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A simple ‘rule of thumb’ for estimating tidal height: the rule of twelfths

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What is the issue?
Tide is a vertical movement of water, around the north eastern European coast. This happens twice in approximately 25 hours (called semi-diurnal tides). During this period two low waters and two high waters occur. In other parts of the world diurnal tides occur where there is only one low water and one high water each day.

The times and heights of high and low water for standard ports can be found by reference to the appropriate tide tables. Differences based on these standard ports are given for other places utilising tidal curves for specific harbours. By utilising this information sailors may precisely plot the tide depth and timing that enables depth restricted vessels to pass into shallow waters supported by tidal water.

However plotting tide to this level of detail is an onerous and time consuming task. It is really the world of merchant sailors and tidal curves would only be available for major ports where most leisure vessels would have ample water. In the real world few sailors would go to this level of detail.

Why address this?
Having a good understanding of tidal depth and pattern is important when navigating or anchoring a vessel in waters with limited deapth. For instance where you are anchoring you need to know what the current state of the tide is should you come back to find the boat high and dry. Or you may need the additional height of the tide to get into an anchorage or harbour or over a sand bar you may need to know the water that is available to you at any time. It is also important when launching and retrieving boats on slipways on a tidal shore. Having a simple feel for tidal depth is key to successful costal cruising.

How to address this?
Used the simplified ‘Rule of Twelfths’ as a rule of thumb for estimating the tidal height. It is an easy way to approximate the amount of water available at any time. All that is required to operate the rule of thumb is the time of the tide, or the time that may be referenced as a difference from a standard port, plus the tidal range - the height of high and low water.

The rule states that in the first hour after low tide the water level will rise by one twelfth of the range, in the second hour two twelfths, and so on according to the sequence:

Hour Proportion of Tidal Range
1st 1/12
2nd 2/12
3rd 3/12
4th 3/12
5th 2/12
6th 1/12

The rule of twelfths is based on the assumption that the tide does not rise or fall at a constant rate throughout its duration. It also assumes the curve for any particular port is symmetrical.

Example calculation

Lets work an example to make this real. If a tide table states that tomorrow's low water is noon and that the water level at this time would be two metres above chart datum and further, that at the following high tide the water level would be 14 metres. We could work out the height of water at 3:00 p.m. as follows:

(i) The total increase in water level between low and high tide would be: 14 - 2 = 12 metres.

(ii) In the first hour the water level would rise by 1 twelfth of the total (12 m) or: 1 metre.

(iii) In the second hour the water level would rise by 2 twelfths of the total (12 m) or: 2 metres.

(iv) In the third hour the water level would rise by 3 twelfths of the total (12 m) or: 3 metres.

This gives us the increase in the water level by 3:00 p.m. as 6 metres. This represents only the increase - the total depth of the water (relative to chart datum) will include the 2 m depth at low tide: 6 m + 2 m = 8 metres.


Please be aware of the rules’ limitations.

Generally the ‘Rule of Twelfths’ is an excellent everyday tidal indicator. However the rule assumes that the rate of tidal flow increases smoothly to a maximum halfway, between high and low tide, before smoothly decreasing to zero again and that the interval between low and high tides is approximately six hours. This is not always true for some geographical locations. In places such as in the Solent, or Poole Harbour where there is "double" high water or Weymouth Bay where there is a double low water the rule of the twelfths cannot be used and officially produced tide tables are critical.

With thanks to:
Michael Harpur, Yacht Obsession.

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