One inch of mercury is 33.86389 hectopascals. The pair exists almost entirely for one purpose: aviation altimeter settings differ between North America and the rest of the world, and a pilot crossing that boundary has to convert.
About the units
An inch of mercury is the pressure exerted by a one-inch column of mercury under standard conditions, the imperial counterpart of the millimetre of mercury. It descends directly from Torricelli's barometer of 1643, where the height of a mercury column in a sealed tube measured atmospheric pressure. American meteorology and aviation retained it while the rest of the world moved to millibars and then hectopascals. The two systems describe the same physical quantity with different rulers, and the conversion is fixed and exact enough for operational use.
The exact factor
The value is 33.86389 hPa per inHg, derived from 25.4 mm per inch times 1.333224 hPa per mmHg. The reference points that matter in aviation: standard pressure is 1,013.25 hPa, which is 29.92 inHg — the setting used above the transition altitude worldwide. A QNH of 1,000 hPa is 29.53 inHg, and 1,030 hPa is 30.42. A one-hectopascal error corresponds to roughly 27 feet of altitude, so a misread altimeter setting of ten hectopascals puts an aircraft 270 feet from where it believes it is.
Where you meet this conversion
Aviation above all. Altimeter settings are broadcast in hectopascals in Europe, Asia and most of the world and in inches of mercury in the United States and Canada, so transatlantic and cross-border flights convert routinely. American weather reports give barometric pressure in inches of mercury for the general public. Older barometers, particularly domestic aneroid instruments sold in Britain and America, are marked in inches. Vacuum measurements in American industry sometimes use inches of mercury below atmospheric, which is a gauge reading measured downwards.