Ah... okay, so your statement that the button's diameter is 24mm was an eyeballed estimation using an inches-ruler. Saying it is 24mm sounded like you'd measured it with a digital caliper. Since you are (apparently) using an inches-ruler, 1.0-inch precisely equals 25.4 millimeters.
About it being a "coat-size" button... in civil war American Military button sizes, 24-to-26 millimeter buttons are "overcoat-size." Here is a table of the sizes, from that time-period in America (the British used a larger size-system):
11-13mm = kepi size
14-16mm = cuff size
17-18mm = vest size
19m-23mm = coat size
24-26mm = overcoat size
Note: there are some exceptions in usage... such as, the 26mm CSA-in-the-shield buttons were worn on the officer's normal uniform, rather than a winter uniform overcoat.