Energy Payback Calculator Formula

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

Use the Energy Payback Calculator

Formulas Used

Energy Payback Time

epbt = payback_years

Energy Return on Investment

eroi = annual_production_mwh * system_lifespan / embodied_energy_mwh

Net Lifetime Energy

net_lifetime = net_energy

Net Energy Ratio

net_pct = net_energy / embodied_energy_mwh * 100

Variables

VariableDescriptionDefault
embodied_energy_mwhEmbodied Energy (Manufacturing)(MWh)20
annual_production_mwhAnnual Energy Production(MWh)12
system_lifespanSystem Lifespan(years)25
payback_yearsDerived value= embodied_energy_mwh / annual_production_mwhcalculated
net_energyDerived value= annual_production_mwh * system_lifespan - embodied_energy_mwhcalculated

How It Works

How to Calculate Energy Payback Time

Energy payback time (EPBT) measures how long a system must operate to produce the energy used in its manufacture.

Formula

EPBT = Embodied Energy / Annual Production

EROI = Lifetime Production / Embodied Energy

Typical Values

  • Solar PV: 1-3 years EPBT
  • Wind turbine: 0.5-1 year EPBT
  • Nuclear: 5-7 years EPBT
  • Coal plant: 1-2 years EPBT (but never net-zero CO2)

    • Worked Example

    A solar system with 20 MWh embodied energy producing 12 MWh/year over a 25-year lifespan.

    embodied_energy_mwh = 20annual_production_mwh = 12system_lifespan = 25
    1. 01Energy payback: 20 / 12 = 1.7 years
    2. 02Lifetime production: 12 * 25 = 300 MWh
    3. 03Net energy: 300 - 20 = 280 MWh
    4. 04EROI: 300 / 20 = 15x

    Ready to run the numbers?

    Open Energy Payback Calculator