Editing Proportional–integral–derivative controller (section)

===Reciprocal gain, a.k.a. proportional band===
In many cases, the manipulated variable output by the PID controller is a dimensionless fraction between 0 and 100% of some maximum possible value, and the translation into real units (such as pumping rate or watts of heater power) is outside the PID controller. The process variable, however, is in dimensioned units such as temperature. It is common in this case to express the gain <math>K_p</math> not as "output per degree", but rather in the reciprocal form of a ''proportional band'' <math>100/K_p</math>, which is "degrees per full output": the range over which the output changes from 0 to 1 (0% to 100%).  Beyond this range, the output is saturated, full-off or full-on.  The narrower this band, the higher the proportional gain.