Tidal Prism & Spring/Neap Tidal Range Calculator
Calculate tidal prism, spring and neap ranges, inlet discharge and O'Brien equilibrium area.
Last reviewed by the myCalculator Editorial Team
Input Parameters
The minimum flow area at the inlet throat, below mean sea level.
Calculation Results
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Formula & How Tidal Prism & Spring/Neap Tidal Range Calculator Works
The tidal prism is the volume of water exchanged between high and low tide, and it governs flushing, water quality and inlet stability. Spring tides occur near new and full moon when solar and lunar forcing align, producing the largest range; neaps occur at the quarters when the two oppose. O'Brien's empirical relationship links the equilibrium inlet cross-section to the tidal prism — an inlet smaller than equilibrium scours wider, while a larger one shoals and infills. Worked example: spring tides with a high of 2.1 m and a low of 0.3 m give a range of 1.8 m. Over a 12 km² basin, the tidal prism is 12,000,000 × 1.8 = 21.6 million m³. O'Brien's relationship, A = 4.69 × 10⁻⁴ × P^0.85, then gives a stable inlet cross-section of about 804 m², close to the 850 m² entered, which suggests an inlet in rough equilibrium. A much smaller area suggests a risk of siltation, and a much larger area suggests scour.
- Enter Mean High Water Springs (m) (m): Input your target parameter value.
- Enter Mean Low Water Springs (m) (m): Input your target parameter value.
- Enter Mean High Water Neaps (m) (m): Input your target parameter value.
- Enter Mean Low Water Neaps (m) (m): Input your target parameter value.
- Enter Tidal Basin Surface Area (km²) (km²): Input your target parameter value.
- Enter Inlet Throat Cross-Section (m²) (m²): Input your target parameter value.
- Apply Formula: Calculate using
P = Basin Area × Tidal Range | Q_peak = (P / T_half) × π/2 | O'Brien: Ac = 4.69e-4 P^0.85. - Review Results: View exact computed answers, metrics, and worked mathematical proofs.
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Frequently Asked Questions (FAQs)
What is a tidal prism?
The volume of water that flows into and out of a bay, estuary or inlet between low and high tide. It equals the basin surface area multiplied by the tidal range, and drives flushing and inlet stability.
Why are spring tides bigger than neap tides?
At new and full moon the sun and moon align so their tidal forces add, producing the largest range. At the quarter moons the forces act at right angles and partially cancel, giving the smaller neap range.
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