A good ordinary book or body-text font should come with smallcaps. How high should the smallcaps be? I suppose this would be expressed as either relative to the x-height (i don't think all smallcap designs make them exactly the x-height), or relative to the cap-height.
Not sure if all, but most small caps fonts I've seen are slightly taller than the X height, although the amount varies. I don't think there is anything set in stone. It's ultimately up to the designer.
Some examples pulled from Adobe Fonts.
And of course the ubiquitous Copperplate Medium, which only comes in small caps anyway, has small caps slightly smaller than the large caps height.
I am taking it that you are asking this question in order to synthesize a set of small caps by scaling the caps in a typeface, rather than designing a set of small caps.
This is a bit of a “How long is a piece of string?” question. The problem being that there are a lot of variables:
- Style of typeface
- Weight of typeface
- Size of text
- Relative size of caps to x-height
- The exact problem you are trying to solve in using small caps…
As a generalisation, I would expect small caps to be around 10-20% taller than the x-height. If you size the small caps at the x-height it will tend to look “old fashioned”, and you will almost certainly have an issue with the relative weight of the small caps/lowercase/caps.
You might run into problems with some typefaces where the normal cap height is not much higher than the x-height, or, at least, is significantly below the lowercase ascender height (which is typical of modern text faces). In these cases you should probably try to align the small cap height somewhere between the x-height and cap height – about halfway should do it.
The overall problem is to distinguish the small caps from the lowercase, and from the caps, which is a fairly subtle problem.