Resistors are combined in two basic ways. In series the same current flows through each one and their resistances simply add. In parallel the same voltage appears across each one and the reciprocals of the resistances add. Combining resistors lets you create values you can't buy off the shelf, share current between paths, and set precise gains and bias points. This calculator handles any number of resistors in either configuration.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Wikipedia: Series and parallel circuits.
Resistors in series
Series resistors are connected end-to-end so the same current flows through all of them. The total resistance is the sum:
The total is always larger than the biggest individual resistor. Series strings are used to drop voltage, add up to a needed value, or share power dissipation across several resistors.
Resistors in parallel
Parallel resistors are connected across the same two nodes, so each sees the same voltage. The reciprocal of the total equals the sum of the reciprocals:
For exactly two resistors there is a convenient shortcut, the product over sum rule:
The parallel total is always smaller than the smallest resistor. N equal resistors in parallel give R/N — four 100 Ω resistors in parallel equal 25 Ω.
Worked example 1 — three resistors in series
Scenario: 100 Ω, 220 Ω and 330 Ω in series.
If 5 V is applied across the string, the current is I = 5 / 650 = 7.7 mA, and each resistor drops a share of the voltage proportional to its value — the basis of a voltage divider.
Worked example 2 — making a 3.2 kΩ value from standard parts
Scenario: You need 3.2 kΩ but only have standard E-12 values. Put 4.7 kΩ and 10 kΩ in parallel:
This is how you reach values between stocked parts. The calculator above does the same for any list of resistors.
Mixing series and parallel
Real networks combine both. Solve them in stages: collapse each purely-series or purely-parallel group into a single equivalent resistor, then combine those equivalents, working from the innermost group outward until one value remains. For example, two 1 kΩ resistors in parallel make 500 Ω, and putting that in series with a 470 Ω resistor gives 970 Ω.
Frequently Asked Questions
Add them: Rtotal = R1 + R2 + R3 + … Series resistors share the same current and the total is always larger than the largest single resistor. Example: 100 + 220 + 330 = 650 Ω.
Add the reciprocals: 1/Rtotal = 1/R1 + 1/R2 + …, then invert. Parallel resistors share the same voltage and the total is always smaller than the smallest resistor. For two, use R = (R1R2)/(R1+R2).
Rtotal = (R1 × R2) / (R1 + R2) — the product-over-sum rule. Two equal resistors in parallel give exactly half their value.
Series is always higher (resistances add). Parallel is always lower than the smallest resistor, because extra paths give the current more ways to flow.
Yes. Reduce each purely-series or purely-parallel group to one equivalent resistor, then combine those, working from the innermost group outward until a single value remains.