What is the Rule of Twelfths?

The Rule of Twelfths is a sailor's approximation of the tide curve. Over the roughly six hours between high and low water, the tide changes by 1, 2, 3, 3, 2, then 1 twelfths of the total range in each successive hour — slow at the turns and fastest at mid-tide.

How accurate is this method?

It approximates the real sinusoidal tide curve well for typical semi-diurnal tides where the period is close to six hours and the curve is symmetrical. It is less accurate where tides are strongly diurnal, in shallow estuaries, or during unusual surge or weather conditions.

What units does it use?

The calculator works in metres relative to your chart datum, but any consistent unit works because it operates on the tidal range. Just enter high and low in the same units and read the result in those units.

Can I use it for a rising tide?

Yes — the cumulative twelfths are symmetrical, so the same hourly fractions apply whether the tide is rising or falling. Enter the high and the adjacent low, and the percentage of the cycle elapsed is the same in both directions.

Should I rely on this for navigation?

No. For passage planning and clearance under keels or bridges, always use official tide tables and add a safety margin. This tool is a quick estimate for when you do not have a chart to hand.

Simplified Tide Height Calculator

The tide height calculator uses the classic mariner’s Rule of Twelfths to estimate the water level at any point between high and low tide. It is the fastest way to answer “how much water is under me right now?” when you only know the high and low tide heights from a table.

How it works

A semi-diurnal tide takes about 6 hours to go from high to low. Rather than a straight line, the water moves slowly near the turns and quickly through mid-tide. The Rule of Twelfths captures this by dividing the total tidal range (high minus low) into twelve parts and spreading them across the six hours:

Hour 1: 1/12 of the range
Hour 2: 2/12
Hour 3: 3/12 (fastest)
Hour 4: 3/12
Hour 5: 2/12
Hour 6: 1/12

The cumulative fall after each whole hour is therefore 1, 3, 6, 9, 11, 12 twelfths. The calculator interpolates within a partial hour, so 2.5 hours after high water it has fallen (1 + 2 + 1.5) / 12 = 4.5/12 of the range. Current height = high tide minus that amount.

Example and notes

Suppose high tide is 5.20 m and the following low is 0.80 m, giving a range of 4.40 m. At 3 hours after high water, 6/12 (half) of the range has gone, so the level is 5.20 − 2.20 = 3.00 m. Because the rule assumes a symmetrical, six-hour, sinusoidal curve, it works best for standard ocean tides and least well in shallow estuaries or under storm-surge conditions. Always carry official tide tables for real navigation decisions.