This is typical average height black wool top hat is about the most common top hat you will find.
On this hat the brim is turned up and the crown while still the top cylinder tapers out towards the top.
Top hat can be taller or lower than this, the cylindrical crown can taper in, be straight or in the case of mad hatter style top hats taper out even more, the brim can be flat or turned up, all these are variations are top hats, some have sub type names others are just a tall top hat or low height top hat.
The black felt top hat like this one has been around since about 1900 for funeral services and still in use today.
I consider a average height top hat to be between 12 and 13 cm high.