Understanding tidal coefficients

Where the number comes from

The coefficient is a French convention, and it answers one question: how big is today’s astronomical tide compared with an ordinary one? Three facts about the Moon and the Sun decide it, and nothing else does.

• Phase. At new and full Moon the Sun and the Moon pull along the same line and their effects add; at the quarters they pull at right angles and partly cancel each other out. The Sun’s tide-raising force is about 46 per cent of the Moon’s, so this alone swings the number a long way. One spring tide to the next takes 14.77 days, with a neap falling halfway between them, about 7.4 days after each — see spring and neap tides.
• Distance. The Moon averages 384,400 km away, but closes to about 356,000 km at perigee and retreats to about 406,700 km at apogee, returning to perigee about every 27.55 days. Tide-raising force falls off as the cube of the distance, so a perigee Moon pulls roughly a fifth harder than an average one, and an apogee Moon about a sixth less.
• Declination. The Moon is not always over the equator. It swings to about 28.6° north and south, and the size of that swing itself varies over 18.6 years. A Moon near the equator produces the largest twice-daily tide.

Line all three up on the same day — new or full, close to perigee, near the equator — and the number approaches 120. Set them against each other and it falls to about 20. Nothing else is in the formula: no coastline, no depth, no weather.

Because only astronomy goes in, the coefficient is location-free. The same day carries the same number at Brest and in Bali. We sample it once a day, at local noon, which is the only reason two time zones can print a figure a point or three apart.

The bands we use

Every coefficient on this site is coloured by one of four bands — on the month strip, in the tables and on the day chips.

The boundaries are ours, but they follow the astronomy. Ninety is where we call a peak a spring tide, and 100 is the line we use for a king tide: eight spring tides reached it in the year we checked, which sits inside NOAA’s “six to eight times a year” for perigean spring tides, and that guide lists the dates for this year. The practical floor is about 20 and the practical ceiling about 120, so almost every day you will ever see falls between them.

This month at a glance

One day’s number tells you little. A month of them, one bar a day, tells you which week to take off work.

Two things stand out in any month’s strip. The shape is a slow sawtooth with two peaks and two troughs, because the Moon runs through its phases every 29.53 days and the coefficient answers to the phase. And the peaks sit on the new and full Moon rather than after them, because the coefficient is pure astronomy: it answers to the alignment itself and carries no lag at all. The water is slower than the sky. On most coasts the biggest tide arrives one to two days after the exact alignment — a lag old enough to have its own name, the age of the tide — and that lag is not in this number.

Every station page carries the same strip for the month you are reading, in the same four colours, with today marked. That is the quickest way to answer “when is the next big tide here” without opening thirty pages.

What a high coefficient actually buys you

A bigger range, and with it faster water. The coefficient is proportional to the astronomical range at a given place, so a day at 100 moves roughly twice as much water as a day at 50 on the same coast, in the same twelve hours and a bit. In practice that means:

• More foreshore uncovered at low water — the ledges, sandbars and mussel beds a neap tide never reaches.
• More water over a bar, a sill or a shallow entrance at high water.
• Faster flow through narrows, around headlands and in and out of estuaries, which matters far more to a small boat than the height does.
• More movement for fish to feed in, which is the reason most anglers watch the number at all.

Every one of those cuts both ways. A very high coefficient means the low is lower, the flood that follows it is quicker, and the walk out to a sandbar that is comfortable at 45 can leave you cut off at 105. Read the big days as more of everything, not as better.

What it does not tell you

The coefficient is one number about the sky. Four things it is not:

• Not a height. A coefficient of 100 in the Mediterranean still means a range of a few tens of centimetres — under half a metre along most of that coast — while 45 in the Bay of Fundy, where spring ranges reach about 16 m, is still a great deal of water on the move. Boston, a middling coast, has a mean range of about 2.9 m.
• Not the weather. Pressure and wind are in no tide prediction. About a centimetre of sea level answers to each hectopascal of pressure, and a storm can move the water half a metre or more, up or down, for a day at a time.
• Not the timing. The number says how big, never when. Times of high and low water are local, and come from your station’s own curve.
• Not the conditions. Swell, wind and daylight are separate questions with separate answers, and a huge tide on a bad day is still a bad day.

The coefficient tells you which days are big. Only your station tells you what big means there.

Coefficient vs tidal range

The two are easy to confuse, because they describe the same event from opposite ends. The coefficient is the astronomy, and it is the same for everyone; the tidal range is what that astronomy does to your particular stretch of water.

The coefficient scales; the coast sets the scale. That is why the same 95 is a spectacular day at Avonmouth in the Severn Estuary, where spring ranges approach 15 m, and an unremarkable one at Venice.

Using it to plan

Open any station page and the coefficient is already there: on the month strip, and beside every day in the table. Three habits get the most out of it.

1. Pick the week from the strip. Find the run of bars in the band you want, then look at the individual days inside it rather than the other way round.
2. Read the day’s own numbers. The band says the day is big; the high and low figures say what big means at that station, measured from the zero we publish — see what is chart datum.
3. Check the weather separately. The tide is astronomy. The wind, swell and pressure that will actually meet you are a different forecast, and on a marginal day they decide it.

If the day matters more than the tide — a dive, a launch, a long walk out to a reef — the Best Day Finder ranks a week by tide, wind, waves and daylight together, and the Fish tab lays the solunar windows over the same curve. Both live in the tool behind a free account; the station pages are open to everyone. The coefficient itself we compute from the Moon’s and the Sun’s positions with the JPL DE421 ephemeris — how we compute sets out the rest of the chain.

Questions people ask