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Catenary Height and Arc Length

Online catenary height and arc length. Symmetric ideal catenary with minimum height set to zero.

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catenary height and arc length calculator online

Use catenary height and arc length online for scale, half span. Symmetric ideal catenary with minimum height set to zero. Finite floating-point calculation with the displayed domain; large integer counts can lose exact precision.

How to use it

Enter scale. Set half span. Select Calculate and check the labeled output. Copy or download the JSON result.

Options and example settings

OptionChoices / valueExample default
scaleMain input. Positive values. 2
half spanOption. Zero or positive values. 3

Calculation method

rise = scale*(cosh(half_span/scale)-1); arc_length = 2*scale*sinh(half_span/scale) (^ means exponentiation; trig functions ending in d use degrees).

Worked examples

Apply catenary height and arc length to the case below, keeping the displayed units and assumptions. Symmetric ideal catenary with minimum height set to zero.

Catenary Height and Arc Length — worked case

Settings: half span: 3

Input:

2

Calculated result for these inputs:

Output:

{
  "rise": 2.7048192304864944,
  "arc_length": 8.51711782037927
}

Choose the right tool

Choose number theory for exact integer relationships, distribution tools for a declared random model, and geometry tools for coordinates. A density is not a probability and a statistical model does not establish a real-world outcome.

Limitations and common mistakes

  • Symmetric ideal catenary with minimum height set to zero. Finite floating-point calculation with the displayed domain; large integer counts can lose exact precision.
  • Use the displayed unit in every field. Ratios and percentages are different inputs; percent fields use values such as 25 rather than 0.25.

Frequently asked questions

How can I use catenary height and arc length calculator online?

Enter scale. Set half span. Select Calculate and check the labeled output. Copy or download the JSON result.

Where is my input processed?

The bundled tool processes input in your browser. It does not upload tool input to a conversion service. Other site plugins, analytics, advertising and browser extensions may have separate behavior.

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