Calculate tidal range or reverse-solve signed high and low water levels, with an entered-pair midpoint, vertical quarter-range levels and a second-cycle comparison. Use compatible vertical datums; these arithmetic outputs are not tide-time or current forecasts.
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Tidal Range Formula
The following formula is used to calculate the tidal range.
Variables:
- TR is the tidal range (meters)
- HT is the high tide level (meters)
- LT is the low tide level (meters)
Subtract low-water level from high-water level for the same location and tide cycle on a common vertical datum. Signed levels may be negative, but high water must be at or above low water and the resulting range is nonnegative. The calculator’s midpoint is only the midpoint of the entered pair, not the long-term Mean Tide Level tidal datum. Its 25% and 75% levels are vertical fractions above low water, not timestamps or current predictions. Use official local predictions and safety information for navigation.
What is Tidal Range?
Tidal range is the vertical difference between the water surface at high tide and low tide at a specific location. It is driven primarily by the gravitational pull of the Moon and, to a lesser extent, the Sun acting on Earth’s ocean water. Because the Moon is roughly 390 times closer to Earth than the Sun, its tide-generating force is about 2.2 times greater despite the Sun’s far larger mass. The interplay between these two bodies, combined with Earth’s rotation, produces the semi-diurnal (two highs and two lows per day) or diurnal (one high and one low per day) tidal patterns observed at different coastlines.
Tidal range is not constant. It changes on daily, monthly, and even annual cycles depending on the relative positions of the Moon, Sun, and Earth, as well as local geography. Narrow bays, funnel-shaped estuaries, and continental shelf width all amplify or dampen the astronomical tidal signal, producing dramatically different ranges at locations only a few hundred kilometers apart.
Tidal Range Classifications
Microtidal, mesotidal and macrotidal are common descriptive tidal-range categories. State the averaging statistic and observation period used by the source study; mean range and mean spring range are different summaries. A single high/low pair entered in this calculator does not establish a coastline’s long-term tidal regime.
| Classification | Reference Tidal Range | Typical Coastlines | Dominant Processes |
|---|---|---|---|
| Microtidal | Less than 2 m (6.6 ft) | Mediterranean, Baltic, Gulf of Mexico, Caribbean | Wave-dominated; barrier islands, beach ridges |
| Mesotidal | 2 to 4 m (6.6 to 13.1 ft) | U.S. East Coast, most of Australia, North Sea | Mixed wave and tidal; tidal inlets, salt marshes |
| Macrotidal | Greater than 4 m (13.1 ft) | Bay of Fundy, Bristol Channel, Cook Inlet | Tide-dominated; wide tidal flats, funnel estuaries |
Additional descriptive categories and thresholds appear in the literature. Check the study’s stated convention and range statistic instead of treating these categories as a classification of one observed tide cycle.
Coastal tidal-range examples
Coastal geometry can amplify tidal ranges through resonance, funneling or shoaling. The figures below are illustrative unit comparisons combining different statistics, not verified official station records or a comparable ranking. For site-specific work, use official records with their stated datum, observation period and statistical definition.
| Location | Country | Example range | Larger example range |
|---|---|---|---|
| Bay of Fundy (Burntcoat Head) | Canada | 11.7 m (38.4 ft) | 16.3 m (53.5 ft) |
| Ungava Bay (Leaf Basin) | Canada | 9.8 m (32.2 ft) | ~12.5 m (41 ft) |
| Severn Estuary (Avonmouth) | United Kingdom | 12.2 m (40 ft) | ~15 m (49 ft) |
| Mont-Saint-Michel | France | 10.5 m (34.4 ft) | ~14 m (46 ft) |
| Cook Inlet (Anchorage) | United States | 9.2 m (30 ft) | ~12 m (39 ft) |
| Rio Gallegos | Argentina | 8.1 m (26.6 ft) | ~10.4 m (34 ft) |
The Bay of Fundy holds the record largely because of tidal resonance: the bay’s natural oscillation period of roughly 12.5 hours nearly matches the dominant semi-diurnal tidal period of 12.42 hours. Each incoming tide reinforces the previous oscillation, progressively building the range.
Spring Tides vs Neap Tides
Tidal range at any location follows a roughly 14.8-day cycle driven by the relative alignment of the Sun and Moon.
Spring tides occur at new moon and full moon when the Sun, Moon, and Earth are approximately aligned (syzygy). These alignments generally produce larger tidal ranges, but the local increase is not a universal fixed percentage of mean range. The term “spring” has no connection to the season; it derives from an Old English word meaning to rise or swell.
Neap tides occur at first quarter and third quarter moon when the Sun and Moon are at roughly 90 degrees relative to Earth (quadrature). These alignments generally produce smaller tidal ranges, but the local decrease is not a universal fixed percentage of mean range. The calculator’s range ratio is an ordinary comparison of two ranges. The harmonic tidal form factor uses (K1 + O1) / (M2 + S2), the relevant constituent amplitudes; it is not the spring-range to neap-range ratio.
There is also a perigean spring tide that occurs when the Moon is at perigee (closest approach to Earth, about 356,500 km) during a spring tide alignment. Perigean spring tides can raise high-water levels, but annual maxima also depend on local and seasonal conditions and need not be perigean. The term “king tides” is informal. The Moon’s elliptical orbit causes its distance from Earth to vary by about 50,000 km over a month, directly affecting tidal force magnitude.
The Rule of Twelfths
The Rule of Twelfths is an illustrative heuristic for roughly regular semidiurnal rise or fall over an assumed six-interval period. It does not replace official tide predictions or local safety information. The calculator’s quarter-range heights do not implement this time sequence or predict tide/current timing.
The rule divides the total tidal range into 12 equal parts and distributes them across 6 hourly intervals in a 1:2:3:3:2:1 pattern. In the first hour after low tide, the water rises by 1/12 of the total range. In the second hour, it rises by 2/12. The third and fourth hours each see 3/12 of the range, meaning half the total range change occurs in the middle two hours. The fifth hour adds 2/12, and the final hour adds 1/12.
For example, at a location with a 6-meter tidal range, each twelfth equals 0.5 m. One hour after low tide the water has risen 0.5 m; after two hours, 1.5 m; after three hours, 3.0 m (half the range); after four hours, 4.5 m; after five hours, 5.5 m; and after six hours, the full 6.0 m. This approximation works best at locations with regular semi-diurnal tides and should not replace official tide tables for critical navigation.
Tidal Range and Energy Generation
Tidal range directly determines the energy potential of a tidal barrage or lagoon. The theoretical energy per tidal cycle from a barrage is proportional to the basin surface area multiplied by the square of the tidal range (E = 0.5 x rho x g x A x R squared), which means doubling the range quadruples the available energy. This is why most tidal power projects target macrotidal sites.
The world’s two largest commercial tidal power plants are the Sihwa Lake Station in South Korea (254 MW, operational since 2011) and the La Rance Barrage in France (240 MW, operational since 1966). La Rance was commissioned in 1966 and remains in service, illustrating the long service life of a maintained tidal power plant. Canada’s Annapolis Royal station was North America’s first tidal plant; it had a nameplate capacity of about 20 MW and ceased generation in January 2019.
Technical and extractable tidal-energy capacity depend on site conditions, technology, environmental constraints and development assumptions. Tidal range alone does not determine a site’s practical project capacity. Scotland’s MeyGen has an operational 6 MW first phase and a further 59 MW phase supported by Contracts for Difference; its operator lists up to 398 MW as longer-term potential, subject to further consents and development. Unlike barrage systems that rely on tidal range, tidal stream turbines harness tidal current velocity, but both technologies benefit from locations with large tidal ranges since greater ranges generally produce stronger currents.
Factors That Influence Tidal Range
Tidal range at a specific location is shaped by a combination of astronomical, geographic, and meteorological factors. Astronomical forces set the baseline through the gravitational interactions of the Moon and Sun with Earth, but local geography often amplifies or diminishes the signal by an order of magnitude.
Coastal geometry: Funnel-shaped bays and estuaries compress the incoming tidal wave into a narrowing channel, forcing the water level higher. The Bay of Fundy and the Severn Estuary are textbook examples of this amplification. Conversely, open ocean islands and straight coastlines typically exhibit smaller ranges.
Continental shelf width: Broad, shallow continental shelves create friction that slows the tidal wave, often increasing local range through energy piling. The North Sea and the Yellow Sea both experience amplified ranges due to their extensive shallow shelves.
Basin resonance: When the natural oscillation period of a bay or sea matches the tidal period (approximately 12.42 hours for the dominant M2 constituent), resonance occurs and ranges grow dramatically. This is the primary driver of the extreme tides in the Bay of Fundy.
Meteorological effects: Sustained onshore winds and low barometric pressure can produce storm surges that temporarily add 1 to 3 meters to the predicted high tide. Conversely, high-pressure systems and offshore winds suppress the tide. These non-astronomical contributions are sometimes called the “meteorological tide” or “surge residual.”
Local tidal pattern: Astronomical constituents, lunar declination and the response of the local basin all affect the observed pattern. Check local station records and predictions rather than using latitude alone to infer range, diurnal inequality or current timing.
