The rule of twelfths: how to calculate tide height

What the rule of twelfths is

Most tide charts only list the highs and lows. For anything in between, there’s the rule of twelfths, which rests on one fact: the tide doesn’t rise at a steady rate. It starts slowly, speeds up in the middle and slows again near high tide.

Take the range, the difference in height between low and high tide, divide it into twelve equal parts, and spread them over the six hours of the rise:

Tide hour	Rises that hour	Total so far	Percent
1st	1/12	1/12	8%
2nd	2/12	3/12	25%
3rd	3/12	6/12	50%
4th	3/12	9/12	75%
5th	2/12	11/12	92%
6th	1/12	12/12	100%

A falling tide works the same way, subtracting from high tide. Three ideas let you use it in your head:

• Half the time, half the water. Three tide hours after low tide, the water is halfway up.
• Half the change happens in the two middle hours. That’s when the water rises or falls fastest and when currents run hardest, as we explain in tidal currents.
• Near high and low tide, the water barely moves. The first and last hours each bring only one twelfth.

Why does it work? A regular tide follows the shape of a cosine curve, and twelfths are an easy way to trace it. At hours 2, 3 and 4, the rule and the curve match exactly (25%, 50% and 75%). At hours 1 and 5, they differ by less than 2% of the range, a little over an inch on a 6-foot tide.

A tide “hour” isn’t always an hour

The rule talks about six hours because on a semidiurnal coast, with two highs and two lows a day, the rise from low to high takes about six hours. But it’s rarely exactly six. So the right way to use the rule is to divide the real time between low and high tide into six equal parts. Each part is a tide “hour.” If the rise takes 6 hours and 8 minutes, each tide hour is about 61 minutes. If it takes 5 hours and 30 minutes, each is 55 minutes.

The hydrographic offices of Australia and New Zealand, which publish a similar method based on the cosine curve, say it gives acceptable results when the rise or fall lasts between 5 and 7 hours. Outside that window, the tide no longer has the shape the rule assumes.

A worked example in Boston

Here’s a real day. NOAA’s predictions for Boston on Monday, October 26, 2026, in feet above mean lower low water (MLLW):

Tide	Time	Height
Low	5:29 a.m.	0.1 ft
High	11:37 a.m.	11.2 ft
Low	6:02 p.m.	−0.9 ft

Let’s follow the morning rise:

1. Find the low and high on either side of your time. The 5:29 a.m. low (0.1 ft) and the 11:37 a.m. high (11.2 ft).
2. Work out the range. 11.2 − 0.1 = 11.1 ft. One twelfth is 11.1 ÷ 12, a little over 0.9 ft.
3. Work out the tide hour. From 5:29 to 11:37 is 6 hours and 8 minutes. Divided by six, about 61 minutes.
4. Add the twelfths to the low. Three tide hours later, at 8:33 a.m., you’re 6 twelfths up: 0.1 + 6 × 0.93 = 5.7 ft.

Here’s the full rise, next to NOAA’s official prediction for each time:

Time	Twelfths so far	Rule of twelfths	NOAA prediction
5:29 a.m. (low)	0	0.1 ft	0.1 ft
6:30 a.m.	1	1.0 ft	0.9 ft
7:32 a.m.	3	2.9 ft	3.1 ft
8:33 a.m.	6	5.7 ft	5.8 ft
9:34 a.m.	9	8.4 ft	8.4 ft
10:35 a.m.	11	10.3 ft	10.4 ft
11:37 a.m. (high)	12	11.2 ft	11.2 ft

The rule never misses by more than 0.2 feet, a couple of inches. Notice the pace, too: between 7:32 and 9:34 a.m., the water climbs more than 5 feet.

What about a time in between? Within each tide hour, split the difference in a straight line. At 8:00 a.m. you’re 28 of the 61 minutes into the third hour, a bit under halfway. That hour adds 3 twelfths, about 2.8 ft, so take the 7:32 height (2.9 ft) and add a bit under half of that: about 4.2 ft. NOAA’s curve says 4.3 ft. You can see today’s tides for this harbor on the Boston tide page.

Can I cross the bar? Draft, charted depth and chart datum

The most useful job for the rule is working out when there will be enough water to cross a bar, a shoal or a creek mouth. On a nautical chart, the charted depth is the depth of the bottom below chart datum, which in the US is mean lower low water (MLLW). Tide heights are measured up from that same zero. So:

water depth = charted depth + tide height

What you need is your draft plus a safety margin under the keel. We cover chart datum in detail in chart datum and MLLW.

Let’s use the Boston day. A bar is charted at 1 foot. Your boat draws 2.5 feet and you want a foot of water under it, so you need 3.5 feet of water. The tide must be at least 2.5 feet (3.5 − 1).

• Going out on the rising tide: at 6:30 a.m. the tide is at 1.0 ft, and the second tide hour adds about 1.9 ft. You need 1.5 ft more, about four-fifths of that hour, so the tide passes 2.5 ft at about 7:20 a.m. NOAA’s curve says 7:16.
• Coming back on the falling tide: after the 11:37 a.m. high, the tide falls 12.1 ft to the 6:02 p.m. low, with tide hours of about 64 minutes. The rule gives 5.2 ft at 2:50 p.m. and 2.2 ft at 3:54 p.m., so the tide drops below 2.5 ft at about 3:47 p.m. NOAA’s curve says 3:54.

That gives you a window from roughly 7:30 a.m. to 3:30 p.m., with a few minutes of margin at each end. Three warnings:

• Minus tides mean less water than charted. At the 6:02 p.m. low of −0.9 ft, that 1-foot bar would have about an inch of water over it.
• If the bar dries at low tide, the chart shows its height above datum as an underlined figure. Then you subtract: water depth = tide height − drying height.
• Weather and waves count. Strong high pressure or an offshore wind can leave the water several inches below the prediction, and in a swell your boat drops into each trough. Leave a much bigger margin, or don’t cross.

Shortcuts and variations: quarters and the cosine curve

A few variations say the same thing in different ways:

• The rule of quarters. In the first two hours, the tide rises a quarter of the range; in the third, another quarter; in the fourth, another; and in the last two, the final quarter. It’s simply the rule of twelfths grouped, since 1 + 2 = 3 twelfths make a quarter.
• The one-quarter, one-tenth rule, used in the US to sketch the day’s tide curve by hand. Join the low and high with a straight line split into four parts. At the halfway point, the curve crosses the line. At the quarter point next to high tide, it sits one-tenth of the range above the line; at the quarter point next to low tide, one-tenth below.
• The cosine formula. This is the method published by the hydrographic offices of Australia and New Zealand, developed from the one in the British ADMIRALTY Tide Tables. If f is the fraction of time elapsed since low tide (from 0 to 1): height = low + range × (1 − cos(180° × f)) ÷ 2. At 8:00 a.m. in Boston, f = 151 ÷ 368 = 0.41, which gives 4.1 ft, a tenth of a foot below the rule.

All three assume the same thing: a tide with a smooth, regular curve. So they fail in the same places.

When the rule of twelfths fails

The rule works well on coasts with regular, twice-daily tides: most of the US East Coast, Atlantic Canada and Europe’s Atlantic coast. It fails in four situations.

Mixed and diurnal tides

On the West Coast, tides are mixed: the two highs and lows of the day are very different, and a rise can last 7 or 8 hours. In Seattle on October 30, 2026, NOAA predicts the tide will climb from −2.7 ft at 2:05 a.m. to 11.8 ft at 9:41 a.m., which takes 7 hours and 36 minutes. At 5:53 a.m., the rule gives 4.6 ft while NOAA’s prediction gives 5.6 ft, a full foot more. Check any day’s curve on the Seattle tide page. In much of the Gulf of Mexico, there’s one high and one low a day, so a rise takes 12 hours or more and the range is often just a foot or two. See our guide to types of tides.

The Solent and double high water

The classic failure is the Solent, the strait between England’s south coast and the Isle of Wight. According to the Port of Southampton’s vessel traffic service, the flood and the double high water there last about nine hours, while the ebb takes only about three and a half. Especially on spring tides, around two hours after low tide, the rise also slows sharply for about two hours before the final push to high water.

With a curve like that, the rule is useless. In Southampton on October 26, 2026, the tide rises from 2.1 ft at 4:14 a.m. to 15.4 ft at 10:52 a.m. At 8:39 a.m., the rule says 12.1 ft but the harmonic calculation says 9.9 ft: 2.2 feet too high, and in the dangerous direction, because it promises more water than there is.

Tidal rivers and estuaries

When the tide moves up a shallow estuary, the crest of the wave travels faster than the trough and the curve gets lopsided. According to SHOM, France’s hydrographic office, the rise then becomes faster than the fall: even at Brest the difference is 16 minutes, and in estuaries it’s much larger. In extreme cases, the tide arrives as a wave, a tidal bore. The farther up a river or creek you go, the less you can trust the rule.

Places with tiny tides

Where the tide is only a foot or two, weather can move the water more than the tide does: a front, a few days of wind or a change in air pressure. The rule still gives you a number, but that number doesn’t tell you much. We explain why in why some seas have almost no tide.

The tide height calculator: what it actually does

If you’d rather skip the math, the tide height calculator does it for you, and not only with the rule:

• You pick the place, the day and the time, in local time, with daylight saving time included.
• The height comes from a harmonic calculation: the sum of dozens of tidal waves measured for years at the nearest tide station, the same method NOAA uses for its official predictions. Next to it, you’ll see what the rule of twelfths would give.
• It tells you whether the tide is rising or falling and how long until the next high and low, with the day’s tide curve.
• It includes an hour-by-hour table with the rule and the harmonic calculation side by side, so you can see whether the rule works at your harbor.
• Heights are above the local chart datum: MLLW in the US and the lowest astronomical tide in much of Europe. Where there’s no station nearby, it uses a global model, which is more approximate, and measures from mean sea level.

It’s an astronomical prediction for fishing and recreation that doesn’t include the weather. For navigation, always use official publications and leave a safety margin. To brush up on reading the highs and lows themselves, see how to read a tide chart.