Units

There are two (okay, three) major systems used across the world:

Metric

The standard set of internationally recognised units used by people of most countries and all scientists and most engineers.

American Customary

The American version of the British Imperial system (or the British system prior to some standard changes). It has some subtle differences particularly with the way liquid volumes are handled.

British Imperial

The standardised British units prior to metrication. Still commonly used in the UK and other parts of the Commonwealth if you are of a certain age.

If you are familiar with only one set of units, then information presented in another one can be either confusing or impenetrable. Your story setting may determine which system is appropriate to use when characters are talking. But giving players the option to see conversions to their familiar units can aid their understanding. If your world has its own set of fantasy units, players will need conversions to real-world units.

Computation

I'd recommend doing any computation with units in metric if you are going to be offering presentation conversions for your players. If this approach was good enough for NASA when they built the Apollo Guidance Computer (AGC) back in the sixties then it's good enough for your game! The internal computation was all metric, it was just converted into customary units for display to the astronauts.
See Wikipedia: Apollo Guidance Computer