There are 13 inch beagles and 15 inch beagles, but those are adult sizes. Yours appears unusually tall and lanky. Did someone tell you he's a purebred? If I just met your dog on the street, I'd guess Harrier or even foxhound, but neither if those is as common as beagles.
According to the UK Kennel Club breed standard "Desirable minimum height at withers: 33 cms (13 ins). Desirable maximum height at withers: 40 cms (16 ins)". That's not saying that you won't get individuals over or under those heights. If he's from working or hunting lines, those breeders tend to care less about meeting the standard than ability, so you will see splits in the breed's appearance between show and field/working lines. Some breeds are so divergent between show and working/field lines that they barely resemble each other.
UK standards are 13 inch and American standards are 15 inch. Both sizes show separately but they are both beagles. When I had a beagle, my 15 inch beagle was sometimes referred to as an American beagle and the 13 inch dogs were called English beagles.