One BTU is 0.000293071 kilowatt-hours, so a kilowatt-hour is 3,412.14 BTU. This is the conversion that makes an American heating system comparable to a European one, since the two are rated in different units for identical work.
About the units
The BTU is the energy to raise one pound of water by one degree Fahrenheit, about 1,055 joules. The kilowatt-hour is 3.6 megajoules. Both measure energy, but they belong to different industries: the BTU to American combustion heating, the kilowatt-hour to electricity everywhere. The collision happens with heat pumps and air conditioning, where an appliance may be rated in BTU per hour for its thermal output and in kilowatts for its electrical input, and the ratio between those two numbers is the coefficient of performance.
The exact factor
The exact relationship runs through joules: 1 BTU = 1,055.05585262 J and 1 kWh = 3,600,000 J, giving 3,412.142 BTU per kWh. For power rather than energy the same number applies: 1 kW is 3,412.14 BTU per hour. That figure is worth memorising for anyone comparing heating equipment, because it turns a furnace rated at 80,000 BTU/h into 23.4 kW, which is directly comparable to a heat pump specification.
Where you meet this conversion
Heating and cooling equipment comparison. American air conditioners are rated in BTU per hour, European ones in kilowatts, and the same room needs the same capacity either way. Efficiency ratings compound the problem: SEER is BTU of cooling per watt-hour of electricity, so a SEER of 20 corresponds to a coefficient of performance of 5.86. Energy audits, building simulations and utility rebate programmes all move between the two units, and gas and electricity on the same bill are often metered in different ones.