Environmental · the sea

Tide Curve & Rule of Twelfths

The height of tide at any hour, the window you can cross in — and an honest look at how good the rule of twelfths really is.
1·2·3·3·2·1
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This tide

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Can I get over it

Typical ranges

nominal
Nominal mean ranges, for scale and for seeing how wildly ports differ — not a tide table. Choosing one keeps the mean level and sets the range for springs, neaps or between. Take the actual heights and times for your date from an almanac or a tidal app and type them in above.

Height of tide

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—height of tide at the chosen time

Hour by hour

1 · 2 · 3 · 3 · 2 · 1
How it works

Better than its reputation, if the duration is right

One, two, three, three, two, one

The tide moves that many twelfths of its range in six equal slices of the fall, and the same again on the rise.

Out by, back from

Your boat needs a height of tide. The fall takes it away and the rise brings it back, so there are two times to know, not one.

Springs and neaps move both ends

Around the same mean level, neaps bring high water down and low water up. Dover goes from 6.8 and 0.8 m to 5.4 and 2.2 m here.

The duration is what bites

Assume six hours where the fall takes five, and three hours in the rule says 50% has gone when 65% has.

Field notes

Reading water

2.6%of the range

The rule’s worst error

At 2, 3 and 4 hours it is exact: 25%, 50% and 75%. The worst error is inside the first and last hours.

20 cmon a 12 m range

At the end of the first hour

The rule says 8.3% where the curve says 6.7%. On a 2 m neap that same gap is 3 cm.

24 h 50 min

Why the tide is later each day

Half a tidal cycle is 6 h 12 m, not six hours, and the whole pattern slides about 50 minutes later every day.

14½ days

Nothing to do with the season

Springs come when the Sun and Moon pull in line, at new and full moon. Neaps come at the quarters.

1 mb = 1 cm

A low lifts the water

Roughly 1 cm per millibar away from 1013. A 980 mb depression adds about 33 cm, and that is not in your tide table.

LATchart datum

Charts show the worst case

Depths are measured from about the lowest astronomical tide, so the height of tide is almost always something you add.

Questions

What people ask

Which ports break the rule worst?

The ones whose curve is not a sine wave at all. Southampton and the Solent have a double high water and a long stand, Poole is similar, and parts of the Bristol Channel have a much faster flood than ebb. There a published tidal curve for the port is the only thing that works.

Why 6 hours 12 minutes rather than 6?

Because the tide follows the Moon, not the Sun. The Moon returns to the same meridian every 24 hours 50 minutes, so a semidiurnal cycle is 12h 25m and each half is 6h 12m. That is why tides run about 50 minutes later each day.

Why are the fall and the rise separate controls?

Because they often differ. In many estuaries the shape of the seabed distorts the wave as it runs in, so the flood is shorter than the ebb. Set each to what your almanac gives.

Are neaps better or worse for a shallow spot?

It depends where the height you need sits. Neaps raise low water, so a spot that shuts for an hour or two at springs can stay open all tide. They also lower high water, so a bar you can only cross near the top of a spring tide can stay shut.

What is the height measured from?

Chart datum, approximately the lowest astronomical tide. That is why charted depths look alarmingly shallow: they are the worst case, and the height of tide is what you add. A negative height of tide is possible and rare.

What this page assumes

That the tide is semidiurnal: one smooth fall and one smooth rise, with the next high water the same height as this one. Both curves are approximations to a real tide, which is the sum of dozens of harmonic constituents.

That the numbers you type are right. This page does no astronomy and has no tide table in it, so garbage in is garbage out, and at sea that has consequences.

That the weather is doing nothing. Pressure and wind move real tides by more than the rule’s own error, and surge is not in this page or in your tide table.

Port ranges are nominal typical figures for scale, and the neap heights come from holding the mean level still, not from a tidal prediction. Verified in tide_model.py.

Version history · 2 releases
  1. v6.492026-10-03Tide Curve: the clearance window from the earlier of the rule and the true curve - on the defaults the rule was 16 minutes optimistic
  2. v6.512026-10-03Homepage ask bar leads with the tool; the guitar tuner number no longer flickers every frame

Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.

Not for navigation. This draws a curve between the two numbers you give it; it contains no tide table, no harmonic constituents and no weather. Port ranges are nominal figures for scale only. Use an official almanac or tidal prediction for the actual heights and times, keep a real safety margin, and remember that pressure and wind routinely move the sea further than any error in the arithmetic. See Sources.

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