How this instrument works
Hydroelectric power converts the potential energy of water sitting at height into electricity by letting it fall through a turbine, and the amount of power available depends on exactly two physical quantities: how much water is moving (flow rate) and how far it falls (head). More water falling a greater distance carries more energy, in direct proportion to both — double either one and available power doubles with it.
The underlying physics is gravitational potential energy released per second: power equals water density times gravitational acceleration times flow rate times head, giving the theoretical maximum power in the falling water before any losses. Real installations never convert all of that into electricity — friction in the penstock, turbine blade losses, and generator inefficiency all take a cut, which is why the formula includes a combined efficiency term for the turbine and generator together.
This scales from massive utility dams generating gigawatts down to micro-hydro systems that power a single off-grid cabin from a small stream — the same formula applies at every scale, since it's describing the same underlying physics of falling water, just with vastly different flow rates and heads plugged in.
- Enter Water density (kg/m³) — 1000 for fresh water is the standard default and rarely needs changing.
- Enter Gravitational acceleration (m/s²) — 9.81 is standard Earth gravity and is the default.
- Enter Flow rate (m³/s) — the volume of water passing through the turbine per second.
- Enter Head (m) — the vertical drop of water from intake to turbine.
- Enter Turbine + generator efficiency (0-1) — the combined fraction of theoretical power actually converted to electricity, commonly 0.80-0.90 for well-designed systems.
- Read Power output (W) — the electrical power the installation generates under these conditions.
Worked example — 10 m³/s over a 20 m head
A small-hydro installation moves 10 m³/s of water through a 20 m head, with standard water density (1000 kg/m³), standard gravity (9.81 m/s²), and a combined turbine-generator efficiency of 0.85. Power = 1000 × 9.81 × 10 × 20 × 0.85 = 1,667,700 W.
That works out to roughly 1.67 megawatts — enough to supply on the order of a thousand typical homes, illustrating how even a modest flow rate generates substantial power once combined with a meaningful head, since power scales directly with both quantities multiplied together.
Questions
Which matters more for power output, flow rate or head?
Neither inherently — power is directly proportional to both, so doubling either one doubles the output, all else equal. In practice, site geography usually dictates which one an installation has more of: a mountain stream might offer a large head with modest flow, while a wide lowland river offers large flow with very little head, and both can generate comparable power if the product of the two is similar.
Why isn't all the theoretical power actually captured as electricity?
Every stage between falling water and usable electricity loses some energy to friction and inefficiency: water moving through a penstock (pipe) loses energy to pipe friction, the turbine itself can't extract 100% of the water's kinetic energy, and the generator loses a small amount converting mechanical rotation to electrical current. The efficiency term in this calculator bundles all of those losses into one combined figure, typically 0.80-0.90 for a well-designed modern system.
What's a realistic efficiency figure to use for a small or DIY hydro system?
Well-engineered commercial turbines with matched generators commonly reach 0.85-0.90 combined efficiency, but small, DIY, or older/simpler micro-hydro setups (a basic pelton wheel or simple waterwheel generator, for instance) often run meaningfully lower, sometimes 0.50-0.70, due to less refined turbine design and smaller-scale mechanical losses. Using a conservative efficiency estimate avoids overestimating what a modest system will actually deliver.
How is 'head' measured for a real site?
Head is the vertical drop in elevation between where water enters the system (the intake) and where it reaches the turbine, not the length of pipe or channel it travels through, which is often longer than the straight-line vertical drop. It's typically measured with a surveying instrument, GPS elevation readings, or a pressure gauge at the turbine (since static water pressure converts directly to head).
Does flow rate stay constant, or does it vary throughout the year?
For a run-of-river installation without a large reservoir, flow rate typically varies significantly with rainfall and season — often highest during spring snowmelt or wet seasons and lowest during dry summer months. Power output calculated here reflects instantaneous output at whatever flow rate is entered; a full site assessment for an installation would use flow data across the year, not a single figure.