Why carat weight alone does not tell you a size
A carat is a unit of weight — exactly 0.2 grams, fixed since 1907 — and weight is volume multiplied by density. Two stones of the same carat weight in two different minerals occupy different volumes whenever their densities differ, so they measure different millimetres. This is the single fact that trips people up when they picture a "1 carat stone" from the diamond figure alone: a 1 carat ruby is a smaller, denser lump than a 1 carat diamond, and a 1 carat opal is a noticeably bigger one.
The trade handles this with weight-estimation factors: published constants, specific to a shape, that relate a stone's length, width and depth in millimetres to its weight in carats for a stone of normal proportions. Round brilliant is 0.0061, princess is 0.0083, and so on for each of the eleven common shapes — these are the same factors this site's diamond size calculator uses. They are calibrated to diamond's specific gravity of 3.52.
To use them for anything else, the species' own specific gravity has to enter the calculation. A ruby is corundum at SG 4.0 — about 14% denser than diamond — so a ruby weighing the same number of carats as a diamond has about 14% less volume, and reads visibly smaller face-up. An emerald, by contrast, is SG 2.72, lighter than diamond, so an emerald outweighs a diamond of the same apparent size, or equivalently looks bigger for an equal carat weight. This chart runs that correction for every listed species so the millimetre figures are for the actual mineral, not a diamond wearing the ruby's name.
What the chart assumes, and where it stops being reliable
Every figure here assumes a normally proportioned, well-cut stone — the standard depth percentage and length-to-width ratio published for that shape. Real stones are not always cut that way. A stone cut noticeably deep carries more of its weight in the pavilion and reads smaller face-up than the chart predicts for its weight; one cut shallow spreads wider and reads larger. The gap is usually a few percent, not enough to matter for browsing a listing, but enough that it should never substitute for an actual measurement when money is on the line.
The other place this needs care is with stones sold by millimetre rather than carat — moissanite is the common example, priced and listed by mm diameter precisely because its lower density (SG 3.21) makes carat weight a poor proxy for how big it looks. The chart still computes an honest carat-to-mm figure for it, but a moissanite retailer's own mm-based sizing is the number that actually matches what is on their site.