One calorie is exactly 4.184 joules. This is the small calorie of physics and chemistry, not the food Calorie — the one on a nutrition label is a thousand of these, and conflating them is the most persistent unit error in popular science writing.
About the units
The calorie was defined as the energy required to raise one gram of water by one degree Celsius, which made it a natural unit when heat was studied by measuring water temperature. That definition turned out to depend on the starting temperature, since water's heat capacity varies slightly, so several calories were defined: the thermochemical calorie at exactly 4.184 J, the 15 °C calorie at 4.1855 J, and the International Steam Table calorie at 4.1868 J. The joule superseded all of them once heat and mechanical work were understood as the same quantity — a realisation credited to James Prescott Joule, whose experiments in the 1840s measured the mechanical equivalent of heat.
The exact factor
The thermochemical calorie is defined as exactly 4.184 J, so the conversion is exact by convention rather than by measurement. The relationship that causes trouble is the factor of a thousand to the food Calorie: 1 kcal = 1 Cal = 4,184 J. A physics problem quoting 500 calories means 2,092 joules; a food label quoting 500 calories means 2,092 kilojoules. The two differ by three orders of magnitude and are written identically.
Where you meet this conversion
Chemistry and physics, particularly thermochemistry, where reaction enthalpies were traditionally tabulated in calories per mole and are now given in joules per mole. Older textbooks and datasheets use calories throughout, so converting historical thermodynamic data is a routine task. Explosives and propellant energetics still use calories per gram in some literature. Outside science the unit survives only in its capitalised nutritional form, which is why the small calorie now appears mainly as a source of confusion.