Heat pumps move heat rather than create it, which is why they can deliver 2.5-4 units of heat per unit of electricity (COP 2.5-4.0). That's the whole secret — and why they can cost less to run than gas in most U.S. climates, if sized and installed correctly.
Ducted central heat pump: Drop-in replacement for a traditional central air + furnace. Best for homes with existing ductwork. Typical install: $10,000-$18,000.
Ductless mini-split: Multiple wall-mounted heads. Best for homes without ducts, additions, or zone-by-zone control. Typical install: $4,000-$12,000 for 2-3 zones.
A seasonal COP of 2.5 means the heat pump uses 1 kWh of electricity to deliver 2.5 kWh of heat. At $0.17/kWh and a 100,000 BTU/yr heating load, that's $1,990/yr in heating. The same load delivered by an 85%-efficient gas furnace at $1.80/therm costs $2,120 — a ~6% savings.
The savings amplify when you're replacing oil ($4/gal) or propane ($2.80/gal), or when electricity is cheap.
Modern cold-climate heat pumps (Mitsubishi H2i, Fujitsu XLTH, LG "Low Temp") maintain 100% capacity down to -5°F and operate down to -15°F. The "heat pumps don't work in cold weather" myth is 15 years out of date.