What is tidal range?

What tidal range means

Tidal range is the vertical distance between a low water and the next high water. It is a height, not a time and not a distance along the beach, and it is always a local number: two harbours on the same coast can be reading the same Moon on the same afternoon and see quite different ranges.

Range is what most people are actually asking about when they ask how big the tide is. It sets how far the water uncovers at low tide, how much clearance a boat has over a bar, how quickly a channel fills, and how hard the current runs — the same volume of water moving through the same gap in the same six hours moves faster when the range is bigger.

Mean range, spring range, neap range

The range changes every tide, so a coast is usually quoted with three numbers rather than one. The spring range is what you get around new and full Moon, when the Sun’s tide adds to the Moon’s. The neap range is what you get at the quarters, when the Sun works across the Moon and partly cancels it. The mean range is the average over the whole cycle — the difference between mean high water and mean low water — and it is the single number usually quoted to describe a place.

The swing between them is large. On this site the size of the day’s astronomy is summarised by a tidal coefficient running from 20 to 120, and a coast’s range broadly follows it: the biggest spring of the year at a place can be several times its smallest neap, with everything in between happening on a 14.77-day rhythm. Two further wrinkles ride on top. The Moon’s distance matters, because a spring tide near perigee runs higher than one near apogee — that is what makes a king tide. And the peak lags the alignment: on most coasts the biggest tide arrives one to two days after the exact new or full Moon.

How to calculate tidal range from a tide table

Take the high-water height and subtract the low-water height either side of it, using two rows of the same table so that both are on the same datum. That is the whole calculation; the care is all in which two rows you pick.

1. Find the two consecutive rows you care about — one high and the low immediately before or after it.
2. Subtract the lower height from the higher one. A high of 3.1 m and a low of −0.9 m give 3.1 − (−0.9) = 4.0 m of range.
3. Take both numbers from the same table for the same station. A height is meaningless without the zero it is measured from.

The minus sign in that example is the part that trips people up, and it is not an error. Every height is quoted above some agreed zero level, called a datum, and different tables use different ones. The predictions on this site are relative to mean sea level, so a low water that falls below the local average prints as a negative number — the water is below the average level, not below the sea bed. Official navigation tables usually use a lower zero instead, so the same tide reads as a positive number there. The chart datum guide covers the ladder of zeros in full.

The consequence for the arithmetic is simple: the range is the same whichever datum you use, because shifting both heights by the same amount leaves the difference alone. The individual heights are not, so never take a high from one source and a low from another.

Why some coasts have huge ranges

A bay whose natural period is close to the twice-daily tide resonates with it, and a funnel shape and a wide shelf both amplify the wave further. The starting point is the same everywhere: in the open ocean the astronomical tide is under a metre. Every large range in the world is made at the coast, out of that.

Resonance does the most work. A basin has a natural period at which water sloshes from end to end, set by its length and its depth. Where that period lands near 12 hours 25 minutes, each incoming tide arrives in step with the water already moving, and the two reinforce each other tide after tide. The Bay of Fundy is the textbook case: its natural period sits close to the semidiurnal one, and the result is the biggest tides on Earth.

Funnelling does the rest. A tidal wave running into a bay that narrows and shallows has the same volume of water to move through a smaller and smaller cross-section, and the only direction left is up. A wide continental shelf in front of the coast helps again, because shallow water slows the wave and lets it steepen. Coasts that have all three — a shelf, a funnel and the right resonant period — are the ones that appear on the list below.

The reverse holds too. A nearly enclosed sea with one narrow entrance never receives much of the ocean tide in the first place, and if its basin is the wrong length it cannot amplify what little it does receive. Nothing about the Moon is different over the Mediterranean or the Baltic; those basins simply have no way to build a large tide out of it.

The largest tidal ranges in the world

The figures below are the widely published spring ranges for each coast. They are the size of the tide at its biggest, not an everyday number, and the exact value depends on where in the bay you stand: a range measured at the head of an estuary is considerably larger than one measured at its mouth.

At the other end of the scale, most of the Mediterranean sees under half a metre and the Baltic a few centimetres. For a middling coast, Boston’s mean range is about 2.9 m. Anything under about two metres counts as a small range, and enclosed seas are where you find them.

Nowhere on that list makes its own tide. Every range in it is the same sub-metre ocean wave amplified by the shape of one particular coast — which is why a range quoted for the next harbour along the same shore is not yours.

Tidal range vs tidal coefficient

The range is local metres; the coefficient is a location-free number describing how big the astronomical tide is that day. They answer different questions and are easy to confuse, because both of them get bigger at springs.

• Range is measured at one place, in metres or feet, from one low water to the next high. Two harbours on the same coast will not share it.
• Coefficient is a single number from 20 to 120 for the day, computed from the Moon’s and the Sun’s phase, distance and declination. Every station on the planet shares it, give or take a point or three: the number is sampled at local noon, so two stations in different time zones can print 98 and 100 for the same date. How we compute it is on our how we compute page.

Use them together. The coefficient tells you whether today is a big day or a quiet one anywhere in the world; your station’s own table tells you what that means in metres where you are standing. A coefficient of 100 in the Bay of Fundy and a coefficient of 100 in the Baltic are the same astronomy producing utterly different water. The tidal coefficients guide has the bands and how to read the month strip.

Questions people ask