Free guide Tides
The rule of twelfths
The rule of twelfths says that in the six hours from low water to high water the tide rises by 1, 2, 3, 3, 2 and 1 twelfths of its range, hour by hour: slowly at first, fastest in the middle two hours, slowly again near high water. Add the twelfths to the low-water height and you have a rough height of tide for any hour. It is an approximation, and it fails where the tide is irregular.
The rule
Take the range, the high-water height minus the low-water height, and divide it into twelve. Over the six hours of the rise:
- hour 1: 1/12 of the range
- hour 2: 2/12
- hours 3 and 4: 3/12 each
- hour 5: 2/12
- hour 6: 1/12
So half the range (1 + 2 + 3 = 6 twelfths) comes in during the first three hours, and a quarter of it in the third hour alone. The rule assumes a regular rise of about six hours with a smooth, sine-shaped curve.
A worked example
Port Kerran is a fictional practice port. Today the tide table gives low water at 0600, 0.6 m, and high water at 1200, 4.8 m. Heights are above chart datum, the level the chart's depths are measured from.
Range = 4.8 − 0.6 = 4.2 m. One twelfth = 4.2 ÷ 12 = 0.35 m.
| Time | Twelfths this hour | Rise | Height of tide |
|---|---|---|---|
| 0600 | LW | – | 0.60 m |
| 0700 | 1 | 0.35 m | 0.95 m |
| 0800 | 2 | 0.70 m | 1.65 m |
| 0900 | 3 | 1.05 m | 2.70 m |
| 1000 | 3 | 1.05 m | 3.75 m |
| 1100 | 2 | 0.70 m | 4.45 m |
| 1200 | 1 | 0.35 m | 4.80 m (HW) |
At 0800, two hours after low water, the tide has risen 1 + 2 = 3 twelfths, 1.05 m, so the height of tide is 0.6 + 1.05 = 1.65 m.
From height of tide to depth
The height of tide on its own is not the depth. Add it to the charted depth: depth = charted depth + height of tide. Over a patch that dries (an underlined figure on the chart), depth = height of tide − drying height. Then subtract your draught for the clearance under the keel, and keep at least 1 m, more in waves or swell.
Say the Port Kerran harbour bar is charted at 1.2 m. A boat needs draught + 1 m − 1.2 m of tide to cross it with a metre to spare.
A Lagoon 42 draws 1.25 m, so it needs 1.25 + 1 − 1.2 = 1.05 m of tide: from about 0800 by twelfths. A Beneteau Oceanis 40.1 draws 2.17 m and needs 1.97 m: from about 0900. Same method, different answer.
Where the rule lets you down
The rule is a rough approximation. It assumes about six hours from low to high water and a regular curve, and many places don't oblige. Where there are double high or low waters, as in the Solent, Poole Harbour and Weymouth Bay, it gives the wrong answer. For a standard port, the tide tables and the port's own tidal curve give a better figure: work out the range, draw a line from the low-water height to the high-water height, and read the height off the curve for your time.
Check your tides in the taster exam
Ten questions from across the Day Skipper theory syllabus, marked on our server, no account needed. Module 01 is free as well.
The full lesson, with chart datum, springs and neaps, and the tidal curve method step by step, is Module 09: Tides, heights & the rule of twelfths. Secondary ports follow in Module 10.
All 18 modules for £12 a month
A plan opens every module with its narrated film and quiz, the 50-question mock exam marked by module, and the berthing and anchoring games. £12 a month or £79 a year. Sail Academy is exam preparation: it is not affiliated with the RYA and does not issue an RYA certificate.
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