Define the heat service first
Annual heat needed is delivered heat, measured in million British thermal units (MMBtu). Comparing systems per delivered unit helps keep the useful heat service consistent even when equipment efficiencies differ. The existing fuel price must match the selected fuel: dollars per therm for natural gas, dollars per gallon for propane or heating oil, and dollars per kWh for electric resistance. For resistance heating the tool fixes the efficiency equivalent at 100%, consistent with the direct conversion of electricity to heat at the point of use.
AFUE is the seasonal fraction of fuel energy delivered as heat for a furnace-type system. The calculator converts one MMBtu of delivered heat to required fuel input by dividing by AFUE. The EIA conversion values used here are 100,000 Btu per therm, about 91,500 Btu per gallon of propane, and about 138,500 Btu per gallon of heating oil. For a heat pump, one kWh contains 3,412 Btu; one MMBtu therefore requires about 293.07 kWh before accounting for the heat pump's seasonal COP. Multiplying that electricity by the electricity price gives the modeled heat-pump cost per delivered MMBtu.
A transparent hypothetical comparison
For an example only, suppose the annual delivered load is 50 MMBtu, gas costs $1.50 per therm, and the existing furnace AFUE is 90%. One MMBtu of delivered heat requires 10 therms divided by 0.90, or 11.11 therms, costing about $16.67. The annual gas cost is therefore about $833.33. At an assumed heat-pump COP of 2.5 and electricity price of 18.16¢/kWh, modeled heat-pump cost per MMBtu is 293.07 ÷ 2.5 × $0.1816, about $21.29; annual cost is roughly $1,064. This hypothetical result shows how the user-provided assumptions drive the comparison; it says nothing about a specific home.
Using the cost-based load option
When annual heat demand is unknown, it can be estimated from a current heating bill only if the bill covers the relevant fuel and period and you know the system efficiency. Convert the bill amount to fuel units using the price per unit, convert those units to Btu using the EIA factors, then multiply by AFUE to estimate delivered heat. Separate cooking, water heating, or other gas use from space heating first. This form accepts delivered MMBtu directly; the unit conversion page explains the arithmetic so you can make that derivation carefully.
Climate, operation, and installation limits
A seasonal COP depends on outdoor temperatures, equipment selection, sizing, controls, defrost cycles, duct condition, backup heat and installation quality. A single COP is a simplification across a whole season. Performance can vary in cold conditions, and electric resistance backup can change the blended result. DOE describes heat pumps as moving heat rather than generating it directly, but a general description cannot establish the performance of a particular installation. AFUE and COP also describe different system properties, so they should not be compared as if they were the same rating.
The cost difference field is the additional installed cost of the heat-pump option. It can be negative when the heat-pump option costs less to install than the alternative. Simple payback divides that amount by annual operating-cost savings only when savings are positive (a negative cost difference then shows a payback of 0 years); otherwise it reports that the modeled cost difference is not recovered from those inputs. It excludes financing, maintenance differences, equipment life, cooling value, comfort, future fuel prices and repairs. Break-even electricity price is the price at which modeled annual operating costs are equal, expressed in cents per kWh. It is a mathematical threshold, not a rate forecast.
Common errors include mixing fuel units, entering an AFUE as 0.9 instead of 90, assuming COP is guaranteed, or using a whole-house gas bill that includes water heating. No federal Energy Efficient Home Improvement Credit is assumed; IRS information says qualifying improvements must be made through 2025. Check IRS guidance, state energy offices and utilities for current programs. The running-cost guide discusses these inputs and cold-weather caveats.