Heat Pump COP Calculator Formula

Understand the math behind the heat pump cop calculator. Each variable explained with a worked example.

Use the Heat Pump COP Calculator

Formulas Used

Coefficient of Performance

cop_out = cop

Annual Heating Cost

annual_cost = annual_kwh * elec_rate

Equivalent Gas Furnace Cost

gas_equivalent = heat_output_btu * heating_hours / 100000 * 1.5 / 0.92

Savings vs Gas Furnace

savings_vs_gas = (heat_output_btu * heating_hours / 100000 * 1.5 / 0.92) - annual_kwh * elec_rate

Variables

VariableDescriptionDefault
heat_output_btuHeat Output(BTU/hr)36000
power_input_wattsElectrical Input(watts)3000
heating_hoursAnnual Heating Hours(hours)2000
elec_rateElectricity Rate(USD/kWh)0.15
copDerived value= heat_output_btu / (power_input_watts * 3.412)calculated
annual_kwhDerived value= power_input_watts * heating_hours / 1000calculated

How It Works

How to Calculate Heat Pump COP

COP measures how efficiently a heat pump converts electricity into heat.

Formula

COP = Heat Output (BTU/hr) / (Electrical Input (W) * 3.412)

A COP of 3 means the heat pump produces 3 units of heat for every 1 unit of electricity. This is possible because heat pumps move existing heat rather than generating it.

Typical COP Values

  • Air-source heat pump: 2.5-4.0
  • Ground-source (geothermal): 3.5-5.0
  • Resistance heating: 1.0

    • Worked Example

    A heat pump producing 36,000 BTU/hr using 3,000W of electricity, running 2,000 hours/year at $0.15/kWh.

    heat_output_btu = 36000power_input_watts = 3000heating_hours = 2000elec_rate = 0.15
    1. 01COP: 36,000 / (3,000 * 3.412) = 36,000 / 10,236 = 3.52
    2. 02Annual electricity: 3,000 * 2,000 / 1,000 = 6,000 kWh
    3. 03Heat pump cost: 6,000 * $0.15 = $900
    4. 04Gas furnace equivalent: 36,000 * 2,000 / 100,000 * $1.50 / 0.92 = $1,174

    Frequently Asked Questions

    What is a good COP for a heat pump?

    A COP of 3.0+ is good for air-source heat pumps. Ground-source systems can achieve 4.0-5.0. COP decreases as outdoor temperature drops for air-source units.

    How does COP relate to HSPF?

    HSPF (Heating Seasonal Performance Factor) is the seasonal average efficiency. COP is measured at a specific condition. Roughly, HSPF / 3.412 = seasonal average COP.

    Do heat pumps work below freezing?

    Modern cold-climate heat pumps maintain efficiency down to -15F or lower. Older models lost significant capacity below 30F, but newer variable-speed compressors have largely solved this.

    Ready to run the numbers?

    Open Heat Pump COP Calculator