Tide Height Calculator
This tide height calculator estimates the water level at a given time using the single-constituent harmonic model that underlies the tide predictions published by the US National Oceanic and Atmospheric Administration. Real tides are the sum of many harmonic constituents, but a useful first approximation treats the dominant semidiurnal tide as one cosine wave: the height rises and falls smoothly around mean sea level, reaching high water when the cosine peaks and low water half a period later. Enter the mean sea level (the long-term average height), the tidal amplitude (half the range from low to high water), the tidal period in hours (about 12.42 hours for the principal lunar semidiurnal tide), and the number of hours elapsed since the last high water. The calculator returns the predicted height above the chart datum at that moment. Use it to judge clearance under a keel, plan a beach walk around low water, or sense-check a tide table. The single cosine captures the rise and fall but not the smaller constituents a full prediction combines. Every figure is computed deterministically from the harmonic cosine formula shown in full below, with a worked example that reconciles exactly to the calculator so you can follow each step yourself.
A single harmonic models the tide as a cosine around mean sea level: with mean sea level 2.00 m, amplitude 1.50 m, period 12.42 h and 3 hours since high water, the height is 2.08 m. High water is amplitude above the mean, low water amplitude below.
Tide height formula
h(t) = MSL + A x cos( 2 pi x t / T )
MSL = mean sea level
A = tidal amplitude (half the range)
T = tidal period in hours
t = hours since high water
At t equals zero the cosine is one, so the height is mean sea level plus the full amplitude, which is high water. As t advances the cosine falls, reaching minus one at half a period, which is low water.
Worked example
Predict the tide 3 hours after high water with mean sea level 2.00 m, amplitude 1.50 m and a period of 12.42 hours.
- phase = 2 pi x 3 / 12.42 = 1.517628 rad = 86.96 deg
- cos(1.517628) = 0.053066
- departure from mean = 1.50 x 0.053066 = 0.08 m
- h = 2.00 + 0.08 = 2.08 m
The predicted tide height is 2.08 m, just above mean sea level as the tide falls from high water toward the mid-tide point. These are the calculator's default inputs, so the result above matches the widget exactly.
Tide height through one cycle
With mean sea level 2.00 m and amplitude 1.50 m, the harmonic model gives these heights across the 12.42 hour cycle.
| Hours since high water | Height (m) |
|---|---|
| 0.00 | 3.50 |
| 3.00 | 2.08 |
| 3.11 | 2.00 |
| 6.21 | 0.50 |
| 9.32 | 2.00 |
| 12.42 | 3.50 |
Method and tide prediction reference: US National Oceanic and Atmospheric Administration (NOAA).
Tide Height Calculator: frequently asked questions
Is a single harmonic accurate enough?
A single cosine captures the dominant semidiurnal rise and fall but ignores the dozens of smaller constituents (solar, fortnightly, shallow-water) that NOAA combines for an official prediction. It is a sound teaching and planning approximation where the principal lunar tide dominates, typically good to a few tens of centimeters. For navigation or any safety-critical use, always rely on the official tide tables for the specific station.
What is tidal amplitude versus tidal range?
The tidal range is the full vertical distance from low water to high water. The amplitude is half of that, the height of the wave measured from mean sea level to the crest. So if the range is 3.0 m, the amplitude is 1.5 m. This calculator asks for the amplitude because it is what multiplies the cosine in the harmonic formula.
Why is the period 12.42 hours?
The principal lunar semidiurnal constituent, called M2, has a period of about 12.42 hours, which is half a lunar day. Because the Moon is the largest tide-raising body, most coastlines see two high waters and two low waters roughly every 24.84 hours. Some locations are diurnal (one cycle a day, near 24 hours) or mixed, so you can change the period to match your station.
What does hours since high water mean?
It is the time elapsed since the most recent high water at your location, which you read from a tide table or observe directly. At zero hours the model returns high water; at half a period it returns low water. Entering a negative value or a value beyond one period simply continues the cosine, which repeats every period.
What datum is the height measured from?
The height is measured from whatever datum your mean sea level value refers to. Official US charts use mean lower low water as the tidal datum for depths. If you enter mean sea level relative to chart datum, the predicted height is also relative to chart datum, so it can be added to charted depths to estimate water under the keel.
Official sources
- Tide prediction method and datums reference: US National Oceanic and Atmospheric Administration (NOAA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.