Rule of twelfths tide calculator

Take the low and high water heights and times from a tide table. Enter the heights, whether the tide is rising or falling, the hours between low and high water and how long after the turn you want the height. The calculator applies the rule of twelfths and shows a cosine-curve estimate for comparison.

Units
Tide
ft
ft
h
h
Tide height3.25 ft
Change since the turn
2.25 ft
Share of the range
37.5 %
Rate in this tidal hour
1.5 ft/h
Cosine-curve estimate
3.22 ft

Runs in your browser: nothing you enter is sent anywhere.

How to use

  1. Choose metres or feet and whether the tide is rising or falling.
  2. Enter the low and high water heights from the tide table.
  3. Enter the hours from low to high water and the hours since the turn of the tide.

How it works

  • range = high water − low water;
  • tidal hour = duration ÷ 6; in each tidal hour the water moves 1, 2, 3, 3, 2, 1 twelfths of the range, spread evenly within the hour;
  • rising tide: height = low + range × share; falling: height = high − range × share;
  • rate = twelfths of the current hour × range ÷ 12 ÷ length of a tidal hour.

Example

Low water 0.5 m, high water 4.1 m six hours later. How high is the water 2½ hours after low water?

  • range 4.1 − 0.5 = 3.6 m;
  • after 2 hours: 1 + 2 = 3 twelfths; half of the third hour adds 1.5 more: 4.5/12 = 37.5 %;
  • 3.6 × 0.375 = 1.35 m, so the height is 0.5 + 1.35 = 1.85 m;
  • in the third hour the water rises 3/12 × 3.6 = 0.9 m per hour; the cosine curve gives 1.83 m.

Tips and common mistakes

  • Heights are above chart datum; add the charted depth to get the depth of water.
  • Use times corrected for summer time and for your port (secondary port corrections) before you start.
  • Leave a margin under the keel: weather and pressure change the real tide.

Frequently asked questions

What is the rule of twelfths?

A rule of thumb for a tide that takes about six hours from low to high water: in the first hour it rises 1/12 of the range, then 2/12, 3/12, 3/12, 2/12 and 1/12. Half the range comes in during the middle two hours.

What if the tide does not take six hours?

Split the actual time into six equal 'tidal hours'. With 6½ hours from low to high, each tidal hour is 65 minutes. The calculator does this when you enter the duration.

How accurate is it?

It assumes a smooth, symmetric tide. Where tides are irregular (double high waters, shallow estuaries, strong weather effects) it can be well off. Use the tidal curves for your port when clearance matters.

What is the cosine estimate?

The rule of twelfths approximates a sine-shaped tide. The cosine line uses that curve directly: height = low + range × (1 − cos(π × t ÷ duration)) ÷ 2. The two agree closely; a large difference means you are between whole tidal hours on a steep part of the curve.

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