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.

What is the Simplified Tide Height Calculator?

Free tide height calculator using the Rule of Twelfths. Enter the high tide height, the following low tide height, and the hours elapsed since high water to estimate the current tide level. For coastal anglers, kayakers, and sailors without a tide chart. It runs free in your browser on Gera Tools, with nothing uploaded.

Simplified Tide Height Calculator

Name: Simplified Tide Height Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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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.

Why the tide follows this pattern — not a straight line

The tide’s rise and fall approximates a cosine curve rather than a straight ramp. Near high and low water the rate of change is small — the tide “stands” briefly before turning. Through mid-tide the speed is greatest, which is why the 3/12 twelfths are assigned to hours 3 and 4. The Rule of Twelfths is simply a practical approximation of that cosine without the need for trigonometry or a calculator.

Worked example

Suppose high tide is 5.20 m and the following low is 0.80 m, giving a tidal range of 4.40 m. You want to know the height 3.5 hours after high water.

The cumulative fall to 3 hours is 6/12 = half the range = 2.20 m. The 4th hour adds another 3/12 = 1.10 m over 60 minutes, so the additional fall at 0.5 hours into hour 4 is roughly 0.55 m. Estimated height at 3.5 hours:

5.20 − 2.20 − 0.55 = 2.45 m

The exact answer from the cosine formula would be close but slightly different. For passage planning add a safety margin on top of this estimate.

Practical uses

Coastal anglers use it to judge when a beach gutter or rock platform will be fishable. Many marks fish best in the two hours either side of low water — this calculator shows when those windows open.

Kayakers and small-boat sailors use it to decide when a bar or shallow channel will have enough depth to cross safely, especially on a falling tide where mistiming means waiting six hours for the next high.

Rock poolers and foragers use it to predict when lower pools, accessible only near low water, will be exposed.

Important: The Rule of Twelfths is only an approximation for semi-diurnal tides with a roughly six-hour half-period. It is less reliable in shallow estuaries (where tidal bores or tidal asymmetry distort the curve), near river outflows, during storm surges, and at diurnal-tide locations. Always consult official tide tables and apply a generous safety margin for any decision involving real navigation risk.