The resistance taper or “curve” (or law) describes the relationship of the shaft rotation to the change in resistance.  There are several commonly used tapers as well as many custom types.  Tapers are generally plotted on a graph with the mechanical rotation plotted on the X axis (horizontal) and the resistance change on the Y axis (vertical).

The most common taper or curve is linear and is not actually a curve but a straight line when plotted on a graph. 

The easiest way to determine if you have a linear taper is to place the shaft at the mid-point of the rotation and measure the resistance between the center terminal and either end terminal.  If the shaft has a slot in it, then simply line up the slot with the center terminal of the potentiometer for the mid-point of the rotation.  At that point the resistance measured between the center terminal and terminal 1 would be 50% of the total resistance of the pot. Don’t forget to take into consideration the overall tolerance of the potentiometer which is typically +/- 10% when measuring the midpoint resistance.

The next most popular curve would be the Audio curve which is also known as a log, Z, and depending on the manufacturer either A or B.  An audio taper is usually referred to by the percentage of resistance change measured at the midpoint of the shaft rotation.

The industry standard method of designating a non-linear taper consists of the taper resistance percentage at the midpoint of the rotation and the taper curve.  For example a 10% audio taper would be designated as a 10A curve

There are two basic types of audio curves; 10% and 15%.
 

A 10% audio curve would measure 10% of the total resistance of the potentiometer when the shaft is at the midpoint.  If the shaft has a slot in it, then simply line up the slot with the center terminal of the potentiometer for the midpoint of the rotation.  Most audio taper commercial potentiometers manufactured to meet mil-spec requirements would correspond to a 10% audio curve.

A 15% audio curve would measure 15% of the total resistance of the potentiometer when the shaft is at the midpoint.  If the shaft has a slot in it, then simply line up the slot with the center terminal of the potentiometer for the midpoint of the rotation.  Most off-shore manufacturers use a 15% audio taper for their audio taper designs.

The next most popular curve would be the reverse audio taper also known as a reverse log, reverse z, or depending on the manufacturer, and A or B.  Determining if you have a reverse audio taper is basically the same as an audio except the result would be the inverse; i.e. for a 10% reverse audio taper, you would see a measurement of 90% of the total resistance at the midpoint of the shaft rotation.

There are a few more common tapers which are illustrated in the chart below and in theory, any taper curve can be made but minimum order quantities would apply.