pound-force
Forceexact by definition
The pound-force is the weight of one avoirdupois pound under standard gravity, exactly 4.4482216152605 newtons. The definition is exact because it fixes standard gravity at exactly 9.80665 m/s² and the pound at exactly 0.45359237 kg. Pound-force is a force unit and pound is a mass unit, a distinction that causes more engineering confusion than any other pair in the customary system.
Watch out: Standard gravity is a defined constant, not the local value. Actual gravity ranges from about 9.78 m/s² at the equator to 9.83 m/s² at the poles, so a scale calibrated in one place and used in another reads slightly differently unless it has been recalibrated. The definition of the pound-force does not vary with location, only the actual weight of a real object does.
| 1 lbf | 4.4482216 N |
About the pound-force
The pound-force exists because customary practice wanted the number on a scale and the number in a force equation to look the same. Fixing standard gravity at exactly 9.80665 m/s² achieves that: one pound of mass weighs one pound-force, to the digit, everywhere by definition. The cost is that a system which previously had one unit called "pound" now has two, and the equations no longer tell you which one is meant.
Newton's second law is where it bites. In SI, \(F = ma\) works with newtons, kilograms and m/s². In customary units, if you put pounds of mass and ft/s² into the right side you get poundals, not pounds-force, because 1 lbf accelerates 1 lb at 32.174 ft/s². Engineers resolve this two ways. The slug is defined as the mass that 1 lbf accelerates at 1 ft/s², so it equals 32.174 lb, and with slugs the law is clean again. Alternatively you carry the constant \(g_c = 32.174\ \mathrm{lb\,ft\,lbf^{-1}\,s^{-2}}\) and write \(F = ma/g_c\), which is the convention in most US thermodynamics and fluids texts.
A practical tell: if a quantity is going to be multiplied by an acceleration, integrated over time as an impulse, or divided by an area to give a stress, it needs to be a force. If it is going to be multiplied by \(g\) or divided into a momentum, it needs to be a mass. Writing "lb" for both and hoping is the origin of a long list of expensive mistakes.