Mach 1 is 1,225.044 kilometres per hour on this site — but that figure is only true under specific conditions. Mach is not a speed at all: it is a ratio to the local speed of sound, and the local speed of sound changes with temperature.
About the units
The Mach number is named after Ernst Mach and expresses speed as a fraction of the speed of sound in the surrounding medium. The value used here corresponds to 340.29 metres per second, the speed of sound in dry air at 15 °C at sea level — the International Standard Atmosphere reference. At altitude the air is colder and sound travels more slowly: at 11,000 metres, where the temperature is about −56 °C, the speed of sound is 295 m/s, so Mach 1 is only 1,062 km/h. This is why an aircraft can cross Mach 1 by climbing at constant airspeed, and why supersonic flight is easier high up.
The exact factor
Using the sea-level standard value, Mach 1 is 340.29 m/s or 1,225.044 km/h. The dependence is on temperature alone, not pressure or altitude directly: the speed of sound in an ideal gas goes as the square root of absolute temperature. Practical reference points: Concorde cruised at Mach 2.02, about 2,140 km/h at cruise altitude; a typical airliner cruises at Mach 0.78 to 0.85; and the fastest air-breathing aircraft, the SR-71, exceeded Mach 3.2.
Where you meet this conversion
Aviation and aerodynamics. Aircraft are limited by Mach number rather than by airspeed at high altitude, because the onset of shock waves depends on the ratio and not the absolute speed — which is why airliner cockpits display both indicated airspeed and Mach, and switch which one is limiting as the aircraft climbs. Rocketry, ballistics and wind tunnel testing all use it. The number also appears in weapons specifications, where it is often quoted without stating the reference conditions, making a direct conversion to kilometres per hour unreliable.