Aquifer Storativity Calculator — Confined Aquifer
Solve the confined-aquifer storage relation S = Ss · b for any of its three unknowns — storativity, specific storage or aquifer thickness — with step-by-step math, a live cross-section schematic, and companion metrics including water released from storage and aquifer compressibility.
Thicker aquifer → higher S
Storativity scales linearly with thickness. A 100 m confined sandstone has ten times the storativity of a 10 m one, because ten times as much compressible aquifer volume responds to each unit of head decline.
Compressibility sets Ss
Specific storage depends on aquifer-matrix compressibility α and porosity n through Ss = ρg(α + nβ). Soft, poorly-cemented sediments have high α and high Ss; hard crystalline rock has low α and low Ss.
Confined vs. unconfined
Confined storativity (10⁻⁵ – 10⁻³) is roughly 100 to 10,000 times smaller than unconfined specific yield (10⁻² – 10⁻¹). In a confined aquifer, water comes from compression of the matrix and expansion of water — not from draining pores.
Water released per unit head
Because S is dimensionless, 1 m of head decline over 1 km² of confined aquifer releases S × 10⁶ m³ of water. That is why confined storage is small per unit area but enormous over regional scales.
How to Use This Calculator
The confined-aquifer storage relation links three quantities: specific storage Ss, aquifer thickness b, and storativity S. Pick which one you want the tool to solve, then fill in the other two.
1. Choose what to solve for
Pick S (storativity from Ss and b), Ss (specific storage from S and b), or b (thickness from S and Ss) — the tool rearranges the formula automatically.
2. Pick a quick preset, or type your own
Use a preset pill for common specific-storage values (10⁻⁶–10⁻⁴ m⁻¹), thicknesses (10–250 m) or storativities (10⁻⁵–5×10⁻³), or drag the log-scale slider to any value.
3. Read the result and the schematic
The result card shows the solved value in scientific notation plus a classification of the aquifer. The live cross-section below the calculator shows the aquifer between two aquitards, with the well, water flow and thickness labelled.
4. Check the thickness curve
The chart plots storativity against aquifer thickness at your specific storage, with reference lines at S = 10⁻⁴ and S = 10⁻³ so you can see immediately where your aquifer sits.
5. Switch to Advanced for more depth
Advanced mode adds a 1 % sensitivity check plus water released per unit area, compressibility estimate, barometric efficiency and an equivalent field-scale figure.
6. Convert to real volumes, or copy the result
Use the water-released converter further down the page to turn storativity into an actual volume of water for a given area and head decline, or "Copy result" to grab the solved value.
What This Tool Offers
Built around the fundamental confined-aquifer storage relation S = Ss · b — the parameter that converts a measured water-level decline into the volume of water actually produced from a confined aquifer.
Solve in three directions
Go from specific storage and thickness to storativity, or work backwards from a storativity to either Ss or b.
Quick presets
One-click values for specific storage (10⁻⁶ to 10⁻⁴ m⁻¹), aquifer thickness (10 to 250 m) and storativity (10⁻⁵ to 5×10⁻³).
Live cross-section
A confined-aquifer schematic showing the aquifer sandwiched between two impermeable aquitards, with a pumping well, water-release arrows and thickness label.
Thickness curve
Storativity plotted against thickness at your specific storage, with reference lines at S = 10⁻⁴ and S = 10⁻³ to anchor the result.
Full companion metric set
Advanced mode reports water released per unit area, per km², matrix compressibility and barometric efficiency estimates.
Water-released converter
Turn storativity into an actual volume of water released for any chosen area and head decline, with a one-click preset to 1 km² and 1 m of drawdown.
Reference Tables & Conversions
A water-released converter, plus lookup tables for typical storativity, specific storage and the relation between storativity and field quantities.
Water released from storage
Storativity Classification — Confined Aquifers
Qualitative ranges used in hydrogeology to describe the storage coefficient of a confined aquifer. Confined S is fundamentally different from unconfined specific yield.
| Storativity S | Class | Typical material |
|---|---|---|
| < 10⁻⁵ | Very low | Tight crystalline rock, well-cemented aquitard |
| 10⁻⁵ – 10⁻⁴ | Low | Fractured granite, dense limestone |
| 10⁻⁴ – 10⁻³ | Moderate | Typical confined sandstone |
| 10⁻³ – 5×10⁻³ | High | Unconsolidated confined sand |
| 5×10⁻³ – 10⁻² | Very high | Soft, compressible confined sediment |
| > 10⁻² | Unusually high | Very thick, highly compressible clay-rich unit |
Typical Specific Storage & Storativity of Confined Materials
| Material | Specific storage Ss (m⁻¹) | Thickness b (m) | Storativity S |
|---|---|---|---|
| Fractured granite | 10⁻⁷ – 10⁻⁶ | 50 – 200 | 10⁻⁵ – 2×10⁻⁴ |
| Dense limestone | 5×10⁻⁷ – 5×10⁻⁶ | 20 – 100 | 10⁻⁵ – 5×10⁻⁴ |
| Confined sandstone | 10⁻⁶ – 10⁻⁵ | 20 – 200 | 10⁻⁴ – 10⁻³ |
| Unconsolidated sand | 10⁻⁵ – 10⁻⁴ | 10 – 100 | 10⁻⁴ – 10⁻² |
| Confined clay / silt | 10⁻⁴ – 10⁻³ | 5 – 50 | 10⁻³ – 10⁻² |
Storativity vs. Specific Storage × Thickness
| Ss (m⁻¹) | b = 10 m | b = 50 m | b = 100 m | b = 500 m |
|---|---|---|---|---|
| 10⁻⁶ | 10⁻⁵ | 5×10⁻⁵ | 10⁻⁴ | 5×10⁻⁴ |
| 10⁻⁵ | 10⁻⁴ | 5×10⁻⁴ | 10⁻³ | 5×10⁻³ |
| 10⁻⁴ | 10⁻³ | 5×10⁻³ | 10⁻² | 5×10⁻² |
| 10⁻³ | 10⁻² | 5×10⁻² | 10⁻¹ | 5×10⁻¹ |
What Does S = Ss · b Measure?
Storativity — also called the storage coefficient — is the volume of water that a confined aquifer releases from storage per unit surface area per unit decline in hydraulic head. It is dimensionless, because it is a volume of water divided by a volume of aquifer per unit head change. Together with transmissivity, storativity is one of the two parameters that fully define the behaviour of a confined aquifer in the Theis and Cooper-Jacob well-test solutions.
Storativity Formula
The defining relationship for a confined aquifer is:
Rearranged to solve for the two other variables:
b = S / Ss
The specific storage itself derives from material compressibility and porosity:
where ρw is water density, g is gravitational acceleration, α is aquifer-matrix compressibility, n is porosity and β is water compressibility (≈ 4.4 × 10⁻¹⁰ Pa⁻¹).
Storativity Variables
| Symbol | Meaning | Units / notes |
|---|---|---|
| S | Storativity (storage coefficient) | Dimensionless; volume of water per unit area per unit head decline |
| Ss | Specific storage | m⁻¹; volume of water per unit aquifer volume per unit head decline |
| b | Aquifer thickness | m; saturated thickness of the confined aquifer |
| α | Aquifer-matrix compressibility | Pa⁻¹; typically 10⁻¹⁰ to 10⁻⁸ |
| β | Water compressibility | Pa⁻¹; ≈ 4.4 × 10⁻¹⁰ |
| n | Porosity | Dimensionless; typically 0.05 – 0.35 |
How Aquifer Thickness Affects Storativity
Storativity scales linearly with thickness. This is the defining structural difference between a confined and an unconfined aquifer. In an unconfined aquifer, specific yield is a material property independent of thickness — all of the drainable pore space lies within the fluctuating water table. In a confined aquifer, however, the entire saturated thickness is under pressure, so all of it compresses when head declines. Doubling the thickness doubles the storativity, and this is why even a modest specific storage of 10⁻⁵ m⁻¹ in a 100 m thick sandstone produces a storativity of 10⁻³ — large enough to matter on regional scales.
Storativity Calculation Examples
S = Ss · b = 10⁻⁵ × 30
S = 3.000 × 10⁻⁴ (dimensionless)
Ss = S / b = 5 × 10⁻⁴ / 50
Ss = 1.000 × 10⁻⁵ m⁻¹
b = S / Ss = 2 × 10⁻³ / 10⁻⁵
b = 200 m
Frequently Asked Questions
Storativity is the volume of water that a confined aquifer releases from storage per unit surface area per unit decline in hydraulic head. It is dimensionless. A storativity of 10⁻³ means that a 1 m drop in head over 1 m² of aquifer releases 10⁻³ m³ (1 litre) of water.
Because the water comes from entirely different mechanisms. In an unconfined aquifer, a decline in the water table drains pore space under gravity — releasing up to 30 % of the pore volume. In a confined aquifer, the aquifer remains fully saturated; water is released only by compression of the matrix and expansion of the water itself, which is a much weaker effect. Storativity values of 10⁻⁵ to 10⁻³ are typical for confined aquifers versus 10⁻² to 10⁻¹ for unconfined.
From pumping-test analysis. The Theis and Cooper-Jacob methods fit the observed drawdown versus time at an observation well to a theoretical curve, yielding both transmissivity T and storativity S. Storativity is also estimated from tidal efficiency, barometric efficiency and earth-tide analyses in some settings.
Yes, weakly. The expression Ss = ρg(α + nβ) shows that Ss increases linearly with porosity through the nβ term, but in most rocks the matrix-compressibility term α dominates. So a high-porosity sandstone may have only a modestly larger Ss than a lower-porosity one unless its matrix is also more compressible.
It can be approximated by measuring the compressibility of a core sample and combining it with porosity and water compressibility in the relation Ss = ρg(α + nβ). But core-scale measurements often miss fractures and larger-scale heterogeneities, so field estimates from pumping tests are usually preferred.
Yes. Because both matrix compressibility and porosity depend on effective stress, storativity typically decreases as an aquifer is dewatered and effective stress rises. Long-term pumping can therefore produce a smaller apparent storativity than the value measured early in a test — a well-known effect in over-pumped confined aquifers.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| S | Storativity (storage coefficient) | |
| Ss | Specific storage | 1/m |
| b | Aquifer thickness | m |
What it means
Storativity (S) is a dimensionless parameter that measures the amount of water released from or taken into storage in a confined aquifer per unit change in hydraulic head, per unit area. It is the product of specific storage (Ss) and the aquifer thickness (b). Storativity is a key parameter in transient groundwater flow modeling and is used in pumping test analysis to determine aquifer properties. Understanding storativity is essential for predicting water level changes, for groundwater resource evaluation, and for managing aquifer storage and recovery systems.
Worked example
Aquifer Storativity – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Ss (1/m) | 1.0e-5 |
| b (m) | 20 |
| Parameter | Value |
|---|---|
| Ss | 3.0e-5 |
| b | 40 |
Common mistakes
- Storativity S: S = Ss·b – for confined aquifers.
- Specific storage Ss: Volume of water released per unit volume of aquifer per unit head change – in 1/m.
- b: Aquifer thickness – in metres.
- Units: S is dimensionless – Ss (1/m) × b (m) = dimensionless.
- For unconfined aquifers: Storativity approximates specific yield (Sy) – not this formula.
Applications
Aquifer storativity (confined), S = Ss·b, is the volume of water released from storage per unit decline in head per unit area, where Ss is specific storage and b is aquifer thickness. This parameter is essential for transient groundwater flow modelling and for predicting water‑level changes in response to pumping. Hydrogeologists use storativity to evaluate the response of aquifers to stresses, to design water‑supply systems, and to assess subsidence potential. By measuring S, professionals can manage groundwater resources effectively, especially in areas with high pumping demands. Understanding storativity is crucial for sustainable groundwater management and for avoiding environmental degradation.
- Transient groundwater modelling and flow prediction
- Analysis of aquifer response to pumping and recharge
- Assessment of land subsidence and compaction
- Design of aquifer storage and recovery (ASR) projects
- Environmental impact assessment of groundwater development
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