About the Hydroelectric Power Calculator
Hydroelectric power converts the energy of falling or flowing water into electricity. The amount of power a hydro turbine can generate depends on just three things: how much water flows through it, how far that water falls (the "head"), and how efficiently the turbine and generator convert that mechanical energy into electrical energy. This calculator uses the standard engineering formula for hydropower to estimate real power output in kilowatts and megawatts.
The formula
The power available from falling water is:
P = η × ρ × g × Q × H
- P = electrical power output, in watts (W)
- η (eta) = overall efficiency of the turbine and generator combined, expressed as a decimal (e.g. 0.85 for 85%)
- ρ (rho) = density of water = 1,000 kg/m³ (fresh water at typical temperatures)
- g = acceleration due to gravity = 9.81 m/s²
- Q = volumetric flow rate through the turbine, in cubic meters per second (m³/s)
- H = head, the net vertical drop of the water from intake to turbine, in meters (m)
The term ρ × g × Q × H gives the raw hydraulic (potential) power in the falling water; multiplying by η accounts for real-world losses in the turbine blades, generator windings, and penstock friction. Power scales linearly with both flow rate and head — doubling either one doubles the output, all else equal.
Worked example
A small run-of-river plant has a flow rate of 10 m³/s, a head of 20 m, and an 85% efficient turbine-generator set:
P = 0.85 × 1,000 × 9.81 × 10 × 20 = 1,667,700 W ≈ 1,667.7 kW ≈ 1.67 MW
Running continuously for a full year (8,760 hours) at that output would generate about 1.67 MW × 8,760 h ≈ 14,620 MWh of energy — though real plants rarely run at 100% capacity factor year-round due to seasonal flow variation and maintenance downtime.
Typical efficiency values
- Large modern turbines (Francis, Kaplan, Pelton) at utility-scale dams: 85–92% combined turbine + generator efficiency.
- Small hydro (100 kW–10 MW): typically 80–90%.
- Micro-hydro (under 100 kW): often 60–80%, since smaller turbines and generators are harder to optimize and off-the-shelf components are used.
Typical head and flow ranges
Hydro sites are often classified by head: "low head" sites are under 10 m (common in run-of-river and small community projects), "medium head" is roughly 10–100 m, and "high head" exceeds 100 m (common in mountain reservoir dams using Pelton wheels). Flow rate depends entirely on the river or penstock size — from under 1 m³/s for micro-hydro on a small stream to thousands of m³/s at facilities like Three Gorges Dam or Itaipu Dam.
Why this matters
Hydropower is the largest source of renewable electricity generation worldwide and one of the few renewable sources that can provide dispatchable, on-demand power (unlike intermittent solar or wind). Sizing a hydro installation correctly — whether for a utility dam, a small community micro-hydro project, or a classroom physics problem — starts with this same P = ηρgQH relationship.