Tide Height Calculator (Rule of Twelfths)
Height of the water at any time between low and high tide, by the rule of twelfths and by a sine curve, from the two tide heights and the time elapsed.
Results
The dashed line marks the value you entered.
What this tool does
The tide does not rise at a steady rate: in the first sixth of the interval it covers a twelfth of its range, then two, three, three, two and one twelfths in the following ones, so most of the movement is in the middle hours. That is the rule of twelfths, a quick approximation of a sine curve. Both are idealised: local geography, wind and pressure bend the real curve. This is for planning a beach walk or launch only; never navigate by it, use official tide tables.
Formula
rule of twelfths: the tide covers 1, 2, 3, 3, 2, 1 twelfths of its range in successive sixths of the interval · sine curve: h = h₁ + (h₂ − h₁)(1 − cos(π t ÷ T)) ÷ 2
Variables
| Symbol | Meaning | Unit |
|---|---|---|
h0 | Water height at the start (high or low tide) | m |
h1 | Water height at the next tide | m |
t | Time since the start | h |
du | Time between the two tides | h |
HT | Height by the rule of twelfths | m |
HS | Height by the sine curve | m |
FR | Share of the range covered | % |
RG | Tidal range | m |
Worked example
- Water height at the start (high or low tide)0.8 m
- Water height at the next tide4.4 m
- Time since the start2.5 h
- Time between the two tides6.2 h
- Height by the rule of twelfths2.08 m
- Height by the sine curve2.06 m
- Share of the range covered35 %
- Tidal range3.60 m
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.