Equal Height Cable Catenary Calculator
Solve an ideal self-weight hanging cable from horizontal span and arc length, then report sag and load components.
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Result
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Calculation steps
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How to calculate
Solve the dimensionless catenary length/span equation by bracketing. Recover the catenary parameter, sag and support forces for uniform self-weight per cable length.
L/S=sinh(u)/u; a=S/(2u); sag=2a sinh²(u/2); H=wa; V=wL/2
Worked example
For span 2 m and cable length 2sinh(1)≈2.350402387 m, u=1 and a=1 m. Sag=cosh(1)−1≈0.543080635 m; at w=1 N/m, horizontal tension is 1 N.
Assumptions and input details
Equal-height fixed supports, flexible inextensible cable, uniform self-weight and no additional loads. Length/span must exceed 1.00000001 and be at most 100; an exactly taut cable has no finite self-weight tension here. Excludes elasticity, wind, temperature, point loads, fittings and allowable-tension checks. The profile uses independent display axis scales.
References: CERN: catenary wire length and sag analysis
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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