = \frac{8 \times 9.80665 \times 200^2}{8 \times 100{,}000} = \frac{3{,}138{,}128}{800{,}000} \approx 3.92 \text{ m}$

Why Sag Matters in Engineering

Sag affects several parts of a project's design:

• Clearance. Codes set minimum distances between power lines and the ground, buildings, or vehicles. Sag calculations confirm a line meets those limits under expected conditions.
• Support height. Towers, poles, and pylons must be tall enough to keep the lowest point of the cable clear of obstacles.
• Tension planning. More tension reduces sag, but it also increases stress on the cable and its supports, so engineers balance the two.
• Temperature and load changes. Heat expands a cable and increases sag; ice or wind adds weight and increases sag further. A cable is usually checked at several temperature and loading conditions, not just one.

Limits of the Parabolic Formula

The parabolic formula is an approximation, not an exact solution. It works best when sag is small relative to span. A few factors it leaves out:

• Elastic stretch. Real cables lengthen slightly under tension, which the basic formula ignores.
• Temperature change. The formula does not account for how heat or cold changes cable length.
• Wind and ice. Extra loads from weather are not included unless added to the weight input.
• Large sag-to-span ratios. When sag exceeds roughly 10% of the span, the full catenary equation, based on the hyperbolic cosine function, gives a more accurate result.

Frequently Asked Questions

What is sag in a power line? Sag is the vertical drop from the straight line between two support towers to the lowest point of the conductor. It results from the conductor's own weight.

What is the sag formula? Sag equals the cable's weight per unit length, times standard gravity, times the span squared, divided by 8 times the horizontal tension: Sag = (w × g × L²) / (8T).

Why does the formula include gravity if I already enter a weight? The input is a mass per length, in kilograms per meter, not a force. Multiplying by gravity (9.80665 m/s²) converts that mass into a force per length, in newtons per meter, so it matches the units of tension.

How does span length affect sag? Sag grows with the square of the span. Doubling the span, with everything else unchanged, roughly quadruples the sag.

Can tension reduce sag to zero? No. Reducing sag to zero would require infinite tension, which no real cable can withstand. Cables are designed to hang with a small, controlled sag instead.

When should I use the full catenary equation instead of this formula? When the sag is large relative to the span, roughly more than about 10%, or when precise results are needed for design or safety checks. The catenary equation is y = (T/w)[cosh(wx/T) − 1], where w is the weight per unit length as a force.