Watch strap size comes down to one number: the lug width, which is the gap between the two lugs where the strap attaches, measured in millimeters. Get that measurement right and any strap in that width will fit, regardless of the watch brand or style.
Finding your lug width
The easiest way to check is to look at the current strap where it meets the case. Most straps are stamped with their width on the underside near the buckle, often as a number like 20mm or 22mm. If your strap is not stamped, use a ruler or caliper to measure straight across the gap between the two lugs, right where the spring bar sits. Common sizes run from 18mm to 22mm for most men's watches, with dress watches often on the smaller end and field or dive watches trending larger.
If you do not have the original strap, you can measure the lug gap directly on the case itself with a small ruler, though a caliper gives a more exact reading if you have one lying around.
What else affects the fit
Lug width gets you a strap that physically fits the spring bars, but overall length matters too, especially for larger or smaller wrists. Most straps come in a standard length that fits average wrists comfortably, but if you have a particularly large or small wrist, check the total strap length in the product details before buying, since NATO and canvas straps in particular can run long. Buckle width can differ slightly from lug width on some straps, tapering down toward the clasp, so double check both numbers if the listing provides them.
When in doubt, going with the exact lug width stamped on your current strap is the safest bet. A strap that is even a millimeter off will not seat properly against the spring bar and can look uneven or work itself loose over time.