In short: a rule of thumb for a well-run small hydro site is about 8.3 kW for every 1 m³/s of flow times 1 m of head, at a typical 85% combined efficiency. For example, 2 m³/s dropping 20 m produces about 333 kW — enough, at a typical 40% capacity factor, to supply roughly 108 average U.S. homes over a year. Use the calculator above for your own flow, head and efficiency.
This is an engineering planning estimate based on the flow, head and efficiency you supply. Confirm site-specific numbers with a hydrology study, a turbine manufacturer's curve and a licensed engineer before design or construction.
How to calculate hydroelectric power output
Hydroelectric power comes from converting the potential energy of falling water into electricity. How much power is available depends on how much water is moving (flow rate) and how far it falls (head). A turbine and generator then convert only part of that raw energy into electricity — the rest is lost to friction, turbulence and electrical resistance, which is why efficiency matters.
Worked example. Take 2 m³/s of flow across a 20 m net head, at 85% combined efficiency. Multiply: 999.7 kg/m³ × 9.80665 m/s² × 2 m³/s × 20 m × 0.85 = 333,326 W, or 333.3 kW. Convert to horsepower (1 hp = 745.7 W) and that is about 447 hp. That single multiplication, repeated for whatever flow and head you enter, is all the calculator is doing.
Power vs. energy, in one line. Power (kW) is the rate of generation right now. Energy (kWh or MWh) is power sustained over time. A site rated at 333 kW does not generate that much every hour of the year — streamflow varies with the seasons — which is why the calculator separates instantaneous power from annual energy using a capacity factor.
Why flow rate and head change the answer
Flow rate is how much mass moves through the turbine each second; head is how far that mass falls before it gets there. Both enter the formula in exactly the same way — power is directly proportional to each of them individually, so doubling either one doubles the power. What differs is how sites are actually developed: increasing head usually means building a taller dam or a longer penstock up a hillside, while increasing flow usually means a larger river or a wider intake. Because head can often be gained through cheaper civil works (a long pipe up a slope) than flow (which is fixed by the watershed), many small hydro developers focus on maximizing usable head first.
Efficiency, the third term, is where turbine selection matters most. A poorly matched turbine — say, a Pelton wheel on a low-head, high-flow river, where it wasn't designed to operate — can lose 20–30 percentage points of potential output compared with a properly matched Kaplan or Francis unit at the same site. See Streamflow Calculator and Watershed Runoff Calculator to estimate available flow from a stream or catchment before sizing a turbine.
Typical power output by flow and head
Illustrative power output at 85% combined efficiency and 999.7 kg/m³ water density — the same assumptions the calculator uses above. Use it to sanity-check the scale of a site before entering your own numbers.
| Flow rate | Net head | Power output |
|---|---|---|
| 0.1 m³/s (small stream) | 10 m | 8.3 kW |
| 0.5 m³/s | 10 m | 41.7 kW |
| 1 m³/s | 25 m | 208 kW |
| 2 m³/s | 50 m | 833 kW |
| 5 m³/s | 50 m | 2,083 kW (2.08 MW) |
| 10 m³/s (utility scale) | 100 m | 8,333 kW (8.33 MW) |
Typical turbine efficiency by type
Combined turbine-and-generator efficiency varies by turbine family and how well it matches the site's head and flow. Use these as a starting point for the efficiency field above.
| Turbine type | Best suited to | Typical efficiency |
|---|---|---|
| Waterwheel | Very low head | 50–70% |
| Crossflow (Banki) | Low to medium head, wide flow range | 60–80% |
| Turgo | Medium to high head | 80–88% |
| Pelton | High head, low flow | 85–90% |
| Francis | Medium head | 90–95%* |
| Kaplan / propeller | Low head, high flow | 85–93% |
*Turbine-only efficiency; combined with a generator, whole-system efficiency typically runs a few points lower, around 85–90%.
Worked examples
Off-grid cabin stream
5.1 kW
A small stream delivering 50 L/s (0.05 m³/s) across a 15 m drop, with a modest 70%-efficient turbine, produces about 5.1 kW (6.9 hp) — enough to run lighting, a well pump and small appliances.
Community-scale run-of-river
333 kW
2 m³/s across a 20 m net head at 85% efficiency produces about 333 kW (447 hp). At a 40% capacity factor, that is roughly 1,168 MWh a year — about 108 average U.S. homes' worth of electricity.
Small utility-scale plant
5.29 MW
15 m³/s across a 40 m head with a well-matched 90%-efficient Kaplan turbine produces about 5,294 kW (7,099 hp). At a 45% capacity factor, annual output is roughly 20,869 MWh — about 1,934 homes' worth.
What else affects the result
Penstock and intake losses. Friction in the pipe or channel carrying water to the turbine reduces net head below the site's gross elevation drop. Longer, narrower or rougher penstocks lose more. Our Darcy-Weisbach and Hazen-Williams calculators estimate this friction loss so you can enter a realistic net head.
Tailwater elevation. Net head is measured to the water surface downstream of the turbine, not to the streambed. High water downstream during floods can reduce usable head at exactly the times flow is highest.
Seasonal flow variability. Most streams run higher in spring snowmelt or rainy seasons and lower in late summer. The capacity factor in the advanced section captures this — a site with highly variable flow needs a lower capacity factor than one fed by a steady reservoir release.
Debris and sediment. Trash racks, intake screens and sediment buildup can gradually restrict flow and reduce output between maintenance cycles, on top of the losses already modeled here.
Frequently asked questions
How much electricity can a small hydroelectric system produce?
Using P = ρgQHη, a modest site with 1 m³/s of flow across a 10 m drop at 85% efficiency produces about 83 kW. Running at a typical 40% capacity factor for a full year, that is roughly 292,000 kWh — enough for about 27 average U.S. homes. Larger flow or head scales the output up linearly.
What is the difference between gross head and net head?
Gross head is the total elevation drop from the water intake to the turbine. Net head is what is left after subtracting losses in the penstock, trash racks and intake structure. This calculator uses net head, because that is the head actually available to turn the turbine.
What efficiency should I assume for a hydro turbine?
Combined turbine-and-generator efficiency typically runs 60–70% for simple waterwheels and crossflow units, 80–88% for Pelton and Turgo turbines on high-head sites, and 85–93% for modern Francis or Kaplan turbines on medium- and low-head sites. 85% is a reasonable default for a well-designed small hydro system.
How is annual energy output different from instantaneous power?
Power in kW is the rate of generation at one specific flow and head. Annual energy in MWh depends on how much of the year the site runs near that output, called the capacity factor. Streamflow varies with the seasons, so annual energy is always less than power times 8,760 hours.
What's the difference between this calculator and the Micro-Hydro Power Calculator?
Both use the same physics. This calculator is set up for general and utility-scale sites, with flow in cubic meters or feet per second and output shown up to megawatts. The Micro-Hydro Power Calculator is scaled for household and off-grid streams, with smaller flow units and a focus on watts rather than megawatts.
Does water temperature affect hydroelectric power output?
Only slightly. This calculator assumes a fixed density of 999.7 kg/m³, typical of cold stream and river water around 10 °C. Density changes less than 2% across the full range from freezing to warm summer water, a far smaller effect than flow rate, head or turbine efficiency.
Sources & references
- U.S. Department of Energy, Water Power Technologies Office. Hydropower Basics.
- U.S. Bureau of Reclamation. Hydroelectric Power (fact sheet).
- U.S. Energy Information Administration (2022). Frequently Asked Questions: How much electricity does an American home use?
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)