There are a couple of ways to handle that if you don't want to measure. The simplest is 4E's "a square is a square" approach, if you don't mind square fireballs. More realistic is 3E's "square and a half diagonals," which is not one hundred percent accurate but comes close enough to not matter in 95% of cases.The thing is, on the surface, grids only let you accurately track distance orthogonally. There is something to be said for a 20' radius actually being a radius. Even when we use gridded maps, the minis often get placed whereever, and important diagonal movement is measured.
IMO, there's really no sense using the 4E approach in 5E. Exact positioning is no longer a big deal, so if you're willing to handwave diagonals, you might as well handwave the whole grid. I can see using the 3E approach if you're looking for precision.
I do think it's funny that gridless is both the most precise (if you measure every move) and least precise (if you eyeball it) option for battlemat play.