TideTutor

The rule of twelfths, explained

The rule of twelfths is a quick way to estimate the height of tide at a time between high water (HW) and low water (LW). It’s one of the first tidal calculations on the Day Skipper theory course, and one of the easiest to get slightly wrong.

It works because the tide doesn’t rise or fall at a steady rate. It starts slowly, speeds up in the middle hours, and slows again before it turns. Over the six hours from low water to high water, it rises roughly 1, 2, 3, 3, 2 and 1 twelfths of the range in each hour.

What you need

  • The time and height of the HW and LW either side of your time
  • The time you want the height for

The method, step by step

  1. Find the range: HW height − LW height.
  2. Work out one twelfth of the range: range ÷ 12.
  3. Count the whole hours since the last LW (rising tide) or HW (falling tide).
  4. Add up the twelfths for those hours: 1, 2, 3, 3, 2, 1, so the running total is 1, 3, 6, 9, 11, 12.
  5. Multiply: twelfths × one twelfth gives the rise (or fall) so far.
  6. On a rising tide, add the rise to the LW height. On a falling tide, take the fall away from the HW height.

The rule assumes about six hours between HW and LW and a smooth, regular tide. It’s an estimate: where a port has published tidal curves, the curves are more accurate, and some places with unusual tides (double high waters, for example) don’t follow it at all.

Always count from the tide you’re moving away from: up from LW on the flood, down from HW on the ebb.

Worked example

Question 222-2239 · fictional practice data

PortAshcove (standard port)
High water0618 3.7 m
Low water1218 0.7 m
Find height at0918

Using the rule of twelfths, find the height of tide at Ashcove at 0918, during the third hour after high water.

  1. Find the range HW − LW = 3.7 − 0.7 = 3.0 m
  2. Work out one twelfth 3.0 ÷ 12 = 0.25 m
  3. Count the hours since high water 0918 − 0618 = 3 hours
  4. Add up the twelfths 1 + 2 + 3 = 6 twelfthsHours 1–6 fall 1, 2, 3, 3, 2, 1 twelfths.
  5. Fall since high water 6/12 × 3.0 = 1.5 m
  6. Height of tide 3.7 − 1.5 = 2.2 mHigh water height minus the fall, rounded to 0.1 m.

Answer: Height of tide at 0918 2.2 m

Common mistakes

These are the slips TideTutor catches in this exact question, in the words it uses to point you back on track:

  • You've found how far the tide has fallen since high water. What do you take it away from?
  • You've used only the twelfths for the third hour. Add up the twelfths for every hour since high water.
  • Check what you took twelfths of. It should be the range (HW − LW), not the high water height.

Questions people ask

What is the rule of twelfths?

A rule of thumb for the height of tide between high and low water. In each of the six hours after LW (or HW), the tide rises (or falls) 1, 2, 3, 3, 2 and 1 twelfths of the range.

Why is it 1, 2, 3, 3, 2, 1?

The tide changes slowly near high and low water and fastest at mid-tide, so the middle two hours carry half of the whole range between them.

How accurate is the rule of twelfths?

Good enough for a quick estimate where the tide is regular and about six hours long. For anything that matters, use the port’s tidal curves, and at sea always use official tidal data.

What if my time isn’t a whole number of hours after HW or LW?

Add the twelfths for the complete hours, then add the right share of the next hour’s twelfths. Halfway through the third hour after LW, for example, is 1 + 2 + 1.5 = 4.5 twelfths.

Practise until it’s easy

TideTutor gives you endless fresh rule of twelfths questions like this one, with three-step hints, feedback on the classic mistakes and the full worked solution. Two questions in every topic are free.

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All ports, charts and tidal data in these guides are fictional, for practice only. Never use them for navigation.