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Online Calculator: Catenary


Catenary calculations only apply to chains and cables that have infinite axial stiffness and negligible bending stiffness.
Refer to the technical help page for the downloadable version of this calculator for additional assistance.

catenary configuration

Enter known properties:

Input Property: Input Data Output Property Output Data
weight per unit length (w): horizontal tension (Tx):
total length (L): vertical tension at anchor (Ty1):
tension at free end (T₂): vertical tension at free end (Ty2):
angle of tension at free end (θ₂): angle of tension at anchor (θ₁):
tension at anchor (T₁):
horizontal distance to free end (x):
vertical distance to free end (y):


This Catenary calculator is accessible from anywhere in the website using the shortcut key; "Alt" + "y".

The vertical tension (Ty) in either end of a catenary is the weight of the cable (or chain) supported by that end.
If the vertical tension at either end is negative, the end concerned is pulling down, i.e. the catenary is tight; there is no loop.
If you want to create a tight loop, you can either enter a negative value for T2, or enter a positive value for 'T2' that generates a vertical tension (Ty2) greater than the total weight of the cable (Ty2 > w.L)

Axial stiffness

Axial stiffness is the amount of growth in a cable due to axial tension. True catenaries only occur in cables with infinitely high axial tension, such as in a chain.
This is because the weight per unit length of a cable that stretches under tension will vary along its length in a catenary, invalidating the calculation formula.

In practice, if a cable stretches less than 1% over its entire length, whilst inaccurate, the catenary calculation remains valid.

Bending stiffness

Bending stiffness will prevent a true catenary from occurring because it influences both horizontal tension and local bend radii; whilst the vertical tensions will be correct, the shape will be incorrect.
Just like axial stiffness, catenary calculations involving cables with low levels of bending stiffness will remain valid.

Downloadable Version

Full downloadable versions of this calculator is available from this website at; Catenary.

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