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I know that adult size violas are sold by length in inches, (i.e. instead of 4/4, 7/8, etc.) and can vary to better fit the player.

Are viola tuning pegs all the same diameter or do those have to change depending on the specific viola size? Are some 4/4 violin tuning pegs interchangeable with some violas, or are all adult viola tuning pegs larger in diameter than their violin counterparts?

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There are different sizes of pegs for violas, but they are not really standardized. And a thick violin peg will fit some viola, but the head is likely to be a bit smaller.

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    The taper of the pegs also needs to match the taper of the holes, otherwise tuning will be somewhere in between difficult and impossible. The taper can accommodate small differences in peg diameter between different instruments.
    – user19146
    Commented Oct 28, 2016 at 21:40
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    True. While there is a modern standard of 1:30 taper for violins and violas, and 1:25 for cello, you can't assume any given hole or peg is going to fit, especially with old instruments.
    – Scott Wallace
    Commented Oct 29, 2016 at 16:47
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From 15 inch Violas and larger the tuning pegs are larger than violin. The 14 inch Viola corresponds in size to the 4/4 violin, and the 13 inch to the 3/4 violin.

Tuning pegs are sold in "blanks" with the taper size large for cutting down to fit. Viola peg blanks often have "Standard" and "Thick" sizes available for the shank size as well. The head sizes change with the different size pegs.

How big the shank ends up being is different for each instrument, dependent on the manufacturer and age of the instrument. Each peg set is shaped specifically for each instrument and peg hole. Eventually with wear and/or reaming the peg holes may become too large and require filling and re-holing.

Taper size is currently standard at 1:30 ratio, and older tapers for gut string instruments may be found down to 1:20.

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