Open calculation notes · Updated July 17, 2026

How the replacement comparison works

This page exposes the calculator’s counterfactual, equations, default values, sources, and blind spots. Nothing here guarantees that a heat pump will save money.

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Decision frame

The alternative is not “do nothing.”

The calculator is designed for a homeowner replacing both heating and central cooling equipment. It compares a heat-pump quote with a comparable furnace plus central-air-conditioner replacement.

Different decision? If existing equipment has useful remaining life, this model does not capture the timing value of keeping it. That requires an early-retirement model with future replacement dates.

Equation 1

Incremental upfront cost

heat pump net price = heat pump gross quote − heat pump incentives baseline net price = furnace + AC gross quote − baseline incentives incremental upfront cost = heat pump net price − baseline net price

Both quote fields are gross prices before incentives. Each incentive is subtracted exactly once. A negative incremental cost means the heat-pump option costs less upfront.

Equations 2–6

Annual heating energy

The model converts current annual heating spend into fuel units, estimates delivered heat using the existing system efficiency, and models both replacements against that same load.

existing fuel units = annual heating spend ÷ fuel price delivered heat (Btu) = existing fuel units × Btu per unit × existing efficiency replacement furnace units = delivered heat ÷ (Btu per unit × replacement AFUE) replacement furnace cost = replacement furnace units × fuel price heat-pump kWh = heat assigned to compressor ÷ (3,412 × seasonal COP) backup units = heat assigned to backup ÷ (backup Btu per unit × backup efficiency)

Seasonal COP is the ratio of useful seasonal heat delivered to electricity consumed. It is not the equipment’s single-temperature laboratory COP. Backup heat is modeled as a share of the same delivered heating load.

EnergyConversion used
Electricity3,412 Btu per kWh
Natural gas100,000 Btu per therm
Heating oil138,500 Btu per gallon
Propane91,452 Btu per gallon

Equations 7–8

Cooling-cost difference

replacement AC cooling cost = current cooling cost × (existing AC efficiency ÷ replacement AC SEER2) heat-pump cooling cost = current cooling cost × (existing AC efficiency ÷ heat-pump SEER2)

Both replacement choices serve the same cooling load inferred from today’s cooling cost and existing AC efficiency. This is a ratio model, not an hourly building simulation.

Equations 9–11

Cumulative cash flow, payback, and ROI

year 0 cash flow = −incremental upfront cost annual difference = baseline operation − heat-pump operation − maintenance difference cumulative year N = prior cumulative cash flow + annual difference ÷ (1 + discount rate)^N

Electric and fuel portions escalate separately. Payback is the interpolated point when cumulative cash flow reaches zero and remains nonnegative through the selected period. A temporary crossing that later reverses is not reported as payback.

period net benefit = final cumulative cash flow period ROI = period net benefit ÷ incremental upfront cost

ROI is shown only when incremental cost is positive. When the heat pump has no upfront premium, the percentage denominator is not meaningful.

Quick mode

Editable starting assumptions

Defaults help a homeowner begin; they are not claims about a specific house. Detailed mode exposes every value.

InputDefaultBasis
Residential electricity$0.173/kWh2025 U.S. residential average, EIA
Natural gas$1.50/thermRounded from 2025 U.S. residential delivered price, EIA
Heating oil$3.98/gallonApproximate Oct. 2025–Mar. 2026 U.S. average, EIA
Propane$2.55/gallonApproximate Oct. 2025–Mar. 2026 U.S. average, EIA
Existing heating efficiency80% gas/propane; 82% oilPlanning assumption; replace with existing equipment rating
Replacement furnace AFUE95% gas/propane; 87% oilPlanning assumption; replace with quote specification
Seasonal COP2.4 cold; 2.8 moderate; 3.2 mildPlanning scenarios, not climate guarantees
Backup share12% cold; 5% moderate; 2% mildPlanning scenarios; controls and sizing can change this sharply
Existing AC efficiency10.0Planning assumption; replace with existing equipment rating
Replacement AC13.4 SEER2Federal minimum reference for a split-system AC in the North
Heat pump15.2 SEER2ENERGY STAR split-system threshold
Gas fixed charge$180/yearIllustrative $15/month; replace with utility bill
Energy escalation2.5%/yearNeutral modeling assumption, not a forecast
Discount rate0%Produces nominal cash flow unless changed

Reproducible check

Worked example

Moderate-climate gas home

  • Heat pump: $18,000 gross − $2,000 incentives = $16,000 net
  • Furnace + AC: $14,000 gross − $0 incentives = $14,000 net
  • Incremental upfront cost: $2,000
  • Existing heating: $1,400/year at $1.50/therm and 80% efficiency
  • Replacement furnace: 95% AFUE
  • Current cooling: $450/year at 10.0 existing efficiency; 13.4 replacement AC SEER2 and 15.2 heat-pump SEER2
  • Heat pump: 2.8 seasonal COP, 5% electric-resistance backup
  • Gas service eliminated: $180/year avoided

Rounded first-year operating cost is about $1,695 for the furnace-plus-AC replacement and $1,770 for the heat pump: roughly $75 higher first-year cost for the heat pump. With both energy prices escalating 2.5%, no discounting, and no maintenance difference, the heat pump does not pay back within 20 years and finishes about $3,900 behind. That unfavorable result is intentional.

Do not overread the output

Limits and exclusions

  • No hourly weather, load, thermostat, defrost, or equipment performance-curve simulation.
  • No duct leakage, envelope improvement, electrical-panel, financing, tax-basis, or opportunity-cost model.
  • No equipment degradation, repair event, mid-period replacement, or resale-value assumption.
  • No demand charges, time-of-use rates, or solar interaction.
  • Annual heating spend can include non-heating usage or fixed fees unless the homeowner removes them.
  • Seasonal COP and backup share are highly sensitive to climate, sizing, controls, and installation quality.
  • The cooling ratio assumes unchanged cooling load and behavior.
  • Incentive eligibility is never guaranteed by the calculator.

An unfavorable result is valid output. The tool does not clamp savings above zero or force a payback.

Primary references

Sources

Sources and defaults last reviewed July 17, 2026.