Most writers refer to speedwork repetitions in meters because they’re often run on a competition track, and such tracks can measure out 100 meter increments. On a track, you can run exactly 200, 300, 400, 1200, 2800, etc, meters.
Of course, many don’t have access to a track, and many American runners don’t use the metric system given our nation refers to distance in imperial miles.
The easy answer for conversions is that 400 meters is about 1/4 mile, 1600 meters is about a full mile, and so on.
But another complication of not running on a track is that measuring out exactly a quarter mile for a rep, let alone 400 meters, on a public right of way is unclear and difficult. Our parks paths, landmarks, etc, aren’t ever spaced out exactly right. A space between two light posts, benches, ends of a stretch of path, city block, can be 530 meters, 0.3 mile, 677 meters, etc.
Plus, relying on your GPS watch for distance doesn’t solve the problem, because your GPS readings aren’t totally accurate. A mapped run often shows you running through landmarks as the GPS signal guesstimates your actual route. It certainly won’t measure out your exact distance or velocity. Map the actual route run on an Open Maps interface, and you’ll find a difference of several tenths of a mile.
So how do you run those 800 meter repeats, or quarter mile repeats?