Pumped storage energy calculator
Gravity storage is simple and enormous: it takes a great deal of mass and height to store a useful amount of energy.
kg/m3
%
kW
Usable stored energy
217.93kWh
- Gross stored energy
- 272.41 kWh
- Mass of water
- 1 000 000
- Discharge time at that power
- 0.436 hours
- Flow rate needed
- 0.6373 m3/s
- Days of electricity for one home At 10 kWh a day.
- 21.79
- Equivalent car batteries At 75 kWh each.
- 2.91
Show the working
- Volume of water = 1000
- Height difference = 100
- Fluid density = 1000
- Round-trip efficiency = 80
- Generating power = 500
- Mass of water = 1000 * 1000 = 1 000 000
- energy_j = 1 000 000 * g0 * 100 = 980 665 000
- Gross stored energy = 980 665 000 / 3600000 = 272.407
- Usable stored energy = 272.407 * 80/100 = 217.926
- Discharge time at that power = 500 > 0 ? 217.926 / 500 : 0 = 0.435 851
- Flow rate needed = 0.435 851 > 0 ? 1000 / (0.435 851 * 3600) : 0 = 0.637 323
- Days of electricity for one home = 217.926 / 10 = 21.7926
- Equivalent car batteries = 217.926 / 75 = 2.905 67
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- E = m g h
- usable energy = E x round-trip efficiency
A thousand cubic metres lifted a hundred metres stores 272 kWh — less than four electric car batteries. Gravity storage only works at enormous scale.
Real pumped hydro runs at 70 to 85% round trip, which is competitive with batteries and lasts a century.
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