What the rule of twelfths actually says
Divide the time between one turn and the next into six equal parts, and divide the range into twelve. The tide moves one twelfth in the first part, two in the second, three in the third, three in the fourth, two in the fifth and one in the sixth. Cumulatively that is 1, 3, 6, 9, 11, 12 twelfths.
It is a mental approximation to a sine curve, and it is a good one. Here is how the two compare, as a percentage of the total range:
| Elapsed | Twelfths, cumulative | Sine curve | Difference |
|---|---|---|---|
| 1/6 of the cycle | 8.33% | 6.70% | 1.63% |
| 2/6 | 25.0% | 25.0% | 0 |
| 3/6 — halfway | 50.0% | 50.0% | 0 |
| 4/6 | 75.0% | 75.0% | 0 |
| 5/6 | 91.67% | 93.30% | 1.63% |
| 6/6 | 100% | 100% | 0 |
The two are identical at four of the six marks. Where they differ, on an 8.4 foot range, the gap is about 1.6 inches — smaller than the error in most people's draft figure. As an approximation it earns its keep.
Where it stops working
The rule is built on two assumptions that are not always true: that the half cycle takes about six hours twelve minutes, and that the rise is symmetric about the halfway point. Both fail in identifiable places.
Rivers and estuaries with a lot of freshwater flow often have a short sharp flood and a long slow ebb — the twelfths are the wrong sizes and in the wrong order. Some harbours have a stand at the top, where the water sits still for an hour before it turns. Parts of the south coast of England have a double high. And anywhere the half cycle is materially longer or shorter than six hours, the sixths are the wrong length before you start.
A tide table that publishes intermediate heights, or a tidal curve for the port, is the answer where any of that applies. The rule of twelfths is for the ordinary semi-diurnal case and it should be treated as a sketch everywhere else. The calculator flags the duration when it strays far from the assumed one, but it cannot tell you the shape is wrong — only local knowledge and the published curve can.
Chart datum, and why the sum is an addition
A sounding on a chart is not the depth you will find. It is the depth there would be if the tide were at chart datum, which is a level chosen to be at or below the lowest tide normally expected. Real depth is that sounding plus the height of tide at the moment, and the height of tide is almost always positive, which is why the printed numbers look pessimistic.
Two consequences matter. The first is that a negative sounding — a drying height, printed underlined or in a different style depending on the chart — is a patch that is above datum, and it dries at low water. Entered as a negative number here, the arithmetic still works: the tide has to bring more than that much water before there is any depth at all.
The second is that heights can go below datum. A big spring low, or a strong offshore wind, can leave less water than the chart promises. Chart datum is a normal minimum, not an absolute one, and negative predicted heights appear in tide tables for exactly this reason.
Under-keel clearance is your number
This page asks what clearance you want and does not suggest one, because the honest answer depends on things it cannot see. Survey error and chart age. Swell, which lowers the water under you for part of every cycle by half its height. Squat, which pulls a boat down by an amount that grows fast with speed in shallow water. Whether the bottom is soft mud or a rock ledge. Whether the boat is alone or in a hurry.
What the page will do is tell you when the number you chose exists and when it does not, given the tide you entered. That is arithmetic. Deciding the number, and deciding whether the arithmetic is enough to go on, is not.
The one thing worth saying plainly is directional: going aground on a rising tide is an inconvenience, and going aground on a falling one is not. The water leaves faster than help arrives, the boat lies over as it goes, and it has to sit there for a full cycle before it floats again. That asymmetry is why the timing of a shallow crossing matters more than the depth of it.
Questions people ask
Is the rule of twelfths accurate enough to plan a crossing?
For an ordinary semi-diurnal tide of about six hours between turns, it agrees with the sine curve exactly at four of the six hour marks and differs by about 1.6 percent of the range at the other two. On an eight foot range that is under two inches, which is smaller than the uncertainty in most stated draft figures and far smaller than the effect of a passing swell. Where it stops being accurate is where its assumptions fail: a half cycle much longer or shorter than six hours, an asymmetric rise and fall, a stand at high water, or a double high. In those places a published tidal curve for the port is the tool, and the rule is a sketch.
Why do I add the height of tide to the charted depth instead of subtracting?
Because chart datum is at the bottom of the normal tidal range, not at the middle or the top. The sounding tells you what the depth would be at that low reference level, so any tide above it is extra water. The confusion usually comes from charts that use a different convention for heights of objects — bridge clearances and light elevations are normally given above a high water datum, so those you do subtract from. Depths go up with the tide and clearances come down with it, and the two use different reference levels for exactly that reason. Check what the chart states in its title block rather than assuming.
What does a negative sounding on the chart mean?
It is a drying height: ground that sits above chart datum and is uncovered at low water. Charts mark it distinctively, usually underlined or with a different symbol, and it is a height rather than a depth. Entered here as a negative number the arithmetic still holds — the tide has to bring more than that height of water before there is any depth over it at all, and your draft plus your clearance on top of that before you can cross. A one foot drying patch needs 1.0 feet of tide to be wet, and 5.5 feet of tide to have 3.5 feet of draft and one foot to spare over it.
Can the tide go below chart datum?
Yes, and tide tables print negative predicted heights when it will. Chart datum is defined as a level the tide rarely falls below, not one it never does, so large spring lows can go under it by a foot or more depending on the station and the definition in use. Weather does it too: a strong offshore wind or a high barometer can hold the water down by a foot beyond the prediction, and both are common enough that they are worth a thought before crossing anything marginal at low water on a clear high-pressure day. The tide table is a prediction of the astronomical tide, and the weather is added to it afterwards by the weather.
Does this account for waves or for the boat squatting at speed?
Neither. It is still-water arithmetic on a tide table. Swell lowers the water under the keel by roughly half the wave height in the troughs, and it does that repeatedly rather than once. Squat is the boat pulling itself down as it moves through shallow water, and it grows quickly with speed and with how little water there is under the hull — it is why a shallow crossing is made slowly. Both belong in the clearance figure you enter, along with survey error and the fact that a bar moves. This page will not choose that figure for you.