Methodology

Core formulas

• Heat pump cost per MMBTU: (electricity_price × 293.071) / COP(T)
• Furnace cost per MMBTU: fuel_price / (AFUE × (BTU_per_unit / 1,000,000))

293.071 is the kWh-equivalent of 1 MMBTU (energy-unit conversion). BTU-per-unit is 100,000 for a gas therm and 91,500 for a propane gallon.

COP(T) model

DualFuelMath uses a linear COP interpolation between 47°F and 17°F for each profile. Outside that band, the curve is extrapolated using the same slope (with a floor at COP=1.0 to remain physically reasonable).

This is a simplified “two-point” model; real equipment has manufacturer-specific performance curves.

Profile anchors (47°F and 17°F)

• Standard (example packaged HP): COP 2.9 @47°F, COP 1.8 @17°F (Carrier product data sheet).
• Cold-climate (spec threshold): COP 3.40 @47°F, COP 2.25 @17°F (NEEP Cold Climate ASHP specification).
• High-efficiency (variable capacity example): COP 4.11 @47°F, COP 2.77 @17°F (Mitsubishi Hyper-Heat catalog example).

Sources are linked on /reference/. If your equipment differs, use the closest profile and treat the output as a range.

What this model intentionally excludes

• Demand charges / time-of-use schedules (unless you adjust the effective $/kWh)
• Defrost penalties and cycling losses
• Capacity limits and auxiliary heat lockout behavior

These factors can matter; they’re not “wrong”, they’re simply outside the scope of a static share-link calculator.