Height of the tide between high and low water
| Time | Rule of twelfths | Sine curve |
|---|---|---|
| 3:21 AM | 0.9 ft | 0.9 ft |
| 4:24 AM | 1.6 ft | 1.5 ft |
| 5:26 AM | 3.1 ft | 3.1 ft |
| 6:29 AM | 5.3 ft | 5.3 ft |
| 7:31 AM | 7.5 ft | 7.5 ft |
| 8:34 AM | 8.9 ft | 9.0 ft |
| 9:36 AM | 9.6 ft | 9.6 ft |
Heights are above chart datum, as in tide tables; use a minus sign for a height below it, such as -0.5. Add a charted depth for the depth of water at that time. The example is NOAA’s prediction for Boston on Oct 23, 2026: low water 0.92 ft at 3:21 AM, high water 9.63 ft at 9:36 AM.
An estimate only: for navigation, use the official tide predictions for your place and date.
The rule of twelfths estimates the height of the tide between a high and a low water: in each sixth of the time from one to the other, the water rises or falls by 1, 2, 3, 3, 2 and 1 twelfths of the range. Enter the times and heights of two tides in a row from a tide table, and the calculator gives the height at the time you want, by the rule and by the sine curve that the U.S. tide tables use for the same job. Both are estimates: for navigation, official tide predictions come first, such as NOAA’s for U.S. waters.
Rule of twelfths: after 1, 2, 3, 4, 5 and 6 sixths of the time, 1, 3, 6, 9, 11 and 12 twelfths of the range · Sine curve: height = first height + (second height − first height) × (1 − cos(180° × t ÷ D)) ÷ 2 · Tidal range = high water − low water · Depth of water = charted depth + height of tide. t is the time since the first tide and D the time between the two.
How to Use the Rule of Twelfths
Take the time and height of a high water and the low water next to it, before or after, from a tide table. Divide the time between them into six equal parts; for a tide with two highs and two lows a day, each is about an hour. Divide the difference in height, the range, into twelve. Over the six parts the tide changes by 1, 2, 3, 3, 2 and 1 twelfths: slowly at first, fastest in the middle and slowly again near the turn. BoatUS Magazine calls the rule an easy guide for semi-diurnal tides, the kind with two nearly identical tidal cycles a day that take about six hours to rise or fall, and its illustration marks 1, 3, 6, 9, 11 and 12 twelfths of the range at the end of each hour. The Wikipedia article on the rule gives an example: low water 2 m at noon and high water 14 m make a range of 12 m, and taking each part as an hour, by 3 p.m. the tide has risen 1 + 2 + 3 = 6 twelfths, or 6 m, to 8 m above chart datum.
The calculator’s example is NOAA’s prediction for Boston on Oct 23, 2026: low water 0.92 ft at 3:21 AM and high water 9.63 ft at 9:36 AM. The rise takes 6 h 15 min, so each sixth lasts 62.5 minutes, and each twelfth of the 8.71 ft range is 0.726 ft. At 7:00 AM, 219 minutes or 3.504 sixths after low water, the tide has risen the 6 twelfths of the first three sixths and 0.504 of the fourth sixth’s 3, 7.51 twelfths in all, so the height is 0.92 + 7.51 × 0.726 = 6.37 ft. Within each sixth, the calculator lets the water rise at a steady rate.
How to Calculate Tidal Range
The range of tide is the difference in height between a high water and the low water before or after it (Bowditch). Take the low water from the high water: 9.63 − 0.92 = 8.71 ft at Boston that morning. When a low water is below chart datum, its height is negative and the range is larger than the high water: a high of 4.0 ft and a low of −0.5 ft make a range of 4.5 ft. The time from low water to high water is the duration of rise, and from high water to low water the duration of fall. Bowditch puts low water about a quarter of a tidal day, roughly 6 h 12 min, before and after high water, and notes that the interval varies from day to day.
The Rule of Twelfths and the Sine Curve
Table 3 of the U.S. tide tables, as Bowditch describes it, finds the approximate height of the tide at any time between high and low water by assuming that the height follows a sine curve, and warns that actual values may vary. The rule of twelfths is a simple approximation of that same curve. At the end of each sixth, the two compare as fractions of the range:
| Sixths | Twelfths | Rule | Sine curve |
|---|---|---|---|
| 1 | 1/12 | 0.083 | 0.067 |
| 2 | 3/12 | 0.250 | 0.250 |
| 3 | 6/12 | 0.500 | 0.500 |
| 4 | 9/12 | 0.750 | 0.750 |
| 5 | 11/12 | 0.917 | 0.933 |
| 6 | 12/12 | 1.000 | 1.000 |
The two agree at two, three and four sixths and differ by 0.016 of the range at one and five sixths. Between the marks, where the rule rises at a steady rate, the difference reaches 0.026 of the range, a quarter of a foot on a 10-foot tide. The calculator shows both.
How Accurate Is the Rule of Twelfths?
Where the tide is regular, close. Against NOAA’s predictions for Boston on the morning of Oct 23, 2026, rounded to 0.01 ft:
| Time | NOAA prediction | Rule of twelfths | Sine curve |
|---|---|---|---|
| 4:00 AM | 1.19 | 1.37 | 1.15 |
| 5:00 AM | 2.42 | 2.49 | 2.33 |
| 6:00 AM | 4.20 | 4.28 | 4.25 |
| 7:00 AM | 6.25 | 6.37 | 6.41 |
| 8:00 AM | 8.21 | 8.13 | 8.30 |
| 9:00 AM | 9.43 | 9.21 | 9.43 |
Over the whole rise, checked every six minutes, the rule stays within 0.22 ft of NOAA’s curve and the sine curve within 0.16 ft. Elsewhere the curve is less regular. At The Battery in New York the same morning, NOAA predicts low water of 0.42 ft at 12:29 AM and high water of 4.95 ft at 6:36 AM; at 3:30 AM it predicts 3.07 ft, while both estimates give 2.64 ft, 0.43 ft too low, about a tenth of the range. Wikipedia’s article on the rule calls it a rough approximation to apply with great caution for navigation, notes that it assumes regular tides, which places such as Poole Harbour and the Solent in England do not have, and that six hours between high and low water is an underestimate that varies; the calculator divides the actual time between your two tides instead. Official tide tables should be used in preference whenever possible. BoatUS adds that the result is approximate and that high winds and storm surges change it, and that in most of the U.S. Gulf Coast states, eastern Mexico and some Caribbean islands the tide is diurnal, with one rise and fall a day, weak currents and little range, while some places have mixed tides with unequal highs and lows.
Weather moves the water too. Bowditch warns that tide predictions may be considerably in error when conditions differ from those assumed: onshore winds raise the level and offshore winds lower it, and the water is lower than predicted when the atmospheric pressure is high. Under a stationary low the sea rises about 1 centimeter for every hectopascal the pressure is below 1010 hPa, which works out to about 33.9 cm, or 13.3 inches, for every inch of mercury. The Barometric Pressure Converter turns a barometer reading into hectopascals.
Depth of Water at a Given Time
Charted depths are measured from chart datum, and the height of tide is added to them: where the chart shows 15 feet and the tide is 3 feet, the depth is 15 + 3 = 18 feet, and with a tide of −1 foot it is 14 feet (Bowditch). Enter the charted depth in the calculator to get the depth of water at the time you want: on the falling tide after the example, from 9.63 ft at 9:36 AM to 0.76 ft at 3:45 PM, a spot charted at 15 ft has about 21.7 ft of water at noon by the rule. Our guide How to Read a Nautical Chart explains chart datum and soundings, and the Anchor Scope Calculator works out how much rode to let out for the rise of the tide.
Frequently Asked Questions
What is the rule of twelfths?
A rule of thumb for the height of the tide between high and low water. Divide the time between them into six parts and the range into twelve: in the six parts the tide rises or falls by 1, 2, 3, 3, 2 and 1 twelfths of the range.
How do you calculate the height of tide at a given time?
Find the high and low water on either side of that time in a tide table, work out the range and the time between them, and count the twelfths up to your time. At Boston on Oct 23, 2026, low water 0.92 ft at 3:21 AM and high water 9.63 ft at 9:36 AM give about 6.4 ft at 7:00 AM.
How do you calculate tidal range?
Take the height of the low water from the height of the high water next to it. For 9.63 ft and 0.92 ft the range is 8.71 ft. A low water below chart datum has a negative height, which adds to the range.
How accurate is the rule of twelfths?
Where the tide is regular, within a few tenths of a foot. At Boston on Oct 23, 2026 it stayed within 0.22 ft of NOAA’s predictions over the morning’s rise, but at The Battery in New York both it and the sine curve were up to 0.44 ft off. Use official predictions for navigation.
Does the rule of twelfths work everywhere?
No. It is a guide for semi-diurnal tides, with two highs and two lows a day about six hours apart (BoatUS). Most of the U.S. Gulf Coast has a diurnal tide, one rise and fall a day with little range, and some places have mixed or irregular tides, such as Poole Harbour and the Solent in England: there, use the official predictions.
How do I find the depth of water at a given time?
Add the height of the tide at that time to the charted depth: with 15 feet charted and a tide of 3 feet there are 18 feet of water, and with a tide of minus 1 foot there are 14 feet. Wind and air pressure can make the real level higher or lower than predicted.
Sources
- NGA, The American Practical Navigator (Bowditch), Vol. I (2019): art. 3525 (charted depth plus height of tide, predictions in error with pressure and wind), art. 3526 (wind and pressure, about 1 cm per hectopascal), art. 3528 (low water about 6 h 12 min from high water, Table 3), art. 3531 (Table 3 and the sine curve) (read Oct 21, 2026).
- NGA, Bowditch, Vol. II (2019), Glossary of Marine Navigation: range of tide; duration of rise and duration of fall (read Oct 21, 2026).
- Mel Neale, The Rule of Twelfths, BoatUS Magazine (October 2016, revised October 2022): a guide for semi-diurnal tides, about six hours of rise or fall, the twelfths hour by hour in its illustration, approximate and changed by high winds and storm surges, diurnal tides on most of the U.S. Gulf Coast (read Oct 21, 2026).
- Wikipedia, Rule of twelfths: the rule, its example and its caveats (read Oct 21, 2026).
- NOAA Tides and Currents, tide predictions for Boston, MA (8443970) and The Battery, NY (8518750), Oct 23, 2026, feet above MLLW, local time: high and low waters and 6-minute predictions (retrieved Oct 21, 2026).