A "true" 15mm miniature (that is, 15mm from foot to eye) is equivalent to 62 inches in height. (I'm assuming the average soldier was a bit on the short side by contemporary standards).
This means that a 15mm miniature is about 0.009525019 the height of the soldier it represents (62 inches = 1574.8 mm; 15mm/1574.8mm = 0.009525019).
The usefulness of these calculations is that they make it possible to accurately scale distances on the battlefield.
For example, let's say a 100 man battalion were to be deployed as a single rank in close order. In close order the interval between files would be about 15 inches (see this page for a discussion of open and close order). Assuming that a typical soldier was something like 18 inches across the shoulders (I'm assuming that they were on the slender side, too), then each soldier would occupy 33 inches of space, and the battalion would have a frontage of 3,300 inches, or 275 feet.
However, at 1:20 scale with 15mm miniatures this translates into 5 miniatures with a frontage of 1.57 inches (3,300 inches * .009525019 / 20). The picture below provides a visual demonstration, although this "battalion" has a frontage that is slightly too wide because the bases could not be pressed further together.
If the same 100 man battalion were to be deployed as a single rank in open order, then the interval between files would be about 24 inches. Again, assuming that a typical soldier was something like 18 inches across the shoulders, each soldier would occupy 42 inches of space. The battalion, in turn, would have a frontage of 4,200 inches, or 350 feet. At 1:20 scale with 15mm miniatures this translates into 5 miniatures with a frontage of 2.00 inches. The picture below provides a visual demonstration.
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