Often, when specifying trimmer resistors (or capacitors, or anything really), you want a desired range, but are limited to common values. And trimmers are selected from a much more crude step size (like 1-2.5-5-10) than fixed resistors are (E24, etc.). You might also want to save on BOM items by reusing a single trimmer part for multiple purposes, even if its value isn't well suited to those places. What to do? You can increase the minimum resistance by connecting more resistance in series, and reduce the range by shunting it in parallel. This does reduce the linearity of the control, but that's not usually a big problem for trimmers (if it works at all, it's okay).
This calculation solves for a desired total range, so you can solve directly for the range you need. Example: an adjustable resistor in an op-amp gain network. 1% resistors are used, so the adjustment needs to cover ±2%, or 200Ω for a 10k nominal resistor.
This equation will break for unreasonable values (you can't get more output range than you put in!), and give negative or imaginary outputs for inputs beyond that range. Which if you think about it, is perfectly reasonable: the only way a range could be increased is by using a negative resistor to cancel some of it. (Imaginary values generate an error, and can be considered an "out of range" indicator.)
Enter new numbers and see the remaining output value change. Floating point format ("1.1E-6") works; engineering units ("1.1u", etc.) do not.
Note that the units are simply ratios, so their actual units do not matter (as long as the same units are used for all steps). They're labeled in Ω and pF as an example.
The resistor/inductor case. R is the adjustable or variable element. Typically, a trimmer, potentiometer or rheostat has a minimum near zero ohms, so you would enter Rmin of 0 and Rmax of the rated value. If a dependent device is used (like a thermistor), enter the resistance of the two endpoints you wish to match to. (For example, this could be used to tame an NTC thermistor into a narrower resistance range.)
Solving for a network's total, given parts values:
Capacitor is separate, because capacitors behaves reciprocally compared to resistors or inductors. Although the results are the same, by employing a series-parallel transformation to the circuit. C is the variable element.
Solving for a network's total, given parts values: