Sag Calculator — Cable & Wire Sag Between Two Poles
Enter the horizontal span between two supports, the cable weight per metre, and the horizontal tension to instantly compute sag and cable length — both the fast parabolic approximation and the exact catenary formula.
m
N/m
N
Maximum vertical drop at the centre — parabolic approximation (wL²/8H)
- 1
Span squared
30² = 900 - 2
Numerator (w × L²)
5 × 900 = 4,500 - 3
Sag
4,500 ÷ (8 × 1,000) = 0.563Parabolic approximation: wL² ÷ (8H)
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Cable sag = w × L² / (8H) (parabolic), where w = unit weight (N/m), L = span (m), H = horizontal tension (N). For exact results use the catenary: sag = (H/w) × (cosh(wL / (2H)) − 1). The parabolic formula is accurate to within ~1% when sag/span < 10%. Both cable length and sag are shown.
Foirmle
How this is calculated
When a flexible cable hangs under its own weight between two level supports, it forms a catenary curve — the exact shape of a chain hanging freely under gravity. For engineering and utility-line work, two formulas are commonly used: the catenary (exact) and the parabolic approximation.
The parabolic approximation treats the cable load as uniformly distributed horizontally (rather than along the cable arc) and gives sag = w × L² / (8H), where w is the weight per unit length in N/m, L is the horizontal span in metres, and H is the horizontal tension at the lowest point in N. This formula is accurate to within about 1% when the sag-to-span ratio is less than 10%, covering most practical overhead cable and power-line installations. The approximate cable length adds the correction term L × (1 + 8s²/(3L²)).
The exact catenary formula uses the catenary parameter a = H/w (the ratio of horizontal tension to unit weight). The sag becomes a × (cosh(L / (2a)) − 1) and the true cable length is 2a × sinh(L / (2a)). When sag/span exceeds 10%, the parabolic values diverge noticeably from the catenary results and the exact formula should be used. Both assumes the supports are at equal height; sloped spans require additional geometry.
Ceisteanna coitianta
When the sag-to-span ratio exceeds about 10%, the parabolic approximation introduces noticeable error. For typical power lines (sag ≈ 2–5% of span) the parabola is fine; for highly loaded or long spans, use the catenary. This calculator shows both.
a = H/w is the horizontal tension divided by the unit weight. Geometrically, a is the distance from the lowest point of the catenary to its directrix. A larger a (high tension relative to weight) means a shallower, tighter cable; a smaller a means more sag.
Higher temperatures cause thermal expansion, increasing cable length and thus sag. Overhead power lines are engineered with ground clearance that accounts for maximum operating temperature. This calculator uses your entered tension — you must account for temperature-dependent elongation separately.
TG we-Calculate Editorial Team. (2026). Sag Calculator — Cable & Wire Sag Between Two Poles [Online calculator]. TG we-Calculate. https://we-calculate.com/ga/calculator/sag-calculator
TG we-Calculate Editorial Team. "Sag Calculator — Cable & Wire Sag Between Two Poles." TG we-Calculate. 2026. https://we-calculate.com/ga/calculator/sag-calculator.
TG we-Calculate Editorial Team, "Sag Calculator — Cable & Wire Sag Between Two Poles," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/ga/calculator/sag-calculator
@misc{wecalculate_sag_calculator, title = {Sag Calculator — Cable & Wire Sag Between Two Poles}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/ga/calculator/sag-calculator}}, year = {2026}, note = {TG we-Calculate} }
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