From high water the tide falls 1, 2, 3, 3, 2 then 1 twelfth of its range in each sixth of the time. Never more than 2.6% of the range away from the truth — but only if the fall really does take six equal hours.
It is a hand approximation to a sinusoid, and a startlingly good one. At two, three and four hours after high water the twelfths give 25%, 50% and 75% of the range, which are the sinusoid’s own values exactly. The only disagreement is in the first and last hours — the rule says an eighth of a twelfth too much, 8.3% against 6.7% — and the worst gap anywhere in the tide is 2.6% of the range. On a 12 m Bristol Channel spring that is about 30 cm; on a 2 m neap it is 5 cm. The error people actually meet is not in the twelfths at all: it is in assuming six hours. A semidiurnal tide takes 6h 12m, half the 12h 25m lunar day, and in many estuaries flood and ebb are markedly unequal. Read a five-hour ebb as six and at the three-hour mark you are out by 15% of the range — six times the rule’s own worst error.
Anywhere the tidal curve is not a sine wave. Southampton and Poole have a double high water and a long stand; parts of the Bristol Channel flood much faster than they ebb. In those ports the published tidal curve is the only thing that works. And none of this includes weather: about 1 cm of sea level per millibar away from 1013, so a deep depression raises the water further than the rule is ever wrong by.
Estimate with the rule, then check it against the calculator that models it properly.
Open Tide Curve & Rule of Twelfths →