How Harmonic Tide Prediction Works

Ocean tides are a periodic signal, and periodic signals can be rebuilt by adding up a series of cosine waves. Tide tables around the world are produced exactly that way: each coastal station is analysed to find the amplitude and phase of a set of tidal constituents, and the prediction for any future minute is the sum of those terms. This calculator uses the two constituents that matter most on most coastlines — the principal lunar semidiurnal term (M2, period 12.42 hours) and the principal solar semidiurnal term (S2, period 12.00 hours) — and adds them to a datum height you specify.

The model is written as h(t) = mean sea level + M2 amplitude × cos(2πt / 12.42 − M2 phase) + S2 amplitude × cos(2πt / 12.00 − S2 phase), with t measured in hours from your reference time. Change any amplitude or phase, press Calculate, and the full curve is resampled minute by minute to locate every high and low water in the forecast window.

Reading the Predicted Tide Table

The headline card shows the first high water after your reference time and the low water that follows it, with clock times and heights in metres. Below that, the breakdown table lists each tide event in the window and highlights the highest high and lowest low, which are the two numbers worth memorising for a shallow berth or a bar crossing. The final row reports the largest high-to-low range seen anywhere in the window.

Summary statistics put the window in context. Mean range is the average high-to-low difference, spring range is the maximum the location can deliver when the solar and lunar bulges align (2 × (M2 + S2)), and neap range is the minimum when they partly cancel (2 × |M2 − S2|). The spring/neap cycle tells you how many days separate the biggest and smallest tides — about 14.8 days for these two constituents, which is the familiar fortnightly rhythm of coastal water levels. The clearance pair of statistics counts how many hours the water stays above the depth you need and the next time the falling tide drops below it.

Interpreting Amplitudes, Phases and Local Effects

The amplitude of a constituent is half its contribution to the tidal range, and the phase is simply the time offset — a larger phase angle means the crest arrives later. If you have a published harmonic constant table for your harbour, the M2 amplitude and phase are the first two numbers to copy in; if you are estimating, a solar amplitude around a quarter to a third of the lunar amplitude is typical for exposed ocean coasts, while enclosed seas usually carry much smaller values for both.

Remember that a two-term model is a simplification. Shallow estuaries generate overtides that make the flood shorter than the ebb, atmospheric pressure and persistent winds shift water levels by tens of centimetres over hours, and river discharge can hold a low tide above its predicted height. The tide prediction here is designed for planning, teaching, and quick sanity checks — align it with an official station table before relying on it for navigation, and always carry a margin for the weather.