Anyone sailing the North Sea or Baltic can’t avoid the tides. In the Wadden Sea in particular, the right timing decides whether there’s still enough water under the keel. The rule of twelfths makes it easy to estimate the water level between high and low water – without complicated tables. Here’s how it works.
The basic terms
Before we start calculating, let’s clarify the key terms:
- High water (HW): the highest water level of a tide.
- Low water (LW): the lowest water level of a tide.
- Tidal range: the height difference between high and low water (tidal range = HW height − LW height).
- Chart datum (CD): the reference level the depth figures on the nautical chart relate to. The tidal height is added to it to get the actual water depth.
On most German coasts there are two high waters and two low waters per day. There are roughly six hours between one high water and the following low water.
The rule of twelfths
The idea behind it: the water doesn’t rise (or fall) evenly. It moves fastest in the middle of the tide and slowest at the “turning points” at high and low water. The rule of twelfths captures this in simple fractions.
You mentally divide the tidal range into twelve equal parts. During the six hours between low and high water, the level changes per hour by:
| Hour | Change | Share of tidal range |
|---|---|---|
| 1st hour | 1 twelfth | 1/12 |
| 2nd hour | 2 twelfths | 2/12 |
| 3rd hour | 3 twelfths | 3/12 |
| 4th hour | 3 twelfths | 3/12 |
| 5th hour | 2 twelfths | 2/12 |
| 6th hour | 1 twelfth | 1/12 |
So the sequence to remember is 1 – 2 – 3 – 3 – 2 – 1. Added together, these shares come to exactly 12 twelfths – the full tidal range. The same sequence applies when the water falls – the amounts are simply subtracted instead.
Worked example
Let’s assume:
- Low water at 08:00 with a height of 1.0 m
- High water at 14:00 with a height of 4.0 m
The tidal range is 4.0 m − 1.0 m = 3.0 m. One twelfth of that is 3.0 m ÷ 12 = 0.25 m.
Question: How high is the water at 11:00, i.e. three hours after low water?
In the first three hours the water rises by 1 + 2 + 3 = 6 twelfths, i.e. half the tidal range:
6 × 0.25 m = 1.5 m
You add this rise to the low water height:
1.0 m + 1.5 m = 2.5 m
So at 11:00 the water stands about 2.5 m above chart datum.
How much water is under the keel?
In practice what counts is the actual water depth at a given spot. It’s the charted depth (relative to chart datum) plus the current tidal height. Subtract your boat’s draft from that, and you get the water under the keel:
Water depth = charted depth + tidal height − draft
Always build in a safety margin – wind and air pressure can make the real water level deviate from the forecast.
How accurate is the rule of twelfths?
The rule of twelfths is an approximation. It assumes a smooth, sine-like tidal curve and roughly six hours between the turning points. The deviation from the ideal curve stays small – usually under 2.5% of the tidal range. For passage planning and the SBF Coastal exam, this accuracy is perfectly sufficient. In areas with irregular tidal patterns (e.g. double high waters), however, the rule reaches its limits.
How to prepare
Tide questions appear in the theory part of the SBF Coastal and are closely linked to the navigation task. Anyone who has a confident grasp of the rule of twelfths and the terms around tidal range and chart datum can reliably collect points here. In the Boatpass app you can practice the relevant questions separately from the rest of the catalog.
Conclusion
The rule of twelfths makes tidal calculation surprisingly simple: divide the tidal range by twelve, apply the sequence 1 – 2 – 3 – 3 – 2 – 1, and add the result to the low water height (or subtract it when the water is falling). Together with the formula for the water under the keel, you have a practical tool – on board as well as in the exam.