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Pumped-Hydro Reference

Turn water head into stored energy.

Use reservoir volume and effective head to estimate potential energy, delivered electricity and average output power for a first-pass water-storage concept.

Water volume and effective head

What can a reservoir return as electricity?

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Water storage is gravitational energy expressed as reservoir volume and usable head. It defaults to fresh water at 1,000 kg/m³ and standard Earth gravity; both assumptions can be adjusted without cluttering the main inputs.

Advanced assumptionsFresh water on Earth by default
Try a scale
Delivered energyReady
217.93kWhafter pumping and conversion losses
E = water density × volume × g × head × efficiency
Water-head yield
2.179kWh / m of head
217.93 Wh per m³ of water
Gross potential272.41kWh
Delivered energy217.93kWh
Average power54.48kW

This is a storage-potential estimate. It does not model reservoir shape, water availability, penstock friction, turbines, environmental flows, civil works, evaporation or permitting constraints.

The water battery formulas

A water battery stores energy by lifting water to a higher reservoir and recovers part through a turbine as the water returns. It defaults to fresh-water density and Earth gravity; both assumptions can be adjusted in the calculator.

Potential energy
E = density × volume × g × head
e.g. 1,000 m³ × 1,000 kg/m³ × 9.80665 × 100 m
Energy in kWh
gross kWh = volume × head × 0.002724
e.g. 1,000 m³ × 100 m = 272.4 kWh
Delivered energy
delivered kWh = gross kWh × efficiency
e.g. 272.4 kWh × 80% = 217.9 kWh
Average power
kW = delivered kWh ÷ discharge hours
e.g. 217.9 kWh ÷ 4 h = 54.5 kW

What changes a water-storage result

Reservoir volume
More usable water volume means more moving mass. The calculator treats the stated volume as the water actually available for a generation cycle.
Effective head
The vertical pressure difference that can do useful work. It determines how much energy each cubic metre of water carries.
Round-trip efficiency
Pumps, turbines, generators, transformers and water-path losses reduce the energy returned compared with the ideal potential.
Discharge duration
Duration sets average power, not stored energy. A short release needs larger hydraulic and electrical equipment for the same kWh.

Reference scale: 1,000 m³ of fresh water

Effective headIdeal potential energyDelivered energy at 80% efficiency
100 m272 kWh218 kWh
300 m817 kWh654 kWh
500 m1.36 MWh1.09 MWh

FAQ

How do you calculate water battery energy?

Use E = ρ × V × g × h, where ρ is water density, V is volume, g is gravitational acceleration and h is effective head. Divide joules by 3,600,000 for kWh, then apply system efficiency for delivered energy.

How much energy does one cubic metre of water store?

It depends on height. At 100 metres of effective head, one cubic metre of fresh water has about 0.272 kWh of ideal potential energy. At 80% efficiency, that becomes about 0.218 kWh delivered.

What is effective head in pumped hydro?

Effective head is the usable vertical pressure difference between upper and lower water levels, after allowing for the operating range and hydraulic losses. It is not simply the dam height.

Does this calculate turbine or reservoir design?

No. It is a first-pass potential-energy estimate. A real project needs hydraulic design, flow rate, turbine and pump selection, penstock losses, water availability, civil works, environmental review and permitting.

Keep exploring the physics

Put the reservoir number in context.

Explore effective head, hydraulic losses and pumped-hydro definitions before carrying a first-pass energy estimate into planning.

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