Sag (Sagitta) Calculator
Construction & Home ImprovementCalculate the sag, or sagitta, of a curved cable, arch, or beam from its radius of curvature and chord length.
Sag (Sagitta)
Distance between the midpoint of the arc and the midpoint of the straight chord.
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Construction & Home Improvement calculators
Frequently Asked Questions
What is sagitta?
Sagitta, or sag, is the distance between the midpoint of a curved arc and the midpoint of the straight chord connecting its two endpoints. It is a common measurement in suspension cable design, arched beams, optics, and dome construction.
What happens if the chord length is close to the diameter?
As the chord length approaches twice the radius, the arc approaches a full half circle and the sag approaches the radius itself. If the chord length exceeds twice the radius, the geometry is not possible and the result is not valid.
Can this be used for a suspended cable rather than a rigid arc?
This formula gives the geometric sag of a true circular arc. A hanging cable under its own weight actually forms a catenary curve, close to but not identical to a circular arc for small sag-to-span ratios, so this is a good approximation for shallow sags.
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