One foot-pound is 1.3558179483 joules. The unit deserves care for a reason unrelated to its size: the foot-pound of energy and the pound-foot of torque have the same dimensions and are not the same quantity.
About the units
A foot-pound is the work done when a force of one pound-force acts through a distance of one foot. Torque, by contrast, is a force applied at a perpendicular distance from an axis, and its imperial unit is the pound-foot — conventionally written with the units in the other order for exactly this reason. Both come out as newton-metres or foot-pounds-force dimensionally, but energy is a scalar and torque is a vector quantity. Adding a torque to an energy is meaningless even though the units cancel identically, and confusing the two is a recognised source of error in mechanical work.
The exact factor
The exact value is 1.3558179483314004 J, from the pound-force of 4.4482216152605 N times the foot of 0.3048 m. Reference points: a bullet from a common rifle cartridge carries 2,000 to 3,000 foot-pounds of muzzle energy, which is 2.7 to 4.1 kilojoules. A car engine producing 300 pound-feet of torque is producing 407 newton-metres — the same arithmetic, different quantity. Hand tools are torqued to specifications in pound-feet in American manuals and newton-metres in European ones.
Where you meet this conversion
Firearms ballistics, where muzzle energy is universally quoted in foot-pounds in American sources and joules in European. Impact testing, drop tests and fastener torque specifications all use the pair. Older mechanical engineering literature in Britain and America uses foot-pounds for work and energy throughout. Anyone reading a specification should check whether the quantity is work or torque before converting, because the correct unit name differs even where the number does not.