Tidal Coefficients Explained

What tidal coefficients mean: the 20 to 120 scale, how spring and neap tides relate to the Moon, and why a higher coefficient brings a bigger tidal range.

A tidal coefficient is a single number that summarizes how large a tide will be on a given day. It is widely used in France and other countries that follow the French hydrographic tradition. The coefficient is dimensionless and normally runs from about 20 to 120: the larger the number, the greater the range between high and low water, and the stronger the associated tidal currents.

The 20 to 120 scale

The coefficient compares the day's tidal range to a long-term reference. Several points on the scale have conventional meanings:

• 20 — the smallest tides, near the minimum astronomical range.
• 45 — an average neap tide, when the range is small.
• 70 — a mean tide, roughly the midpoint between neaps and springs.
• 95 — an average spring tide, when the range is large.
• 120 — the largest tides, near the maximum astronomical range.

Why it changes: the Moon

Coefficients rise and fall on the roughly two-week spring-neap cycle. Spring tides, with high coefficients, occur a day or two after each new and full Moon, when the Sun and Moon pull in line and their tidal forces add together. Neap tides, with low coefficients, occur near the first and last quarter Moons, when the Sun and Moon are at right angles and partly cancel.

The Moon's distance matters too. When a spring tide coincides with perigee (the Moon's closest approach to Earth), the coefficient reaches its highest values. The very largest tides tend to cluster near the spring and autumn equinoxes.

What a coefficient does not tell you

The coefficient describes the astronomical range only. It does not include the effect of weather — wind and atmospheric pressure can raise or lower the actual water level regardless of the coefficient. It is also a property of the tide as a whole for that day, not a height in metres or feet at any single location.