Tide Height Rule of Twelfths Calculator

Enter both tide heights, their times, the target time, and whether the tide is falling or rising. The calculator divides the full interval into six equal periods and applies the traditional 1–2–3–3–2–1 pattern. It is useful for quick planning when a full harmonic curve or official real-time gauge is not available.

What the rule of twelfths estimates

The rule of twelfths is a practical approximation for the change in water height during a roughly sinusoidal tide. It divides the time from one tidal extreme to the next into six equal intervals. During those intervals, the water is assumed to move by one twelfth, two twelfths, three twelfths, three twelfths, two twelfths, and one twelfth of the total tidal range. Those shares add to twelve twelfths, so the estimate reaches the opposite extreme at the end time. This calculator also interpolates inside each interval instead of forcing the target time onto an interval boundary. For example, halfway through an interval assigned three twelfths, it applies one and a half twelfths for that interval. The result is a deterministic estimate expressed in the same unit used for the two heights. If the predictions are in metres, the answer is in metres; if they are in feet, the answer is in feet. No unit conversion is performed, which prevents an accidental mixture of unlike measurements from looking authoritative.

Enter tide times and direction correctly

Use the predicted high-water and low-water heights from the same station and the same tide cycle. Enter clock times in 24-hour HH:MM form. Choose high_to_low when high water occurs first and the target lies on the falling tide; choose low_to_high when low water occurs first and the target lies on the rising tide. When the second event has an earlier clock reading than the first, the calculator treats it as occurring on the following day. This makes windows such as a late-evening low followed by an early-morning high work without dates. The target time follows the same rollover rule and must fall inside the selected event window. The reported interval length is the actual high-to-low or low-to-high duration divided by six, rather than an assumed fixed hour. That matters because published tide events are seldom separated by exactly six hours. Check the direction carefully: identical heights and times describe two different curves depending on whether the sea is rising or falling.

Use the estimate with appropriate caution

Treat the result as a planning estimate, not as a navigation clearance or a replacement for official predictions. The rule works best where the tide curve is broadly regular and the supplied high and low predictions are reliable. Wind, atmospheric pressure, river flow, harbour geometry, shallow-water effects, and mixed or strongly asymmetric tides can make the observed level depart from this simplified curve. Compare the result with local notices, gauges, chart datums, and safety margins whenever depth matters. Also confirm that both published heights use the same chart datum; subtracting values tied to different reference levels produces a meaningless range. The output includes the tidal range, elapsed minutes, interval length, percentage progress, and cumulative twelfths so the calculation can be audited. API automation costs $0.002 per request, while the browser calculation uses the same pure arithmetic. For consequential boating, coastal access, diving, or engineering decisions, consult the responsible hydrographic or harbour authority and account for current conditions.