Catenary Curve Calculator
Evaluate the ideal catenary y=a cosh(x/a) and its rise above the lowest point.
Formula
y=a(e^(x/a)+e^(−x/a))/2; rise=y−a.
Height y (same unit) ≈ (2)×(exp((1)÷(2))+exp(-(1)÷(2)))÷2 · Rise from minimum (same unit) ≈ (2)×(expm1((1)÷(2))+expm1(-(1)÷(2)))÷2
How to use
- Enter positive scale a.
- Enter x in the same length unit as a.
- Read y and rise in that unit.
Examples
- a=1 and x=0 give y=1 and rise=0.
Frequently asked questions
Where is the lowest point?
At x=0, y=a. The rise there is zero.
What does a represent?
The positive scale parameter of an ideal uniform hanging chain.
Why can extreme inputs fail?
A very large |x/a| exceeds floating-point exponential range. This tool evaluates points, not a plotted curve.
Sources
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