Rule of thumb · EnvironmentalNº 171 / 190

The tide moves in twelfths

How much will the tide have fallen by now?

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.

Why it works

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.

When it fails

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.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

Open Tide Curve & Rule of Twelfths →

More in Environmental

← PreviousWeek 1 is the week holding the first Thursday Next →The framing sets the depth of field, not the lens

Browse all 190 rules of thumb →