One imperial gallon is 1.2009499255 US gallons. The two units share a name and differ by twenty per cent, which makes this the most consequential same-name discrepancy in everyday measurement.
About the units
The split happened in 1824. Britain's Weights and Measures Act replaced a confusion of older gallons — wine, ale and corn, all different volumes — with a single imperial gallon defined as ten pounds of distilled water, now fixed at exactly 4.54609 litres. The United States had been independent for nearly fifty years and kept the English wine gallon of exactly 231 cubic inches, 3.785411784 litres. Neither country changed afterwards, so the divergence is permanent. Every unit built on the gallon inherits it: the imperial quart, pint and fluid ounce are all different from their American namesakes.
The exact factor
The exact ratio is 4.54609 ÷ 3.785411784 = 1.20094992550485... In the other direction, a US gallon is 0.832674 imperial gallons. The most visible consequence is fuel economy. A car rated at 40 miles per imperial gallon is rated at 33.3 miles per US gallon — the same car, the same fuel, a difference that looks like a meaningful performance gap and is purely a unit artefact. Any comparison of British and American fuel figures that does not correct for it is wrong by twenty per cent.
Where you meet this conversion
Fuel economy comparisons above all, in motoring journalism and in vehicle marketing. Older Canadian and Caribbean documentation uses imperial gallons while neighbouring American sources use US gallons for the same commodities. Aviation fuel planning, agricultural spray rates and marine fuel calculations all encounter both. The safe practice in any technical document is to write the volume in litres, which is unambiguous, and give the gallon figure only as a parenthetical with the system named.