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”.