mph to Mach Converter - Mile per Hour to Mach

Conversion derivation

Express both mph and Mach in the same base unit m/s (meter per second), then cancel the shared base unit.

1. 1

   Rewrite mph in the base unit

   $$1\mathrm{mph}=0.44704m/s$$
2. 2

   Rewrite Mach in the base unit

   $$1\mathrm{Mach}=343m/s$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{mph}& =\frac{0.44704\cancel{m/s}}{343\cancel{m/s}}\times 1\mathrm{Mach}\\ & =\frac{0.44704}{343}\mathrm{Mach}\\ & =0.001303323615\mathrm{Mach}\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{Mach}& =\frac{343\cancel{m/s}}{0.44704\cancel{m/s}}\times 1\mathrm{mph}\\ & =\frac{343}{0.44704}\mathrm{mph}\\ & =767.269148175\mathrm{mph}\end{array}$$