One mechanical horsepower is 1.0138696654 metric horsepower. Two units share the name, differ by 1.4 per cent, and appear in the specifications of the same cars — which is why a vehicle can be advertised with two different power figures without either being wrong.
About the units
The mechanical horsepower, sometimes called imperial or brake horsepower, is 550 foot-pounds per second: 745.6998715822702 watts. James Watt derived it from measurements of working horses in the 1780s. The metric horsepower was defined later in continental Europe as 75 kilogram-force metres per second, which is 735.49875 watts exactly. It goes by different names in different languages — Pferdestärke or PS in German, cheval-vapeur or CV in French, cavallo vapore in Italian, hästkraft or hk in the Nordic countries — and all of them mean the same 735.5 watts.
The exact factor
The exact ratio is 745.6998715822702 ÷ 735.49875 = 1.013869665424. A car rated at 300 mechanical horsepower is 304.2 metric horsepower. Going the other way, 300 PS is 295.9 hp. The difference is small enough to look like a rounding error in a specification table and large enough that motoring journalists have written entire articles about a manufacturer apparently changing an engine's output when it had only changed the unit. Both are exactly convertible to kilowatts, which is why registration documents across the EU use kW and sidestep the problem entirely.
Where you meet this conversion
Automotive specifications above all, particularly when comparing figures from British and American sources against German, French, Italian or Nordic ones. Motorcycle and marine engine ratings have the same split. Classic car documentation is a common trap, since a period road test may quote either without saying which. Tuning and dyno results are usually stated in the local convention, so comparing a German dyno chart to a British one requires the conversion before any conclusion about which engine is stronger.