Hydroelectric Power Calculator
Estimate the electrical power and annual energy output of a hydroelectric installation using P = η·ρ·g·Q·H. Enter the net head (m), design flow rate (m³/s), and overall turbine-generator efficiency to get power in kW or MW, and optionally the yearly energy production.
m
m³/s
%
h/day
days/year
P = η · ρ · g · Q · H
- 1
Gross hydraulic power
P_gross = 1,000 × 9.81 × 10 × 50 m = 4,905 kWTheoretical power in the falling water: ρ × g × Q × H. - 2
Efficiency fraction
η = 88% ÷ 100 = 0.88 - 3
Net power output
0.88 × 4,905 kW = 4.316
How does this calculator work?
Hydroelectric power P = η·ρ·g·Q·H depends linearly on net head H and flow rate Q. With η = 88%, Q = 10 m³/s and H = 50 m, output is ≈ 43 kW. Multiply by annual operating hours for yearly energy in MWh. Use net head (gross head minus penstock losses) for an accurate result.
Formula
How this is calculated
A hydroelectric plant converts the potential energy of falling water into electricity. The available hydraulic power in the water is P_gross = ρgQH, where ρ = 1000 kg/m³ is water density, g = 9.81 m/s², Q is the volumetric flow rate through the turbine, and H is the net head — the effective head after subtracting penstock friction losses and inlet losses from the gross (physical) head difference.
The overall efficiency η combines turbine efficiency (typically 85–94% for modern Francis or Kaplan turbines), generator efficiency (95–98%), and transmission losses. For a run-of-river plant, overall η is commonly 80–92%. The net electrical power output is P = η × P_gross. Annual energy = P × (hours/day × days/year).
Important caveats: this calculator uses a fixed design-point Q and H. In practice, flow varies seasonally, and turbines have a best-efficiency point — performance drops away from design conditions. Net head must account for penstock head loss (h_f = fLV²/(2gD)), which can be significant for long penstocks. The density 1000 kg/m³ is for freshwater at ≈15 °C.
Frequently asked questions
Gross head is the raw elevation difference between the headwater and tailwater. Net head subtracts hydraulic losses in the penstock (pipe friction, entry/exit, bends). For short penstocks the difference is small; for long or narrow penstocks it can be 10–20% of gross head. Always use net head in the power formula.
Small turbines (< 1 MW) typically achieve 70–85% overall. Large modern Francis turbines reach 90–94% at best efficiency point. Include generator efficiency (95–98%) and transformer losses (~1%) in the overall η. For a preliminary estimate, 80–85% is conservative and reasonable.
Power is directly proportional to Q: double the flow doubles the power (at constant head and efficiency). However, increasing Q also raises penstock friction losses, reducing net head, so the relationship is slightly sub-linear in practice. The power vs head curve (shown in the plot) illustrates how output changes with head at a fixed Q.
Also known as
TG we-Calculate Editorial Team. (2026). Hydroelectric Power Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hydroelectric-power-calculator
TG we-Calculate Editorial Team. "Hydroelectric Power Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/hydroelectric-power-calculator.
TG we-Calculate Editorial Team, "Hydroelectric Power Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hydroelectric-power-calculator
@misc{wecalculate_hydroelectric_power_calculator, title = {Hydroelectric Power Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hydroelectric-power-calculator}}, year = {2026}, note = {TG we-Calculate} }
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