One kilowatt is 3,412.1416 BTU per hour. This is the conversion that lets an American air conditioner be compared with a European heat pump, since the two industries rate identical equipment in different units.
About the units
The BTU per hour is a rate of heat transfer: British thermal units delivered or removed each hour. It is the standard rating unit for heating and cooling equipment in the United States, where a furnace might be 80,000 BTU/h and a window air conditioner 8,000. The kilowatt is the SI equivalent and is what the same equipment carries on its plate in Europe. Both measure power, so the conversion is a pure unit change with no physics in it — but because the numbers differ by a factor of over three thousand, equipment from the two markets looks incomparable until it is done.
The exact factor
The exact chain is 1 BTU = 1,055.05585262 J, divided by 3,600 seconds per hour, giving 0.293071070172 W per BTU/h. Inverted, that is 3,412.141633 BTU/h per kilowatt. Useful anchors: 12,000 BTU/h is 3.517 kW and is also one ton of refrigeration; 24,000 BTU/h is 7.03 kW; and 1,000 BTU/h is 293 W. Efficiency ratings mix the systems inside a single number — SEER is BTU of cooling per watt-hour of electricity, so a SEER of 20 is a coefficient of performance of 5.86.
Where you meet this conversion
Specifying and comparing heating and cooling equipment across markets. A room needing 3.5 kW of cooling needs a 12,000 BTU/h unit, and getting that translation right is the whole of equipment selection. Heat load calculations for buildings are done in watts in metric practice and BTU per hour in American. Radiator output, underfloor heating capacity and ventilation heat recovery all cross the same boundary in international projects.