What this calculator does
Hydroelectric power is the product of how far the water falls and how much of it falls per second, scaled by how much of that the turbine converts. The relationship is linear in both: doubling the head doubles the power, and so does doubling the flow. Two very different sites can therefore produce the same output, one a high mountain drop with a small stream and the other a large river with a modest fall.
Efficiency is high compared with most other generation. Large hydro turbines routinely convert over 90% of the water energy to electricity, against roughly 40% for a thermal plant, because the energy is already mechanical and does not have to pass through heat first.
The formula
The available power is the density of water times gravity times the head times the flow rate, which gives watts directly when the head is in metres and the flow in cubic metres per second. Multiplying by the turbine efficiency gives the electrical output. The calculation uses 998 kg/m³ for water and 9.81 m/s² for gravity.
| Term | Meaning |
|---|---|
| Head | The vertical distance the water falls, in metres. Gross head is the raw drop; net head deducts losses in the pipework. |
| Flow rate (Q) | Volume of water passing per second, in cubic metres per second. |
| Efficiency (η) | The share of the water energy converted to electricity, typically 85 to 95% for large turbines and lower for small ones. |
| ρg | Water density times gravity, about 9,790 newtons per cubic metre, the constant linking head and flow to power. |
The inputs explained
| Field | What to enter |
|---|---|
| Turbine efficiency (%) | Turbine efficiency as a percentage. 85% is a reasonable default; large modern installations reach into the low 90s and micro-hydro is often nearer 60 to 70%. |
| Head (fall height) (m) | The head in metres. Use net head if the penstock losses are known, since those can be several percent over a long run. |
| Flow rate (m³/s) | Flow rate in cubic metres per second. One cubic metre per second is 1,000 litres per second. |
When to use it
Sizing a micro-hydro installation
A stream with a known drop and flow gives a first estimate of what is available, which is usually enough to decide whether a scheme is worth pursuing further.
Comparing two potential sites
Head and flow trade off directly against each other, so a site with ten times the drop and a tenth of the flow yields the same power. Which is preferable comes down to construction cost rather than output.
Checking a seasonal range
Flow varies far more than head across a year. Running the same head at summer and winter flows shows the output range a scheme would actually deliver rather than its best case.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does head affect hydroelectric output?
A fixed flow rate of 2 cubic metres per second across a range of heads.
| Head | Power output | Output in MW |
|---|---|---|
| 10 m | 166.44 kW | 0.1664 MW |
| 25 m | 416.09 kW | 0.4161 MW |
| 50 m | 832.18 kW | 0.8322 MW |
| 100 m | 1,664.36 kW | 1.664 MW |
| 200 m | 3,328.73 kW | 3.329 MW |
Questions
What is the difference between gross and net head?
Gross head is the raw vertical drop from intake to turbine. Net head deducts friction losses in the penstock, which rise with pipe length and fall sharply with pipe diameter. Using gross head overstates output, and on a long small-bore pipe the difference can be 10% or more.
How efficient are hydro turbines?
Large installations commonly exceed 90%, which is high because the energy is already mechanical and never passes through a heat cycle. Small and micro-hydro systems do considerably worse, often 60 to 70%, since the losses that matter scale down less favourably than the output does.
Which matters more, head or flow?
Neither, arithmetically. Power is proportional to their product, so the same output comes from any combination that multiplies to the same figure. Practically, high head is usually cheaper to exploit, because a small pipe and a compact turbine cost far less than the civil works a large low-head flow requires.
Does this account for seasonal variation?
No, it gives the output at the flow you enter. Since flow can vary by an order of magnitude between wet and dry seasons, a single figure is a snapshot. Running the calculation across the expected range gives a far more honest picture than one annual average flow.
For power from wind rather than water, see the wind turbine power calculator. For how the carbon intensity of energy feeds into total emissions, see the Kaya identity calculator.