How this calculation works
A heating bill records fuel or electricity bought, while the building needs delivered heat. Dividing that demand by boiler efficiency or heat-pump performance puts both systems on a consistent basis. Fuel price must be expressed per kWh of input fuel, not per litre or therm without conversion.
Electricity = useful heat × [(1 − backup share) / COP + backup share]; boiler fuel = useful heat / efficiencyA worked example
For 10,000 kWh of useful heat, COP 3 and 10 percent resistance backup, electricity use is 4,000 kWh and cost is 32,000 at a tariff of 8.
Good to know
A seasonal COP represents the heat-pump portion only in this model. The backup input is the share of useful heat supplied separately by resistance heating at a ratio of one. A high performance rating does not eliminate this backup cost, and climate or flow temperature can change the actual seasonal performance.
Reference: US DOE — air source heat pumps (opens in a new tab) ↗
Useful heat is the common denominator
A heating bill records fuel or electricity bought, while the building needs delivered heat.
Dividing that demand by boiler efficiency or heat-pump performance puts both systems on a consistent basis. Fuel price must be expressed per kWh of input fuel, not per litre or therm without conversion.
The Solar self consumption and payback calculator values electricity at entered import and export rates. Heating and generation need a matching time profile before assuming all electricity use can be supplied onsite.
Backup can change the comparison
A seasonal COP represents the heat-pump portion only in this model.
The backup input is the share of useful heat supplied separately by resistance heating at a ratio of one. A high performance rating does not eliminate this backup cost, and climate or flow temperature can change the actual seasonal performance.
Compare all heat-pump heat with all resistance heat
Set backup share to zero and inspect the heat-pump input. It should equal useful heat divided by the entered seasonal COP. At one hundred percent backup the heat-pump COP becomes irrelevant, because all useful heat comes from resistance electricity in this model.
For the boiler, lower efficiency increases purchased fuel while leaving useful demand unchanged. Include an annual standing charge only if switching systems would actually remove that charge. A gas account retained for cooking may still incur it; counting an unavoidable charge as a saving would overstate the comparison.
Work through the entered example
For 10,000 kWh of useful heat, COP 3 and 10 percent resistance backup, electricity use is 4,000 kWh and cost is 32,000 at a tariff of 8.
Start with this case, then change one input and calculate again. Keep the other assumptions fixed so the result has an interpretable cause. The result table exposes intermediate quantities and units rather than hiding them behind a single headline number.
Use the output in a real plan
A seasonal COP represents the heat-pump portion only in this model. The backup input is the share of useful heat supplied separately by resistance heating at a ratio of one. A high performance rating does not eliminate this backup cost, and climate or flow temperature can change the actual seasonal performance.
Before purchasing material or comparing alternatives, check the measurements at the point where they enter the calculation. A mathematically precise answer can still be a poor plan when the measured size, loss allowance or price basis is wrong. Save the input assumptions with any result you intend to reuse.
A few questions, answered
What is the calculation method?
Electricity = useful heat × [(1 − backup share) / COP + backup share]; boiler fuel = useful heat / efficiency
Does this use live prices or automatic measurements?
No. All measurements, prices and allowances come from your entries. The example values are illustrative and are not a recommendation for your situation.
Can I reuse the result for a different case?
Change the inputs and calculate again. Read the stated units and limits; the assumptions must still apply to the new case.