Tides Explained: Tide Times, French Coefficients, and the Rule of Twelfths

High tide, low tide, tidal range: the vocabulary

One port, and an entire coastline that relies on it. France’s tide coefficient is calculated for Brest alone; it’s the precision of that one figure that lets it be used along every coast of mainland France, as long as you account for the time difference between high tide at Brest and high tide at the port you care about [1]. Before you read it, a few words of vocabulary will do.

High tide is the moment the water reaches its highest level, low tide its lowest. The difference in height between the two is the tidal rangeThe difference in height between high tide and the low tide that follows or precedes it.. When the tide is rising, it’s the flood; when it’s falling, the ebb [1]. Tide-table heights are measured from chart datum, the common reference for nautical charts and tide tables, which France sets close to the level of the lowest tides, a level the water drops below only very rarely [1].

Along France’s English Channel and Atlantic coasts, the tide is semidiurnal: two high tides and two low tides a day [2]. Based on their range, SHOM, the French Navy’s hydrographic and oceanographic service, classifies tides as microtidal, under 6.6 ft (2 m); mesotidal, 6.6 to 13 ft (2 to 4 m); and macrotidal, over 13 ft (4 m) [1].

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The coefficient: Laplace’s idea, calculated for Brest

The tide coefficient is a French way of describing the tide, and if you think in spring and neap tides, you already get the idea: it grades each tide on a single scale, from the smallest neaps to the biggest springs. The mathematician Laplace came up with it, to characterize each port by a unit of height, taken from the biggest tide that comes shortly after the full or new moon around the equinoxes. By convention, a coefficient of 100 goes to the average range of equinoctial spring tides; the accepted extremes today run from 20 to 120 [1].

So a high coefficient means a big tide: the water rises higher, drops lower, and uncovers more of the shore. The coefficient doesn’t give you a height in feet or meters; it’s calculated from the semidiurnal constituents alone [2], and SHOM itself notes that it’s rarely used outside France [1]. For a height, you need the tide table for the port.

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The rule of twelfths, step by step

Good news: you don’t need a calculator to figure out how much water there’ll be an hour from now. Sailors use the rule of twelfths, which even shows up on France’s professional maritime exams [3] [4]. You split the duration of the tide, from high tide to low tide, into six “tidal hours.” Over those six intervals, the water rises or falls by 1, 2, 3, 3, 2, and then 1 twelfth of the tidal range [4].

Say high tide is at 6:12 a.m., at 17.1 ft (5.20 m), and the following low tide at 12:24 p.m., at 3.6 ft (1.10 m). The tide runs 6 hours 12 minutes, so each tidal hour lasts 1 hour 2 minutes. The tidal range is 13.5 ft (4.10 m), and one twelfth is just over a foot (34 cm).

The rule is an approximation: it swaps the cosine curve the tide follows for straight-line segments. Before calculators, it was a remarkable tool, and it’s still excellent for a rough estimate in your head [4]. It assumes a regular tide; in ports where the curve is distorted, you’re better off with the tide table and its curves.

Where to find official tide times

In France, SHOM publishes tide times for its ports for free on a dedicated website [6]. Its predictions are based on the analysis of long series of measurements and are accurate to within an inch or two (a few centimeters); but the weather can shift sea level by something on the order of a foot (a few tens of centimeters), and that can’t be predicted in the medium or long term [1]. In its prediction service, the coefficient option is only offered for ports in mainland France on the English Channel and the Atlantic [7].

Outside France, each country has its own official agency. In the UK, the UK Hydrographic Office publishes ADMIRALTY EasyTide [8]; in Germany, the federal maritime and hydrographic agency, the BSH, publishes its tide predictions [9]; in the United States, NOAA publishes its own on Tides and Currents [10]. These services don’t give a coefficient: you read the times and heights of high and low tide directly.

Before a saltwater fishing trip, with your knots tied and tested, or a swim in cool water, in the right wetsuit thickness, checking the tide times is part of the same habit as checking the weather.

So, with a big spring tide on the way (a three-digit coefficient, in France), the tide table in your pocket, and your return time figured out, all that’s left is to head down to the shore, where the ocean has just left its treasures behind.

Worth watching

A tide diagram works through the rule of twelfths hour by hour, turning tide times and the tidal range into a water height at any point between high and low tide.

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Nolwenn Bastide

Trail running, snow, water, nature and destinations

Nolwenn covers trail running, snow, water, nature and destinations for Outfarer. Curious about everything, from meteor showers to night-train schedules, she has a knack for digging up the one detail that changes everything, and nailing it in a single sentence.

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