Catenary Curve Calculator

Find the height and arc length of a hanging catenary y = a·cosh(x/a).

Height y 5.927

Arc length from centre 3.183

Formula: y = a·cosh(x/a); arc = a·sinh(x/a)

Step-by-step with your numbers:

1. Values used:

2. Catenary parameter a = 5

3. Horizontal distance x = 3

5. Height y = 5.927

6. Arc length from centre = 3.183

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A catenary is the curve a chain or cable forms under its own weight.

The math behind it

The shape is y = a·cosh(x/a), where a depends on tension and weight. The arc length from the lowest point to x is a·sinh(x/a).

With a = 5, at x = 3 the height is 5·cosh(0.6) ≈ 5.92.

Is a catenary a parabola?

No — they look similar but a catenary uses the hyperbolic cosine, not a quadratic.