How to display imperial distances rather than metric

Currently the UI for the various routing engines is just that, a thin user interface that calls the routing engines and displays the results. Obviously it would be possible to extend the interface, but for now the answer is to go directly to the websites of the routing engines and use them. However neither OSRM nor graphopper offer such an option at this point in time.

On the OSM website, and throughout most of the project, and on the ground pretty close to everywhere that isn't Liberia or Burma (and even the US officially, even if most DOTs are annoyingly intransigent on putting up modern signs) are using SI units. There are data consumers (mostly personal navigation apps) that will do the conversion to legacy units, but you're probably going to find it easier to convince your region to modernize if you're stuck on legacy units.

It does work on this routing demo: https://fast-routing-api.demo.routingapi.net/ if you have the favored browser language set to "en-US" or "en-GB" (e.g. accept-language set to en-US or en-GB in about:config settings in Firefox). Than you should see imperial measurements in driving directions.

Edit: the new Graphhopper demo at https://graphhopper.com/maps/ also got a metric/imperial measurements switch.

you have to use the language setting in your browser . Set it to English US for non metric or just english for metric