12 to 18", but you'll need to plant the shorter varieties of carrots.

12 inches is minimum for small leaf crops and short root crops. For large, extensive-rooted veggies (e.g., tomatoes, you'll need at least 24 inches and even more is better.

You may find that a 30-inch raised bed (universal height for kitchen counters) not only gives your veggies optimum room, it'll give your back a break.

Joe

I have had raised beds for years and they are 2.5 feet deep which seems to work fine for everything I grow. If you have gophers in your area you might want to line them with wire.