How to use the tide rule of twelfths calculator
- Enter the time and height of one tide (a low or a high) and the time and height of the next, taken from a tide table.
- Enter the time you want, which must fall between the two tides.
- Read the estimated height, the share of the tidal range covered and whether the tide is rising or falling.
- Use the table to see the height at the end of each sixth of the interval and how much of the range changes in each.
Formula
divide the time between the tides into six equal parts
the tide covers 1/12, 2/12, 3/12, 3/12, 2/12 and 1/12 of its range in the six parts
cumulative shares: 1/12, 3/12, 6/12, 9/12, 11/12, 12/12
between those points the height changes in a straight line
Height at a time = first height + (next height - first height) x share of range covered. The share is found by following the straight lines between the cumulative points.
A rising tide from 06:00 to 12:30
Low water is at 06:00 with a height of 0.5, and high water at 12:30 with a height of 3.7, so the range is 3.2 and the interval is 6 hours 30 minutes. One sixth is 65 minutes. At 09:00 the tide is 180 minutes in, which is 2.769 sixths of the way. The third sixth covers 3/12 of the range and the tide is 0.769 of the way through it, so the share covered is 3/12 + 0.769 x 3/12 = 0.4423 and the height is 0.5 + 3.2 x 0.4423 = 1.915.
The table gives 0.767 at 07:05, 1.300 at 08:10, 2.100 at 09:15, 2.900 at 10:20, 3.433 at 11:25 and 3.700 at 12:30. For a falling tide from a high of 3.7 at 06:00 to a low of 0.5 at 12:30, the height at 10:00 is 1.546. The heights can be in feet, meters or any unit.
Why the tide moves fastest in the middle
A tide follows a smooth wave. It changes slowly just after a high or a low, fastest halfway between, and slowly again as it nears the next extreme. The rule of twelfths copies that shape with simple fractions, which is easy to work out in your head. It is an approximation of a sine-like curve.
When not to rely on it
Many places have tides that do not follow a smooth even curve: some have two highs of different heights, some are mostly daily, and rivers, wind and air pressure all distort them. The rule is a rough guide for estimating a depth at a time when you have a table of the high and low tides. It is not a replacement for tide predictions for your location, and it must not be used for navigation or safety decisions. To learn about the moon's role, see the Moon Phase Calculator.
More tools for courses, tides and surveys
For related work with courses, positions and boats, try the Hull Speed Calculator, Wind Triangle Calculator and Traverse Closure Calculator.
Assumptions and limits
- The two times and heights are successive tides from a tide table, one high and one low.
- The time between them is under about 13 hours.
- The tide follows a smooth shape close to the rule of twelfths.
- Heights use one unit, and the time you want is between the two tides.
- The times and heights in the form are examples to replace with values for your own location.
Frequently asked questions
Why twelfths?
Twelve divides neatly by 2, 3, 4 and 6, so the shares of the range per sixth of the interval are whole numbers of twelfths that add up to the whole range. It is a mental arithmetic shortcut.
How accurate is it?
For a regular tide it can be within a modest fraction of the range, but how close depends on the place and the day. This page does not claim a figure, so treat the output as a rough estimate.
What if the second tide is earlier on the clock than the first?
The tool assumes it is the next day. A second time of 01:00 after a first time of 20:00 means a gap of 5 hours.
Does it work for a falling tide?
Yes. Enter the high tide first and the low tide second, and the tool counts the fall in the same proportions.