One kilogram is 0.1574730444 stone, because one stone is exactly 14 pounds, or 6.35029318 kilograms. The stone is a British peculiarity that survives almost entirely for one purpose: stating a person's body weight.
About the units
The stone was originally a trading weight, and it varied enormously by commodity — a stone of wool was not a stone of cheese, and values from 5 to 40 pounds are documented across medieval Europe. English law gradually standardised it, and the Weights and Measures Act of 1835 fixed it at 14 pounds for general use. The kilogram, by contrast, is the SI base unit of mass, defined since 2019 through the Planck constant. The stone was formally removed from British trade use in 1985, which means it cannot legally be used to sell anything — yet it remains overwhelmingly the unit British people use to describe how much they weigh, and medical practice accommodates it.
The exact factor
The exact chain is 1 st = 14 lb = 14 × 0.45359237 kg = 6.35029318 kg. Going the other way, 1 kg = 0.157473044417767 stone. In practice nobody uses decimal stone: body weight in this system is stated as whole stones plus pounds, so 80 kg is 12 stone 8 pounds rather than 12.6 stone. To get there, divide kilograms by 6.35029318 for whole stones, then multiply the remainder by 14 for pounds. Confusing decimal stone with stone-and-pounds is the standard error here, and it is a large one: 12.6 stone read as 12 stone 6 pounds understates the weight by about 1.3 kg.
Where you meet this conversion
Almost exclusively British and Irish body weight. Health services in the UK record weight in kilograms but discuss it with patients in stones and pounds, and BMI calculators aimed at British users offer both. Boxing and other weight-class sports use stones and pounds in British coverage and kilograms in international federations, so the same fighter appears at two numbers. Outside the British Isles the unit is essentially unknown, which is why an unlabelled figure like "11 stone" in an international context often has to be converted before it means anything.