One kilowatt is 1.3410220896 mechanical horsepower. The horsepower is defined as exactly 550 foot-pounds per second, which works out to 745.6998715822702 watts — and it is not the only horsepower in use.
About the units
James Watt devised the unit in the 1780s to sell steam engines to mine owners who thought in horses. He measured how much a dray horse could lift and rounded upwards, arriving at 33,000 foot-pounds per minute, or 550 per second. That is the mechanical or imperial horsepower. The metric horsepower, used across continental Europe and known as PS in German, CV in French and hk in the Nordic countries, was defined instead as 75 kilogram-force metres per second, giving 735.49875 watts — about 1.4 per cent less. A car advertised at 200 hp in Britain has 202.8 PS in Germany, and it is the same car.
The exact factor
The exact value is 745.6998715822702 W per mechanical horsepower, derived from 550 × 1.3558179483314 J. The reciprocal gives 1.34102208959503 hp per kilowatt. The approximation most people use is that a kilowatt is about 1.34 horsepower, or that 100 hp is about 75 kW. Note that electrical horsepower, used for motor ratings in the United States, is defined as exactly 746 W — a third value, differing from the mechanical one by four parts in ten thousand.
Where you meet this conversion
Vehicle power ratings, where the unit refuses to die despite every European regulator requiring kilowatts on registration documents. Car specifications typically list both. Marine engines, generators and industrial motors are all rated in horsepower in American documentation and kilowatts in metric. Lawn equipment, pumps and compressors follow the same split. In electrical work the kilowatt is universal, which is why electric vehicle output is usually quoted in kW even in markets that use horsepower for combustion engines.