A Golf driving range would probably be at least 300 yards long. Depending on how many bays it has it could be anything from 300-700 yards wide. You need to allow the players to hit shots to the left and to the right and vary their shots. There is no standard size, all driving ranges are different.
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The mats are normally 5' by 5' and they allow about a foot behind you and 1-2 feet in front of you for the ball tray. So, we are talking about 6-7 feet wide (maybe 8), and about the same as deep.
Since a golf driving range is for practice there is no set size for a range. However, you probably want at least 100 yards (or meters) wide and much deeper than that, say 300 yards. The wider your driving range the more room on it for golfers to practice and the greater your income. In Japan, due to the cost of land, it is not uncommon to have two story driving ranges!