Hydroelectric Power Calculator
Enter your flow rate and head (or channel velocity for kinetic turbines) to find the electrical power output of a hydroelectric installation. Choose between a dam turbine (gravitational head), a run-of-river or tidal turbine (kinetic energy), and set your turbine efficiency. The calculator returns power in kilowatts, annual energy in MWh, and an optional revenue estimate. Results update as you type.
Formula
Worked example
A dam turbine with flow rate Q = 10 m3/s, head H = 20 m and efficiency 85%: P = 0.85 x 998 x 9.807 x 20 x 10 = 1,661 kW. Over 330 operating days: E = 1,661 x (330 x 24) = 13,135 MWh/yr. At USD 0.10/kWh that is USD 1,313,500/yr in gross revenue.
How hydroelectric power is calculated
Hydroelectric power generation converts the energy stored in moving or elevated water into electricity. For a dam or penstock installation the governing formula is P = eta x rho x g x H x Q, where eta is turbine efficiency (typically 0.80-0.93 for modern Francis and Pelton turbines), rho is water density (998 kg/m3 at 20 C), g is gravitational acceleration (9.807 m/s2), H is the net head in metres, and Q is the volumetric flow rate in m3/s. The result is in watts; divide by 1,000 to get kilowatts. For run-of-river and tidal turbines with no significant head, the formula switches to the kinetic form P = 0.5 x eta x rho x A x v3, where A is the swept cross-sectional area and v is water velocity. The cubic dependence on velocity is important: doubling water speed increases available power eightfold.
Net head versus gross head
The gross head of a hydro site is the vertical elevation difference between the water intake and the turbine. The net head, which is what actually drives the turbine, is smaller because it subtracts losses from pipe friction (penstock losses), entrance and exit losses, and the velocity head at the turbine exit. A good rule of thumb is that net head is typically 85-95% of gross head for well-designed penstocks. Site surveys with pressure gauges or flow models give the most reliable net head figures. Entering gross head without the friction correction will overestimate power output by 5-15%.
Turbine efficiency and the Betz limit
Modern reaction turbines (Francis, Kaplan) reach efficiencies of 88-94% at their design flow point, while impulse turbines (Pelton, Turgo) peak at 85-92%. At partial flows, efficiency drops, so plants are sometimes fitted with multiple smaller turbines to maintain efficiency across seasonal flow variations. For kinetic (run-of-river and tidal) turbines the Betz limit of 59.3% is a theoretical ceiling on how much of the water stream's kinetic energy can be extracted, because the turbine must leave some velocity in the water for it to keep flowing. This calculator automatically caps kinetic efficiency at the Betz limit. Real tidal turbines achieve roughly 35-45% of kinetic energy extraction when mechanical and electrical losses are included.
Annual energy and revenue projection
Electrical power output (kW) multiplied by operating hours gives annual energy in kWh. Full-load hours for a run-of-river plant in a temperate climate are typically 3,000-5,000 hours per year; dam plants with large reservoirs can reach 6,000-8,000 hours. Feed-in tariffs and power purchase agreement rates for small hydro vary widely: USD 0.05-0.15/kWh in North America, EUR 0.06-0.12/kWh in Europe. The revenue output in this calculator is a gross estimate before capital repayment, operations and maintenance (typically 1-2% of capital cost per year), and grid connection costs.
Hydropower installation size classifications
| Class | Capacity range | Typical application | Flow context |
|---|---|---|---|
| Pico hydro | < 5 kW | Remote cabins, water pumping | Small stream (< 0.1 m³/s) |
| Micro hydro | 5 kW - 100 kW | Village electrification, off-grid farms | Stream (0.1-1 m³/s) |
| Mini hydro | 100 kW - 1 MW | Rural grids, small industries | River (1-10 m³/s) |
| Small hydro | 1 MW - 10 MW | Community or industrial supply | River (10-100 m³/s) |
| Large hydro | > 10 MW | National grid, export | Major river (> 100 m³/s) |
International classification of hydropower plants by installed capacity. Actual boundaries vary slightly by country and standard.
Frequently asked questions
What is the main formula for hydroelectric power?
For dam-based installations: P (watts) = efficiency x water density (kg/m3) x gravity (m/s2) x head (m) x flow rate (m3/s). Numerically this is approximately P = 0.85 x 998 x 9.807 x H x Q for a typical turbine. For kinetic turbines: P = 0.5 x efficiency x density x area x velocity cubed. Both formulas output watts; divide by 1,000 for kilowatts.
What is "head" in hydro power?
Head is the vertical height difference (in metres or feet) through which water falls before reaching the turbine. Higher head creates more water pressure and therefore more power per unit of flow. Net head is gross head minus friction and other losses in the penstock - the value you should enter here for accurate results.
What turbine efficiency should I use?
Modern Francis and Kaplan turbines reach 88-94% at design flow. Pelton and Turgo impulse turbines achieve 85-92%. Older or small turbines can be 70-80%. For run-of-river and tidal turbines, the Betz limit caps efficiency at 59.3% theoretically; real installations achieve 35-50% overall. When in doubt, use 80% as a conservative estimate for dam turbines and 40% for kinetic turbines.
How does flow rate affect power output?
In dam mode, power is directly proportional to flow rate: doubling Q doubles P. In kinetic mode, power depends on velocity cubed, and flow rate (Q = area x velocity) is derived from those two inputs. Seasonal variation in river flow is one of the main challenges in hydro project planning: a site must be designed for the minimum reliable flow, not the peak.
Why is my kinetic turbine efficiency capped at 59.3%?
The Betz limit is a fundamental law of fluid dynamics (analogous to Carnot efficiency in heat engines). A turbine cannot extract more than 59.3% of the kinetic energy in a moving fluid stream because the water must retain some velocity to continue flowing through and past the turbine. If it slowed to zero, flow would stop. This limit applies to any open-flow turbine: wind turbines, tidal turbines, and run-of-river turbines alike.
How many homes can a hydroelectric plant power?
A rough benchmark for the United States is that 1 kW of average continuous power supplies about 1 average home. A 1 MW (1,000 kW) plant running 8,000 hours per year generates 8,000 MWh, enough for roughly 700-900 homes at typical U.S. consumption. European homes consume about half as much, so the same plant covers 1,400-1,800 homes. These are approximate: actual household consumption varies widely.
What is the difference between micro-hydro and large hydro?
Classification is by installed capacity. Pico hydro is below about 5 kW (enough for a remote cabin), micro hydro is 5-100 kW (small village or farm), mini hydro is 100 kW to 1 MW, small hydro is 1-10 MW, and large hydro exceeds 10 MW. Smaller plants generally use run-of-river designs with no dam and minimal environmental impact; larger plants often require reservoirs with significant land use and ecological considerations.