In order to describe the amount of taper of a cone several terminologies are currently in use.
In industry the standard terminology is the "Morse Taper". Morse tapers are expressed as a percentage of the length. If for every inch of length a cone increases in radius by 1 percent of the length it is called a one per cent Morse taper.
The standard way of expressing the taper of an endo file (which is a cone) is in the increase in radius per unit length.
In other words if a file has 16mm of blades and the tip is 0.10mm in diameter i.e. 0.05 in radius and is a one per cent Morse taper the increase in radius is 0.01mm per mm of length.
Over the entire 16mm it would increase in radius 0.16mm.
We do not typically measure the radius of a file.
We use diameters.
Since there are two radii in a diameter the 0.16mm increase in radius translates to a 0.32mm increase in diameter.
Thus in a standard endo file, for every mm the diameter increases 0.02mm.
Now that there are files being made with a non-standard taper we have to be cognizant of these tapers.
The common usage in dentistry is to describe the taper,not as a percentage of length, but in terms of increases in diameter per mm of length.
Thus we now have the standard taper of 0.02 and various others up to 0.12 taper.
To get the dental terminology from the Morse Taper terminology multiply the Morse Taper by 0.02 i.e. a 1 percent Morse taper is a .02 taper and a 7 percent Morse Taper would be a .14 dental taper.
Got it?
OK. Now for some mental gymnastics.
If a file is a standard 1 per cent Morse taper (.02 taper) and at it's tip it is a size 15 i.e. 0.15mm in diameter.
How big is it at a point 1mm from the tip...easy...0.17mm. Right?
If a file is a standard .02 taper and is a size 15, at what point is it the same size as a size 20?
In other words, if you wanted to make a size 20 file out of a size 15 you'd cut off 2.5mm (ignoring the shape of the tip for the moment).
OK. Here's another.
If a size 15 file fits a canal exactly at the apex, at what point should a size 20 begin to bind?
Answer, of course, at the 2.5mm point.
If a blunt ended needle is 0.30mm in diameter and you have prepared a canal to size 15, how many millimeters from the end should the needle bind?
Well let's see.
The canal is 0.15mm at the apex, the needle is 0.30mm so the needle is 0.15mm larger and since the canal increases 0.02mm per mm by dividing 0.15 by 0.02 you'd get 7.5mm. Right?
Now let's get real tricky.
Ready?
If a canal is exactly 16 mm from apex to orifice and is exactly the size and shape of a #15 0.02 taper file and we introduce a #15 0.04 taper file into the canal, how many mm of file will enter the orifice before the file binds?
First we have to figure out how big the canal is at it's orifice. 0.15mm plus (16 times 0.02) which is 0.32 plus 0.15 which is 0.47mm.
So now we have to figure out how far from the tip of a 0.04 taper file it is 0.47mm. So we subtract 0.15 from 0.47, get 0.32 and divide by 0.04 and we get 8.
So if a .04 taper size 15 file was used to follow a .02 taper size 15 it would bind 16 minus 8 mm from the apex.
See how easy it is?