Work out tidal height at time instantly with clear inputs, formula shown and shareable results.
The rule of twelfths approximates the tide as a sinusoid: height equals low water plus half the range times (1 - cos(pi x elapsed/duration)). That gives the familiar 1/12, 2/12, 3/12, 3/12, 2/12, 1/12 pattern and shows the fastest rise at mid-tide.
Sinusoidal tide
h(t) = LW + range x 0.5 x (1 - cos(pi x t / duration))
Marine results are planning estimates only. Verify against the vessel's approved stability booklet, loading manual, class society rules and applicable maritime regulations before loading or sailing.
At mid-tide, roughly three hours into a six hour tide, where a quarter of the range passes in one hour.
It is a planning approximation. Use official tide tables and harbour-specific curves for under-keel clearance decisions, especially where the tide is asymmetric.