Tide height calculator
The rule of twelfths estimates the rise or fall of a tide in six equal intervals using fractions of 1, 2, 3, 3, 2 and 1 twelfths of its range.
Reviewed by Ramon Curto, Nautical teacher at IECNPC · Last reviewed:
Explore the tide
Use one time zone for all entries. The end time is the next occurrence after the start; choose rising or falling explicitly.
Rule of twelfths2.95 m
Cosine curve2.95 m
Absolute difference0 m
Use local official predictions and the port’s tidal curve for navigation. These two approximations do not account for weather, swell or squat.
Worked example — fictional training data
- High-water time · High-water height (m)
- 06:12 · 4.80 m
- Low-water time · Low-water height (m)
- 12:24 · 1.10 m
- Target time · Rule of twelfths
- 09:18 · 2.95 m
- Cosine curve · Absolute difference
- 2.95 m · 0.00 m
Rule of twelfths: 4.80 − (4.80 − 1.10) × (1 + 2 + 3)/12 = 2.95 m
Clearance after margin: 0.50 + 2.95 − 2.00 − 0.50 = 0.95 m
Use local official predictions and the port’s tidal curve for navigation. These two approximations do not account for weather, swell or squat.
How it works
Start with consecutive high and low waters from the same port and datum. The tidal range is high-water height minus low-water height. Here, high water is at 06:12 with a height of 4.8 m, and low water is at 12:24 with 1.1 m. The range is 3.7 m and the duration is 372 minutes. Divide that duration by six: each tidal interval lasts 62 minutes, rather than assuming six exact clock hours. All times must use the same time zone, including any summer-time adjustment stated by the tide table.
The twelfths sequence allocates 1/12, 2/12, 3/12, 3/12, 2/12 and 1/12 of the range to successive intervals. Add the completed fractions and interpolate linearly within the current interval. On a falling tide subtract that change from high water; on a rising tide add it to low water. At 09:18, three intervals have elapsed: the fall is 6/12 × 3.7 = 1.85 m, giving 2.95 m above chart datum. The cosine model also gives 2.95 m at this midpoint, but agreement here does not validate either model for a real port.
For a rising tide, the smooth model is h = LW + range × (1 − cos(π × t/duration))/2, with t measured since low water. For a falling tide, subtract the same change from HW and measure t since high water. Spring tides generally have larger ranges near new and full moon; neaps have smaller ranges near the quarter moons. Neither means a fixed height or duration. Semidiurnal tides have two high and two low waters per tidal day; mixed or diurnal regimes, double high waters and strongly asymmetric curves need local predictions.
Charted depth and tidal height must share a datum. LAT, lowest astronomical tide, is commonly used on UK charts, but is not universal: check the chart and tide-table notes. Remaining clearance equals charted depth + tide height − draft − safety margin. With depth 0.5 m, tide 2.95 m, draft 2 m and margin 0.5 m, 0.95 m remains. The inverse calculation gives the earliest sufficient water within your interval, rounding up to a whole minute. RYA Day Skipper and Yachtmaster study tidal heights; Spain’s PER tests depths at high and low water, while Patrón de Yate includes intermediate-height and inverse tide problems.
Frequently asked questions
What is the rule of twelfths?
It divides the change between consecutive high and low water into six equal time parts, with changes of 1, 2, 3, 3, 2 and 1 twelfths of the range.
Does each interval last one hour?
Only when high to low water lasts six hours. In this example each part lasts 62 minutes.
Can I use it at every port?
No. Use the local curve or official predictions for diurnal, mixed, asymmetric or double-high-water tides.
Is chart datum always LAT?
No. LAT is common on UK charts, but other datums exist. Check that depths and tide heights use the same reference.
What does the gate result mean?
A non-negative result meets your entered draft and margin in that model. It does not guarantee safe passage.
When is there enough water on a falling tide?
If the starting height meets the threshold, the first sufficient time is the start. Otherwise it is never reached in this falling interval.
Why do the two models differ?
Twelfths uses straight segments; cosine uses a smooth half-wave. Neither includes local tidal constituents or meteorological effects.