Often asked and a very good question.
Standard widths vary somewhat depending on the lengths.
Aside from the standard slate sizes, you usually are able to have other sizes specially made, but most producers will demand a premium for deviating from standard production. Slate is still split by hand, most often with hammer and chisel , sometimes with pneumatic chisel. As you might guess, slate which is two or three times thicker than standard will usually be significantly more expensive. Slate comes in many colors, and many variations of those colors. From this Slate Valley of roughly 100 square miles, comes the most colorful array of roofing slates in the world.