Series and Parallel Resistor Calculator
The total resistance of up to 12 resistors in series or in parallel, and the current and power they take from a supply voltage if you give one.
Result
Total resistance: 20 Ω
Ideal resistors. Real parts are within their tolerance, so the total is too.
- Resistors
- 3
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How to use the Series and Parallel Resistor Calculator
- Choose whether the resistors are in series or in parallel, and the unit you will enter them in.
- Enter one resistor per row, from two up to twelve.
- Optionally enter the supply voltage to see the total current and power as well.
The formulas
series: R = R1 + R2 + … + Rnparallel: 1/R = 1/R1 + 1/R2 + … + 1/Rncurrent: I = V ÷ R power: P = V² ÷ RAll the resistors in a group are entered in one unit, ohms, kilohms or megohms, and converted to ohms first. The total is shown with whichever prefix suits it.
Zero and negative values
A 0 Ω branch in parallel is a wire across the others, so the whole group is 0 Ω and a supply across it would be a short circuit. The page says so and gives no current. A negative resistance is not a physical resistor, and the page refuses it.
With your numbers
- R = 1 Ω + 6 Ω + 13 Ω = 20 Ω
Quick reference
Ideal resistors. Real parts are within their tolerance, so the total is too.
| Example | Total resistance |
|---|---|
| 1, 6 and 13 Ω in series at 12 V | 20 Ω |
| 1, 6 and 13 Ω in parallel at 12 V | 0.8041 Ω |
| Two 100 Ω in parallel | 50 Ω |
| 4.7, 10 and 2.2 kΩ in series | 16.9 kΩ |
| 4.7, 10 and 2.2 kΩ in parallel | 1.303 kΩ |
| Four 1 kΩ in parallel | 250 Ω |
Common questions about the Series and Parallel Resistor Calculator
- How do I add resistors in series?
- Add them up. The same current flows through each one in turn, so their voltages add, and so do their resistances: 1 Ω, 6 Ω and 13 Ω in series make 20 Ω. The total is always larger than the largest resistor.
- How do I combine resistors in parallel?
- Add their reciprocals and take the reciprocal of the sum: 1/R = 1/R1 + 1/R2 + 1/R3. Each resistor sits across the same voltage and gives the current another path, so the total is always smaller than the smallest resistor. The same 1, 6 and 13 Ω in parallel make about 0.804 Ω.
- Is there a shortcut for two resistors in parallel?
- Yes: product over sum, R1 × R2 ÷ (R1 + R2). Two equal resistors in parallel give half of one, so two 100 Ω resistors make 50 Ω, and n equal resistors give one nth.
- What if the circuit mixes series and parallel?
- Work from the inside out. Combine each group that is purely parallel or purely series into one equivalent resistance, then treat that as a single resistor in the next step. This page does one group at a time, so run it once per group.