SAG Calculator
Nothing strung between two points is ever straight — every cable, rope, wire and clothesline bows into its curve, and the depth of that bow decides clearances, tensions and tempers. Enter the span, the cable’s weight per foot and the tension, and this calculator returns the mid-span sag, plus the true cable length the curve consumes.
The Parabola of Small Sags
The curve a cable takes is, exactly, a catenary — the hyperbolic-cosine shape of a perfectly flexible line under its own weight. But when the sag is small relative to the span (the working territory of every strung line on a construction site), the catenary is approximated beautifully by the parabola sag = wL² ÷ 8T: the cable's weight per foot times the span squared, over eight times the tension. Read the formula as a story and it explains the whole trade: sag grows with the square of span (double the span, quadruple the bow — the tyranny that makes long crossings engineering projects), shrinks only linearly with tension (which is why the last inch of straightness costs a fortune in force — the note's ruler-breaking warning), and scales with the cable's own weight, the one load no installation escapes. Within about 10% sag-to-span the parabola and the true catenary agree to a few percent; beyond it, this page's figure becomes an estimate and the stringing charts of the conductor's manufacturer take over, as they should.
Worked Example: A Hundred Feet at Five Hundred Pounds
The defaults string a utility-class span: 100 feet between supports, a cable weighing 0.5 lb per foot, pulled to 500 lb of tension. Sag = 0.5 × 100² ÷ (8 × 500) = 5,000 ÷ 4,000 = 1.25 feet — 15 inches of belly at mid-span, or 1.25% of the span, squarely in the note's professional band. The true cable length: the curve consumes about 100 × (8/3) × (1.25/100)² ≈ 0.04 ft extra — that span takes 100.04 ft of cable, a reminder that at installation sags the length penalty is trivial while the clearance penalty (15 inches of the span's height, gone at the middle) is the whole design question. Now drag the tension down to 100 lb in your head: sag multiplies by five, to 6.25 feet — the same cable, the same span, a clothesline's droop — which is the tension dial's one lesson: sag is bought with tension, at linear prices, against squared span.
Temperature, Ice and the Stringing Table
Three field realities ride on the clean formula. Temperature: conductors expand in heat (more length, more sag, less tension) and contract in cold — a line strung drum-tight on a January morning is a harp string; strung slack in August, it kisses the treetops by the following July, which is why utilities string from temperature-graded sag charts rather than from courage. Ice and wind: loading adds weight per foot (glaze ice can multiply a conductor's effective w several-fold) and wind pressure bows the whole catenary sideways-upward into its resultant plane — the design cases that set the profession's worst-day sags and clearances. Creep: aluminium conductors permanently stretch a fraction over their first years, a slow sag increase the initial stringing pre-pays by over-tensioning on a schedule. The calculator gives the clean-day figure from which each of these corrections departs — the number the stringing table starts from, not the one it ends at.
Galloping Lines and Aeolian Song
Two phenomena keep transmission engineers humble about the tidy parabola, and a complete page owes them a paragraph. Wind on a conductor excites aeolian vibration — a high-frequency, low-amplitude hum in the line that fatigues hardware at the clamps over years, fought with dampers and armour rods. Ice-loaded lines in wind can gallop: the iced profile becomes an airfoil, the line leaps in slow ellipses of several feet, phases clash, and towers learn about dynamics the hard way — the reason clearance design includes swing and gallop envelopes far beyond the still-air sag this page computes. The calculator's parabola is the calm day's truth, and the profession's respect for the exceptions is written in the damper weights hanging off every long span you drive beneath.
Slack Ropes, Zip Lines and the Honest Middle
Recreational lines live at sags the utility band would blush at, and the formula follows them there cheerfully within its approximation's limits. A backyard zip line is the teaching case: its sag sets both the ride's speed profile (the drop into the middle, the climb out that brakes the rider) and the anchor tensions, which skyrocket exactly as the cable is cranked toward the photogenic straight line of the brochure — 5–10% of span as sag is the considered middle where riders arrive briskly and hardware survives its summers. Slacklines push further still, into tensions that depend on the webbing's stretch as much as on geometry, and the simple parabola hands over to the elastic equations with a bow. Every line in this family is the same negotiation struck at different stakes — geometry visible, tension decisive.
Related Tools
More from the Construction Calculators hub: the Rolling Offset Calculator for the other diagonal a site must measure honestly, and the Ladder Angle Calculator for reaching the supports this page strings between.
Frequently Asked Questions
How much sag should a power line or cable have?
Enough — and the profession's band is the calculator note's: overhead conductors are typically installed to final sags around 1–3% of span under everyday conditions, a compromise among clearance (less sag keeps the line high), tension limits (more sag spares the hardware and the poles), and temperature swing (the summer line must still clear the road). Backyard applications obey the same physics with wider manners: a zip line is designed by its sag and tension together (too little sag stalls the rider mid-span; too much buries the landing's clearance), and a clothesline lives happily at 3–5%. The number is a design decision; this page prices each candidate honestly.
Why can a cable never be pulled perfectly straight?
Because the formula's denominator forbids it: sag = wL²/8T reaches zero only at infinite tension, and long before infinity the cable, its anchors or its supports reach their breaking loads. Every real installation is a negotiation between the sag you can see and the tension you cannot — which is why strain gauges and dynamometers, not eyeballs, set critical stringing tensions, and why "tighten it until it looks straight" is the first sentence in several accident reports. The calculator quantifies exactly how unreasonable "straight" is at any span you enter.
What tension is safe for my cable?
Below the working load limit the manufacturer stamps on it — commonly a quarter to a fifth of the breaking strength for wire rope in overhead duty, with the hardware (thimbles, grips, anchors) rated as a system, not a cable alone. The calculator computes the tension you set, not the tension you may set: enter tensions your hardware's ratings endorse. Dynamic loads — a zip line's rider, a load swinging on a tag line — multiply static tension several-fold at the bounce's bottom, which is why rigging derates so conservatively and why this page's static figure is a floor for design, never the design itself.
Does the sag formula work for ropes and clotheslines?
Yes — the physics has no brand loyalty, and the worked example's second act (100 lb of tension, 6.25 feet of droop) is a clothesline's portrait. Light lines make the formula's sensitivity theatrical: a cord at 0.03 lb/ft across a 20-foot garden span at a hand-pulled 20 lb sags 0.03 × 400 ÷ 160 = about 0.9 inches... enter your own figures and watch how quickly light lines punish long spans — the reason garden lines sprout mid-posts like fence rails. Elastic cords add stretch to the story (the tension then depends on the cord's elongation, an iteration the simple formula waves at), but for static fibre and wire the parabola is the whole tale.
What is the difference between sag and the catenary?
The catenary is the curve itself — the exact hyperbolic-cosine shape any uniform flexible line assumes; sag is one measurement of it, the vertical distance from the supports' chord to the curve's lowest point. Confusing the two is harmless at the dinner table and expensive in a stringing plan, where the clearance at a specific point (a road crossing at the span's third, say) is read from the curve's position there, which is not the mid-span sag. The parabola this page uses places that curve accurately enough at working sags — its ordinate at any fraction of the span is 4 × sag × x × (1 − x) with x the fractional distance — an equation worth the FAQ it lives in.
How do I measure the tension I have?
Indirectly, usually from the sag itself — which closes this page's circle: measure the mid-span sag of an existing line (a laser level or a sighted string from the supports), weigh or look up the cable's pounds per foot, and invert the formula: T = wL² ÷ 8·sag. The line confesses its tension through its belly, which is how inspectors audit installations without cutting anything. The inversion also explains the field test's cousin for zip lines and rigging: press the line sideways at mid-span with a known force on a spring scale and read its deflection — tension estimation by geometry, all the way down.