Hi guest, I think that is like asking how long is a piece of string! It depends on the type of grass, the weather (really short grass doesn't do very well in hot, dry conditions) and of course how good your mower is! I would aim for around a couple of inches minimum.

Cut Utility lawn spring-autumn 1 1/4". Summer 1". Luxury lawn Spring-autumn 3/4". Summer 1/2". Shorter than these will reduce strength of grass. Lawns that are 1 1/2" long swamp finer grasses