Methodology
Every input in our calculators is yours to change. This page documents the formulas and constants we use so you can audit the math.
Heat pump payback
The calculator runs the following sequence:
- Energy delivered by current furnace: fuel units consumed × energy content per unit × furnace efficiency.
- Heat pump electricity needed: energy delivered ÷ seasonal COP.
- Heat pump operating cost: electricity needed × electricity rate.
- Annual savings: current heating cost − heat pump operating cost.
- Net upfront cost: heat pump install − avoided furnace replacement − rebates.
- Cumulative cash flow per year: starts at −net upfront; adds inflated annual savings each subsequent year.
- Payback year: linearly interpolated from the year cumulative cash flow crosses zero.
Energy content constants
Imperial units (default):
- Natural gas: 29.3 kWh per therm
- Heating oil (No. 2): 40.6 kWh per US gallon
- Propane: 27.0 kWh per US gallon
- Electric resistance: 1.0 kWh per kWh (by definition)
Metric:
- Natural gas: 10.55 kWh per m³
- Heating oil: 10.7 kWh per litre
- Propane: 7.08 kWh per litre
Sources include the U.S. Energy Information Administration and Natural Resources Canada. Real-world values vary slightly by fuel grade.
CO₂ emissions
Combustion factors per kWh of fuel input: natural gas 0.18 kg CO₂e/kWh, heating oil 0.27, propane 0.215. Grid electricity is treated at a continental-average 0.4 kg CO₂e/kWh; your local grid may be cleaner or dirtier.
EV vs gas payback
The EV calculator runs the following sequence:
- Annual fuel cost (gas car): miles driven per year ÷ gas MPG × gas price per gallon.
- Annual fuel cost (EV): miles driven per year × EV kWh per mile × electricity rate.
- Annual fuel savings: gas car fuel cost − EV fuel cost.
- Total annual savings: fuel savings + maintenance savings − insurance difference.
- Net upfront premium: EV purchase price − equivalent gas car price − rebates.
- Cumulative cash flow per year: starts at −net upfront; adds inflated annual savings each subsequent year.
- Payback year: linearly interpolated from the year cumulative cash flow crosses zero.
Solar payback
The solar calculator runs the following sequence:
- Annual production (year n): system size kW × annual kWh per kW × (1 − panel degradation rate)n.
- Annual value: production × self-consumption ratio × retail electricity rate + production × (1 − self-consumption ratio) × net metering rate.
- Net system cost: installed cost × (1 − federal tax credit rate) − other incentives.
- LCOE (levelised cost of energy): net system cost ÷ total lifetime production summed over the analysis period.
- Cumulative cash flow per year: starts at −net system cost; adds electricity rate-inflated annual value each subsequent year.
- Payback year: linearly interpolated from the year cumulative cash flow crosses zero.
Combined solar + EV payback
The combined calculator runs both standalone calculations above and adds a synergy term per year:
- EV kWh from solar (year n): pctEVChargedFromSolar × annual EV kWh, capped at the panel's exportable surplus (production × (1 − home self-consumption ratio)) in home-first mode, or at total production in EV-first mode.
- Synergy ($/year): min(EV-from-solar, exportable surplus) × retail electricity rate × (1 − net metering rate). This is the value of routing a kWh through the EV (which would otherwise pay retail) instead of through the grid (which would otherwise earn only the net-metering credit).
- Combined cumulative cash flow per year: solar standalone + EV standalone + cumulative synergy.
- Payback improvement: max(solar payback, EV payback) − combined payback. How many years sooner the bundled investment crosses break-even than the slower of the two on its own.
The panel's LCOE (system cost ÷ lifetime production) is paid up front in the solar net system cost - it is not charged a second time inside the synergy formula.
Induction stove vs. gas range
The induction calculator runs the following sequence:
- Annual cooking hours: cooking hours per week × 52.
- Annual gas energy input: annual cooking hours × 9,000 BTU/hr ÷ 3,412 BTU/kWh (= 2.637 kWh thermal per hour).
- Annual gas fuel units: annual gas energy input ÷ kWh per billing unit.
- Annual gas cooking cost: annual fuel units × fuel price per unit.
- Heat delivered to food by gas: annual gas energy input × 40% (gas range efficiency).
- Annual induction electricity: heat delivered ÷ 85% (induction efficiency).
- Annual induction cost: annual induction electricity × electricity rate.
- Annual savings: gas cooking cost − induction cost (can be negative).
- Net upfront cost: induction range + electrical work − gas range counterfactual − rebates.
- Cumulative cash flow and payback: same interpolation method as other calculators.
9,000 BTU/hr is a published residential average across all burner sizes and typical usage patterns. Gas range thermal efficiency ~40% and induction efficiency ~85% are widely cited values from ACEEE and appliance-efficiency studies.
Heat pump water heater payback
The HPWH calculator runs the following sequence:
- Fuel units consumed: annual water heating cost ÷ fuel unit price.
- Fuel energy input: fuel units consumed × kWh per unit.
- Heat delivered to water: fuel energy input × current tank EF.
- Effective UEF: rated HPWH UEF × ambient temperature adjustment (1.0 warm / 0.9 cool / 0.75 cold).
- HPWH annual electricity: heat delivered ÷ effective UEF.
- HPWH annual cost: HPWH electricity × electricity rate.
- Annual savings: current annual water heating cost − HPWH annual cost.
- Net upfront cost: HPWH installed − replacement standard tank − rebates.
- Cumulative cash flow per year: starts at −net upfront; adds inflated annual savings each subsequent year.
- Payback year: linearly interpolated from the year cumulative cash flow crosses zero.
E-bike vs. car payback
The e-bike calculator runs the following sequence:
- Annual car fuel cost: annual distance ÷ fuel economy × fuel price (imperial: gallons; metric: litres per 100 km converted to total litres).
- Annual car maintenance cost: annual distance × per-mile/km operating cost.
- Annual e-bike electricity: annual distance × Wh per mile/km ÷ 1,000.
- Annual e-bike electricity cost: e-bike kWh × electricity rate.
- Annual savings: (car fuel + car maintenance) − (e-bike electricity + e-bike annual maintenance).
- Net upfront cost: e-bike purchase price − rebates.
- Cumulative cash flow per year: starts at −net upfront; adds inflated annual savings each subsequent year.
- Payback year: linearly interpolated from the year cumulative cash flow crosses zero.
Default per-mile car operating cost ($0.08/mile) reflects AAA-estimated non-fuel operational maintenance. E-bike efficiency default of 15 Wh/mile is a midpoint for moderate pedal-assist use; aggressive assist or hilly terrain increases consumption.
Home battery payback
The battery calculator runs the following sequence:
- Daily energy discharged (kWh): cycles per day × capacity kWh × depth of discharge.
- Annual TOU savings (year 1): daily discharged × 365 × (peak rate − off-peak rate ÷ round-trip efficiency). The RTE adjustment accounts for the extra off-peak kWh needed to recharge what was discharged.
- Annual backup power value: entered directly by the user in $/year.
- Year n TOU savings: year 1 TOU savings × (1 + inflation rate)n−1 × (1 − annual degradation)n−1. Inflation increases the rate spread value; degradation reduces throughput.
- Year n backup value: backupValuePerYear × (1 + inflation rate)n−1.
- Net upfront cost: installed cost − rebates.
- Cumulative cash flow per year: starts at −net upfront; adds year n total benefit each subsequent year.
- Payback year: linearly interpolated from the year cumulative cash flow crosses zero.
Round-trip efficiency of 0.90 reflects typical lithium-ion performance. CO₂ displacement uses a 0.15 kg/kWh differential between peak (typically gas-fired peaking plants) and average off-peak grid generation — a conservative estimate that varies significantly by region and grid mix.
What we deliberately do not model
- Bin-by-bin temperature COP variation. We use a single seasonal COP.
- Equipment degradation or refrigerant leakage over time.
- Time-of-use electricity rates, demand charges, or electrification-specific rate plans.
- Maintenance cost differences between the two systems.
- Income-tax effects of rebates or financing costs.
These omissions keep the inputs manageable. For a detailed engineering analysis you should commission a licensed HVAC consultant.
Versioning
Last updated: 2026-05-15.