The recommended sizes are as follows:

The ball comes with an exercise chart.

How big should my exercise ball chair be?
For a ball chair, most average size people will sit on a 65 cm exercise ball. If you are over 6'0 with long legs you may wish to try a 75 cm. Under 5'3 a partly deflated 65 cm ball will likely be better than a fully inflated 55 cm ball, as it is better if the exercise ball is a little softer than too hard.

General info on Stability Ball Sizing

What we have found is that stability ball sizing is subjective.  Websites, boxes, posters, books, PT recommendations, etc all differ so it is not an exact science. If someone were to be exactly precise, it is by the length of the leg from the heel to the back of the knee. When one sits on it there leg at the knee should not be bent over 90 degrees. So even weight enters into the final sizing as a larger person compresses the ball more than a lighter person so a heavier person at the extreme of the size guidelines would need to move up one size. Also a person with longer lower legs may need to go up a size. We have found it is best to go to the larger size as you can always let air out of it to make it a little smaller but you can't make a smaller ball larger by overinflating it without damaging the ball.