Notation
Two numbers, two different things
A standard taper joint is written as two numbers separated by a slash. They describe completely different measurements, which is why swapping one for another rarely works.
The first number is the outside diameter, in millimetres, of the male cone at its widest point — the top of the ground zone. This is the number that decides whether two pieces will physically mate at all.
The second number is the length of the ground surface, in millimetres. It decides how much sealing area you get, and how far the inner joint reaches into the outer one.
Every standard taper joint shares the same cone angle: a 1:10 taper, meaning the diameter shrinks by 1 mm for every 10 mm of length. That shared angle is what makes the system work — and it is why a 24/40 cone slides into a 24/29 socket even though the pairing is not a standard one.