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Catenary Curve Height — result sheet
Evaluate the height of the canonical symmetric catenary y = a cosh(x/a) at a selected horizontal coordinate.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: y = a cosh(x/a) = a (exp(x/a) + exp(-x/a))/2.
The canonical catenary is symmetric about x = 0. Enter a positive parameter and horizontal coordinate to obtain its y-height in the same length unit.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Catenary parameter a — length units; Positive scale parameter controlling the curve and its lowest height.; minimum 0.1; maximum 1000000
- Horizontal coordinate x — length units; Horizontal position measured from the catenary's lowest point.; minimum -20; maximum 20
Worked example
| Input | Value |
|---|---|
| Catenary parameter a | 2 |
| Horizontal coordinate x | 3 |
The argument is 3/2 and y = 2 cosh(1.5), approximately 4.70482 length units.
Assumptions and limits
- The curve uses the centered canonical form y = a cosh(x/a), with its lowest point at (0,a).
- The parameter a and coordinate x use compatible length units, and the curve is evaluated without a vertical offset or tilt.
- This is an ideal mathematical catenary evaluation, not a tension, load, cable, or structural design calculation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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