What a Knot Costs: Residual Strength of the Knots People Actually Tie

A widely repeated rule of thumb holds that a knot halves the strength of a rope, implying a retained efficiency of 0.50 for every knot. This paper tests that flat claim against stated efficiency ranges for the knots people actually tie when raising water and lifting loads: the figure-eight loop, the bowline, the clove hitch, the sheet bend, the overhand knot, and the timber hitch. Midpoint efficiencies range from 0.775 for the figure-eight loop, a loss of 22.5%, down to 0.475 for the overhand knot, a loss of 52.5% — a spread of 30.0 percentage points and a best-to-worst ratio of 1.632. On a 12 mm nylon rope with a stated unknotted breaking strength of 27.0 kN, the figure-eight loop leaves a residual breaking load of 20.925 kN, or 2133.0 kg, which is 7.425 kN above the 13.5 kN predicted by the flat claim, while the overhand knot leaves 12.825 kN, which is 0.675 kN below the flat prediction. The flat claim therefore understates the strongest common knot by 35.5% and overstates the weakest by 5.3%. It does not survive as a general statement: the cost of a knot depends on which knot it is, and the paper closes with a selection rule that puts the figure-eight loop first when strength matters most, reserves joining and hitching knots for their proper functions, and excludes the overhand knot from load-bearing use where a better knot can be tied.