Pound (force) - Definitions

Definitions

The pound-force is equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in Earth's gravity (which varies from place to place by up to half a percent) can safely be neglected.

The 20th century, however, brought the need for a more precise definition. A standardized value for acceleration due to gravity was therefore needed. Today, in accordance with the General Conference on Weights and Measures, standard gravity is usually taken to be 9.80665 m/s2 (32.174 049 ft/s2).

The acceleration of the standard gravitational field (gn) and the international avoirdupois pound (lbm) define the pound-force as:

\begin{align} 1\,\mathrm{lb}_f &= 1\,\mathrm{lb}_m \cdot g_n \\ &= 1\,\mathrm{lb}_m \cdot 32.174049\,\mathrm{\tfrac{ft}{s^2}}\\ &= 32.174049\,\mathrm{\tfrac{ft\cdot lb_m}{s^2}}\end{align}
\begin{align} or\end{align}
\begin{align} 1\,\mathrm{lb}_f &= 0.45359237\,\mathrm{kg} \cdot 9.80665\,\mathrm{\tfrac{m}{s^2}}\\ &= 4.4482216152605\,\mathrm{N} (\mbox{exact})\end{align}

This definition can be rephrased in terms of the slug. A slug has a mass unit equivalent of 32.174049 lbm. A pound-force is the amount of force required to accelerate a slug at a rate of 1 ft/s2, so:

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