The rule
Between low and high water (or high and low), the tide doesn't rise or fall at a steady rate. It starts slowly, moves fastest in the middle, and slows again at the end. The rule of twelfths splits the range, the difference between high and low water, into twelve equal parts, and says that in each of the six hours the tide moves:
1 · 2 · 3 · 3 · 2 · 1 twelfths
So after one hour, 1 twelfth of the range has gone; after two hours, 3 twelfths; after three hours, 6 twelfths, which is half. That's why the height at half tide is roughly halfway between high and low water.
A worked example
Low water is 1.2m and the next high water is 5.4m, about six hours later. The range is 5.4 − 1.2 = 4.2m, so one twelfth is 4.2 ÷ 12 = 0.35m.
| Time after low water | Rise this hour | Total risen | Height of tide |
|---|---|---|---|
| 1 hour | 1/12 = 0.35m | 1/12 | 1.55m |
| 2 hours | 2/12 = 0.70m | 3/12 | 2.25m |
| 3 hours | 3/12 = 1.05m | 6/12 | 3.30m |
| 4 hours | 3/12 = 1.05m | 9/12 | 4.35m |
| 5 hours | 2/12 = 0.70m | 11/12 | 5.05m |
| 6 hours | 1/12 = 0.35m | 12/12 | 5.40m |
Three hours after low water, the height is 1.2 + 2.1 = 3.3m. Add that to the charted depth for the depth of water, and take off your draught for the clearance under your keel.
Using it in reverse
It also answers “when will there be enough water?”. Suppose you need 2.8m of tide to cross a bar on the rising tide. That's 1.6m above low water, or 1.6 ÷ 0.35 ≈ 4.6 twelfths. After two hours you have 3 twelfths and after three hours 6, so the answer falls in the third hour: about two and a half hours after low water. Leave yourself a margin rather than cutting it fine.
When not to trust it
- It assumes a symmetrical tide with about six hours between high and low water. Many ports are close enough; some aren't.
- Distorted tides: where the tidal curve is lopsided or has a double high water or a long stand, the rule can be badly wrong. The Solent and the coast between Swanage and Selsey are the classic UK examples: use the port's tidal curve or tide tables instead.
- It's an estimate, not a prediction. For exam answers and real decisions in tight water, work it properly from the tidal curve. The standard port tidal height guide shows how.