Tide Height Calculator
Estimate the water level at any time between high and low tide using a simple harmonic (cosine) model of the tidal cycle.
How it works
h(t) = mean + amplitude · cos(2π·t / T) · mean = (high+low)/2, amplitude = (high−low)/2
To a first approximation a tide rises and falls as a smooth cosine wave, oscillating between high and low water over a period of about 12 h 25 min for the common semi-diurnal tide. Modelling it this way — a mean sea level plus a cosine term whose amplitude is half the tidal range — captures the key feature that water moves slowly near the turns of the tide and fastest halfway between them. Real tides are the sum of many such harmonics, so this single-constituent model is an estimate, not a substitute for an official tide table.
Worked example
With a 5 m high and 1 m low tide, the mean is 3 m and the amplitude 2 m. Three hours into a 12.42 h cycle, the phase is 2π × 3/12.42 = 1.517 rad, and cos(1.517) ≈ 0.054, so the height is 3 + 2 × 0.054 ≈ 3.11 m — just past the fast mid-fall of the tide.
Sources: Tide — Wikipedia
Frequently asked questions
Why is the tidal period 12.42 hours, not 12?
The main lunar tide follows the Moon overhead, and because the Moon also moves along its orbit, the interval between successive lunar transits is about 24 h 50 min. Splitting that into two high tides gives a semi-diurnal period of roughly 12 h 25 min (12.42 h).
How accurate is a simple cosine model?
It captures the overall shape well but ignores the many secondary constituents — solar, shallow-water and local effects — that shift the timing and height of real tides. Use it for intuition or rough planning, and consult an official tide table for navigation or safety.
What is the "rule of twelfths"?
It is a mariner's shortcut approximating the cosine curve: the tide moves 1/12 of its range in the first hour after a turn, then 2/12, 3/12, 3/12, 2/12 and 1/12 over the six hours. It mirrors how this harmonic model has the water moving fastest at mid-tide.
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This calculator is for educational purposes. Double-check important results before acting on them.