How to Calculate the Height of the Tide: The Rule of Twelfths Explained
A quick, pencil-and-paper way to work out whether there’s enough water under your keel
I’ve just finished the tidal heights part of my RYA Day Skipper course. The proper method involves tidal curves, almanacs and a fair bit of squinting at graphs. But there’s a shortcut you can do in your head, and it’s worth learning first: the Rule of Twelfths.
It’s a rule of thumb for answering one question: how high will the tide be at a given time? And from that, the question that really matters: will I run aground?
Why tide height matters
Charts show depths measured from chart datum, which is roughly the lowest the tide normally goes. So the depth printed on the chart is close to the worst case. Most of the time there’s more water than that, because the tide has come in on top.
The actual depth is:
depth of water = charted depth + height of tide
Some places, like sandbanks and harbour mud, are above chart datum and dry out at low water. The chart shows these as drying heights, with the number underlined. For those:
depth of water = height of tide − drying height
So if you know the height of the tide, you know how much water you’ve got. That’s where the twelfths come in.
The rule
The tide doesn’t rise at a steady rate. It starts slowly, speeds up in the middle, and slows down again as it approaches high water. If you imagine the tide taking about six hours to go from low water to high water, the Rule of Twelfths says it rises by:
| Hour | Rises by | Total risen so far |
|---|---|---|
| 1st | 1/12 | 1/12 |
| 2nd | 2/12 | 3/12 |
| 3rd | 3/12 | 6/12 (half) |
| 4th | 3/12 | 9/12 |
| 5th | 2/12 | 11/12 |
| 6th | 1/12 | 12/12 (full) |
The pattern is 1, 2, 3, 3, 2, 1. It works the same way in reverse as the tide falls.
The thing to notice is the middle two hours. Half the whole rise happens in hours three and four. That’s also when the tidal streams tend to run hardest, which makes sense: a lot of water is moving in a short time.
A worked example
Let’s say the tide tables give us:
- Low water: 08:00, height 1.0 m
- High water: 14:00, height 5.2 m
Step 1: find the range. That’s the difference between high and low water.
5.2 − 1.0 = 4.2 m
Step 2: find one twelfth.
4.2 ÷ 12 = 0.35 m
Step 3: add up the twelfths hour by hour, starting from the low water height.
| Time | Twelfths risen | Height of tide |
|---|---|---|
| 08:00 | 0 | 1.0 m |
| 09:00 | 1 | 1.0 + 0.35 = 1.35 m |
| 10:00 | 3 | 1.0 + 1.05 = 2.05 m |
| 11:00 | 6 | 1.0 + 2.10 = 3.10 m |
| 12:00 | 9 | 1.0 + 3.15 = 4.15 m |
| 13:00 | 11 | 1.0 + 3.85 = 4.85 m |
| 14:00 | 12 | 1.0 + 4.20 = 5.20 m |
Putting it to work
Can I get through the channel? Say your boat draws 1.5 m, you want at least 0.5 m of water under the keel, and the channel has a charted depth of 0.4 m.
You need 1.5 + 0.5 = 2.0 m of water. The chart gives you 0.4 m, so the tide needs to supply the other 1.6 m.
At 09:00 the height of tide is 1.35 m. Not enough. At 10:00 it’s 2.05 m. Plenty. So you can go from about 10:00, and you’ve got until the same point on the falling tide in the afternoon.
What about the sandbank? There’s a bank with a drying height of 1.2 m. At 11:00:
3.10 − 1.2 = 1.9 m of water over it.
With a 1.5 m draught, that leaves 0.4 m. Possible, but that’s less than the half-metre we said we wanted, and there’s no margin for waves. I’d go round.
Where it goes wrong
The Rule of Twelfths assumes a neat, symmetrical tide that takes about six hours to rise. Plenty of places don’t behave like that, so treat it as an estimate, not an answer.
- Some places have odd tides. The Solent is the famous example, with double high waters and a lopsided curve. The rule is close to useless there.
- Springs and neaps change the range. A bigger range means bigger twelfths, so always work from the heights in the tide tables for the day you’re sailing.
- The weather moves the water. High pressure pushes the sea level down and low pressure lets it rise, and strong winds can pile water up or push it away. Leave extra margin when the weather is doing something unusual.
For planning, the proper method is to use the tidal curves in your almanac or the Admiralty tide tables, which show how the tide really behaves at each standard port. The Rule of Twelfths is what you use to sanity-check that answer, or to make a quick decision on the water when the almanac is below and you’re not.
The nice thing about it
As someone who spends the working week in software, I like that the rule is essentially a lookup table with an interpolation step. It’s approximate, it’s honest about being approximate, and it’s good enough to keep you off the mud most of the time. Plenty of good engineering works the same way.
Fridays are for sailing on this blog. Next week: more from the Day Skipper course. Follow along if you’d like it in your feed.