At this time the only dimension we're reasonably sure of is that the diameter of BB-8's ball in the movie is 506mm, which is 19.92" (inches). If you're dealing in inches then 20" will look fine. I've explained below how I got all the measurements so that if you're making a different sized BB-8, you can still do what I did in order to get the proportions right or as close as you want to.
And here are more details for the head.
How the dimensions were obtained
To get the dimensions I first started with the photo below of J.J. Abrams with BB-8 which has BB-8 standing fairly straight on to the camera. I then brought it into a drawing program, assigned labels to the various dimensions and measured them in the drawing program using the arbitrary units the drawing program gave.
Since I knew that the ball's diameter (balld) is 506mm/19.92" I could say that 4.19 units = 506mm. Therefore to get any other dimension I simply multiply the units for that dimension by 506/4.19 for millimeters and 19.92/4.19 for inches. Or by doing the division that means multiply the units for that dimension by 120.76 for millimeters and 4.75 for inches.
If you're making a BB-8 that's a different size then measure the diameter of the ball, then do as I did above and divide that diameter by 4.19. Take that resulting number and multiply it by the head diameter unit below to get the head diameter.
balld: 4.19 units, 19.92", 508mm (ball diameter)
For the details of the head I started with a photo taken from the Star Wars Celebration in Anaheim in 2015 video where BB-8 walks out on stage. Just as I did for the above photo with J.J. Abrams, I brought BB-8's head photo into a drawing program and took measurements in arbitrary units.
Here are all the head units, as well as the dimensions in inches and millimeters. From the analysis further above of the J.J. Abrams and BB-8 photo I know that the head diameter (hd) is 11.6", 295mm. That means that the 12.70 units above is equivalent to 11.6" or 295mm. So as we did further above, that means for this head photo there are 11.6" per 12.70 units or 11.6/12.70 which is 0.91 inches/unit, or there are 295mm per 12.70 units or 295/12.70 which is 23 mm/unit. Using the same trick as further above, we then multiply all the units except the first one by 0.91 to get their dimensions in inches and by 23 to get their dimensions in mm, resulting in the list below.
hd: 12.70 units, 11.6", 295mm (head diameter)