Hydropower Calculator Formula

Understand the math behind the hydropower calculator. Each variable explained with a worked example.

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Formulas Used

Power Output

power_output = power_kw

Annual Energy

annual_mwh = power_kw * 8760 * availability / 100 / 1000

Homes Powered

homes_powered = power_kw * 8760 * availability / 100 / 1000 / 10.5

CO2 Avoided

co2_avoided = power_kw * 8760 * availability / 100 * 0.92 / 2204.6

Variables

VariableDescriptionDefault
flow_rateWater Flow Rate(m3/s)5
headHead Height(meters)30
turbine_efficiencyTurbine Efficiency(%)85
availabilityAnnual Availability(%)90
power_kwDerived value= flow_rate * head * 9.81 * turbine_efficiency / 100calculated

How It Works

How to Calculate Hydropower Output

Hydropower converts the potential energy of falling water into electricity.

Formula

Power (kW) = Flow Rate (m3/s) * Head (m) * 9.81 * Efficiency

Annual Energy = Power * 8,760 hours * Availability Factor

  • Flow rate: Volume of water passing through the turbine per second
  • Head: Vertical drop from intake to turbine
  • Efficiency: Modern turbines achieve 85-93%

    • Worked Example

    A hydropower site with 5 m3/s flow, 30m head, 85% turbine efficiency, 90% availability.

    flow_rate = 5head = 30turbine_efficiency = 85availability = 90
    1. 01Power: 5 * 30 * 9.81 * 0.85 = 1,250.8 kW
    2. 02Annual energy: 1,250.8 * 8,760 * 0.90 / 1,000 = 9,857 MWh
    3. 03Homes powered: 9,857 / 10.5 = 939 homes

    Frequently Asked Questions

    What is head in hydropower?

    Head is the vertical distance water falls from the intake to the turbine. Higher head means more potential energy. Run-of-river systems have low head; dam-based systems can have high head.

    Is hydropower truly renewable?

    Yes, hydropower uses the natural water cycle. However, large dams can impact ecosystems, fish migration, and sediment flow. Run-of-river systems have less environmental impact.

    What is the capacity factor of hydropower?

    Hydropower has very high capacity factors of 40-60% for conventional dams and up to 90% for some run-of-river installations, much higher than wind or solar.

    Ready to run the numbers?

    Open Hydropower Calculator