# Consistent Unit Systems in FEA

Symbol Quantity Dimension N‐m SI N‐mm SI in‐lb System ft‐lb System
$l$ length $L$ meter($\text{m}$) millimeter($\text{mm}$) inch($\text{in}$) foot($\text{ft}$)
$m$ mass $M$ kilogram($\text{kg}$) tonne($\text{t}$, $10^3\text{kg}$) snail = 386.2 “lb mass” slug = 32.19 “lb mass”
$F$ force $MLT^{-2}$ Newton($\text{N}$) Newton($\text{N}$) pound-force($\text{lbf}$) pound-force($\text{lbf}$)
$v$ velocity $LT^{-1}$ $\text{m/s}$ $\text{mm/s}$ $\text{in/s}$ $\text{ft/s}$
$a$ acceleration $LT^{-2}$ $\text{m/s}^2$ $\text{mm/s}^2$ $\text{in/s}^2$ $\text{ft/s}^2$
$g$ gravity $LT^{-2}$ $9.8\text{m/s}^2$ $9.8\times10^3\text{mm/s}^2$ $386.2\text{in/s}^2$ $32.19\text{ft/s}^2$
$\sigma/p$ stress/pressure $ML^{-1}T^{-2}$ Pascal($\text{Pa}$, $\text{N/m^2}$) MegaPascal($\text{MPa}$, $\text{N/mm^2}$) $\text{psi}$, $\text{lbf/in}^2$ $\text{lbf/ft}^2$
$\rho$ density $ML^{-3}$ $\text{kg/m}^3$ $\text{t/mm}^3$ $\text{snails/in}^3$ $\text{slugs/ft}^3$
$E/W/M$ energy/work/moment $ML^2T^{-2}$ Joule($\text{J}$, $\text{N}\cdot\text{m}$) milliJoule($\text{mJ}(10^{-3}\text{J})$, $\text{N}\cdot\text{mm}$) $\text{lbf}\cdot\text{in}$ $\text{lbf}\cdot\text{ft}$

## Discuss on Imperial Units

It is critical to note that a pound is not a unit of mass for engineers and should not be used as a unit of mass. That is to say:

A pound is a unit of force.

Not so obvious is that mass is now in units of “12 x slugs”. Although some have named this mass unit the “slinch” or “blob”, we prefer the colloquially applied name, the “snail”.