Tidal Height At Time Calculator

Work out tidal height at time instantly with clear inputs, formula shown and shareable results.

About Tidal Height At Time Calculator

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.

Formula

Sinusoidal tide

h(t) = LW + range x 0.5 x (1 - cos(pi x t / duration))

Worked example

With the default values below, Tidal Height At Time Calculator returns Predicted height of tide of 3.02. Change any input above and every figure here is recalculated in your browser.

Inputs used

Low water height: 1.2 m
High water height: 6.4 m
Duration of the tide: 6.2 h
Time since low water: 2.5 h

Results

Predicted height of tide: 3.02 m
Tidal range: 5.20 m
Proportion of range risen: 35.0% %
Rate of rise at this moment: 1.26 m/h

Step by step

1Values used
2Sinusoidal tide
3Predicted height of tide= 3.02 m
4Tidal range= 5.20 m
5Proportion of range risen= 35.0 %
6Rate of rise at this moment= 1.26 m/h

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
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.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

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.

Frequently Asked Questions

When does the tide run fastest?

At mid-tide, roughly three hours into a six hour tide, where a quarter of the range passes in one hour.

Is this accurate enough for navigation?

It is a planning approximation. Use official tide tables and harbour-specific curves for under-keel clearance decisions, especially where the tide is asymmetric.