Sag Calculator

What does sag mean?

Sag is the distance a cable, wire, rope, or beam falls below the straight line between its supports. A cable sags because it carries its own weight and any additional load applied along its span. A beam bends under load because the material and its cross section resist that bending. Both situations show a curve between supports, but the calculations are different. This sag calculator includes separate modes so you can estimate a suspended cable or check a basic simply supported beam case.

For a cable, enter the horizontal span, distributed load per unit length, and horizontal tension. The calculator reports a parabolic estimate and a catenary estimate, plus an approximate cable length. For a beam, enter the span, total point load or uniformly distributed load, elastic modulus, and second moment of area. Results for a beam depend strongly on material stiffness and cross section, so use the correct values for the member you are checking.

How to use this sag calculator

Choose Cable Sag or Beam Sag first. In cable mode, use meters for span, newtons per meter for the load, and newtons for horizontal tension. The distributed load should include the cable's own weight and any added load that acts along the span. The tool assumes the load is spread evenly over the horizontal distance and the supports are at the same height.

In beam mode, use meters for span and newtons for load. Choose center point load when a single load is applied at the middle of a simply supported beam. Choose uniform load when the load is spread evenly along the full span; enter the total load across the whole beam, not a load per meter. Provide elastic modulus in gigapascals and moment of inertia in centimeters to the fourth power. The result is shown in millimeters and meters.

The calculator updates when you change an input. Check that the number and its unit describe the same physical quantity. For example, a cable load of 20 N/m is not the same as a total load of 20 N over the entire span. If the supports sit at different elevations, the formulas here do not represent that full geometry.

Cable sag formula

A flexible cable carrying a uniform load over its horizontal span forms a catenary. When sag is small compared with span, the shape is close to a parabola. The parabolic formula is widely used for a practical estimate and is easier to calculate by hand. The catenary formula represents the ideal flexible cable more closely when the cable's own weight creates a uniform load along its length.

• Parabolic sag: f ≈ wL² ÷ (8H)
• Catenary sag: f = (H ÷ w) × [cosh(wL ÷ 2H) − 1]
• Approximate cable length: S ≈ L + (8f² ÷ 3L)

Cable sag example

Suppose a cable spans 30 meters, carries a uniform load of 20 newtons per meter, and has a horizontal tension of 5,000 newtons. The parabolic estimate is 20 × 30² ÷ (8 × 5,000), which gives 0.45 meters of sag at midspan. Because this sag is small compared with the 30 meter span, a parabolic approximation is often useful for a first estimate. The catenary result is also displayed to compare the two idealized shapes.

If the load increases while tension and span remain unchanged, sag increases. If tension increases while load and span remain unchanged, sag decreases. Span has a squared effect in the parabolic equation: doubling the span with the same load and tension gives four times the estimated sag. This is why a cable's span and tension need to be measured carefully rather than guessed from appearance.

The displayed approximate cable length uses a shallow parabolic curve assumption. It can help with preliminary material estimates, but it is not a replacement for the cable manufacturer's sag tables or a detailed catenary calculation when the span is long, sag is substantial, or loads are unusual.

Beam sag and deflection formulas

A simply supported beam rests on a support at each end and can rotate at those supports. This calculator covers two standard textbook load cases for a straight, prismatic beam made from a linear elastic material. A center point load produces maximum deflection at midspan. A uniform load spread over the full span also produces maximum deflection at midspan, but with a different formula.

• Center point load: δmax = PL³ ÷ (48EI)
• Uniform load (total load W): δmax = 5WL³ ÷ (384EI)
• Flexural rigidity: EI = elastic modulus × second moment of area

Understanding beam inputs

Elastic modulus describes how stiff a material is under elastic loading. A larger modulus means less deflection for the same beam shape and load. The calculator accepts the modulus in gigapascals; steel is commonly around 200 GPa and aluminum alloys are commonly around 69 GPa, although grades and product specifications vary. Use a verified material value for design work rather than relying on a typical number.

The second moment of area, often written as I, describes how the beam's cross section is arranged around its bending axis. It is not the same as mass moment of inertia. A deeper section can have a much larger I than a shallow section of similar area, which can greatly reduce sag. Beam tables and structural section catalogs list I for common shapes and axes. Make sure you select the axis that matches the direction of bending.

The center point load field expects a force in newtons. The uniform load field expects the total force distributed over the complete span, also in newtons. If your source gives a load intensity in newtons per meter, multiply it by the span to find the total load before entering it. This calculator assumes the beam is simply supported and the load is symmetric in the selected standard case.

What changes sag in a cable or beam?

For a cable, the main factors are span, load, and horizontal tension. A heavier cable or extra wind, ice, or carried load increases the downward force. More tension pulls the cable closer to a straight line, though allowable tension is limited by the cable, anchors, fittings, and supports. Temperature can also change cable length and tension, so a cold-weather installation may not have the same sag as a warm-weather installation.

For a beam, span has a strong effect because it appears to the third power in the point-load formula and fourth power when the distributed load is expressed as a load per unit length. Stiffness and section shape matter too: doubling EI cuts the calculated deflection in half for the same load and span. Support conditions change the result substantially; a cantilever, fixed beam, and simply supported beam do not share the same deflection equations.

Real structures can also experience vibration, creep, settlement, uneven loading, joint movement, and local damage. A simple sag estimate does not cover these effects. Consider the actual environment and load combinations when interpreting a result.

Cable tension, catenary shape, and operating conditions

The catenary curve is the natural shape of an ideal flexible cable carrying its own weight. In this calculator, the catenary result assumes the entered load is distributed evenly per unit of horizontal span. That distinction matters: a cable's own weight is more naturally distributed along its curved length, while wind or ice loads may be modeled in other ways. Under modest sag the parabolic and catenary answers are close, which is why the parabolic formula is commonly used for quick field estimates.

Horizontal tension is the horizontal component of the force at the support in the idealized model. It is not necessarily equal to the total force in every part of the cable. As the cable slopes more steeply near its supports, the total tension along the cable increases. Cable, clamp, anchor, and support capacities must be checked against the appropriate forces and installation conditions, not just the horizontal tension number entered here.

Temperature changes can alter cable length through thermal expansion and can change tension in a restrained line. Outdoor conductors may also face changing wind and ice loads. For a long span, a small change in temperature or loading can affect clearance above roads, buildings, equipment, or other conductors. Use the supplier's sag-tension charts or an engineering model that accounts for the conductor and environmental conditions when those clearances matter.

Reading the sag diagram and result

The diagram shows the supports, a straight reference line between their top points, and a bowed member below that line. The sag label represents the greatest vertical distance from the straight reference line to the curve, which occurs at midspan for the symmetric cases included here. The drawing enlarges the curve so it is easy to see on a screen; it does not use a fixed physical scale. Compare the numeric result with the actual span and project limits rather than measuring the picture.

In cable mode, the headline value uses the parabolic sag estimate and the secondary row shows the catenary value. In beam mode, the headline is the maximum midspan deflection for the selected load case. The step-by-step panel lists the equation and substituted values. These details help you review the calculation and spot a unit or input mistake before using the estimate in planning.

Limits and safe use

This tool is an educational and preliminary estimating aid. Cable mode assumes a flexible cable, level supports, a uniform load, and constant horizontal tension. Beam mode assumes a straight, constant cross section, simply supported beam, small deflection, elastic material behavior, and one of the stated symmetric load cases. It does not check bending stress, shear, buckling, vibration, connection strength, anchor capacity, fatigue, code limits, or safety factors.

Do not use a calculator result alone to choose a cable, beam, anchor, or support for a structure that could injure someone or damage property. Structural and overhead installations require appropriate engineering review and compliance with local standards. For a real project, confirm loads, material grade, support details, environmental conditions, and acceptable deflection with a qualified professional.

Frequently asked questions

Cable sag calculators and beam deflection calculators both show how far a member moves under load, but their inputs and formulas are not interchangeable. Cable tension governs a flexible cable's curve, while beam stiffness depends on elastic modulus and section inertia. Select the mode that matches the object you are evaluating and use consistent units throughout.

If you need a beam with a cantilever, fixed ends, an off-center load, multiple loads, or a detailed deflection curve, use a dedicated beam analysis tool with those support and load conditions. If you need conductor sag for an electrical line, also account for the conductor's rated properties, temperature, wind, ice, and required clearance distances.