Catenary Curve Calculator

Your details

Horizontal distance between the two support points at equal height.
m
Vertical drop from the support level down to the lowest point of the cable.
m
Linear weight of the cable. Leave at zero to skip tension outputs.
N/m
Arc length (cable length)
20.5237

True length of the cable from support to support along the curve

Catenary parameter (a)25.3265
Midpoint sag (d)2
Slope angle at support22.06deg
Horizontal tension (H)25.33
Maximum tension (at support)27.33
Tension unitN
Length unitm
Sag2
Arc Length20.5237

Moderate catenary: cable is 20.524 m with 2.000 m sag.

  • The cable is 20.524 m long but spans only 20 m horizontally, requiring 2.62% extra cable to account for the sag.
  • The sag-to-span ratio is 10.0%. Engineering standards for overhead power lines typically keep sag at 2-5% of span; suspension cables for footbridges often run 5-15%.
  • The cable leaves each support at an angle of 22.1 degrees from horizontal, which is the angle the support structure must resist.
  • With a cable weight of 1 N/m, horizontal tension is 25.3 N and maximum tension at the supports is 27.3 N (a 7.9% increase due to the vertical load component).

Next stepUse the maximum tension to size cable cross-section and anchor capacity. Add a safety factor of at least 3 for structural applications.

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