Any mass-production process that is aimed at producing a target value of a measurable quantity will inevitably produce a range of values that are centered around the desired value and for which a maximum **tolerance **can be specified. The tolerance is the maximum difference between any actual value and the target value, usually expressed as a percentage. For example, a 10 kW 20% resistor may have a value of:

Tolerance series of preferred values, shown in Table, are ranges of target values chosen so that no component can be rejected on grounds of incorrect value. They also allow a designer to specify a component whose variation will not be more than that allowed for in calculations. The mathematical basis of these preferred values is the sixth root of ten ( 6 √10*) *for the E6 20% series (there are six steps of value between 1 and 6.8), and the twelfth root of ten ( 12√10*) *for the E12 10% series. The **E-figure **indicates the number of values in each decade (1–10, 10–100, 100–1000, etc.) of resistance value. The figures produced by this series are rounded off. For example:

These figures are rounded to the familiar 1.5, 2.2, 3.3, 4.7 and 6.8 that are used in the 20% series, and similar rounding is used for the 10%, 5%, 1% and other series, with the 5% series using values based on the 18^{th} root of ten. A simple view of the tolerance series is that, taking the 20% series as an example, 20% up on any value will overlap with 20% down on the next higher value.

**Example: **

4*.*7 + 20% *of *4*.*7 = 5*.*64 *and *6*.*8 − 20% *of *6*.*8 = 5*.*44*, allowing an overlap.*

After *manufacture* **resistors** are graded with the 1%, 5% and 10% tolerance values removed, and the remaining resistors are sold as 20% tolerance values. Because of this it is pointless to sort through a bag of 20% 6K8 resistors, for example, hoping to find one that will be of exactly 6K8 value. Such a value will have been removed in the grading process by the manufacturer. When close-tolerance components are specified it will be for a good reason and 20% tolerance components cannot be substituted for 10% or 5% types. Nowadays it is more common to find that the highest tolerance that is sold is of 10%, reflecting the diminished number of carbon composition resistors being manufactured.