For a combined circuit, reduce it piece by piece: series resistors add, parallel ones combine as product over sum. With R1 = 100 Ω in series with two 200 Ω resistors in parallel, the pair gives 100 Ω and the total is 200 Ω. At 12 V that network draws 0.06 A and dissipates 0.72 W.
Mixed networks are where hand calculations usually slip: a student adds a parallel pair as if it were in series, or a hobbyist forgets which resistor sits in which branch. This calculator covers the two three-resistor layouts that appear most often in textbooks and on breadboards, a resistor feeding a parallel pair, and a series string shunted by a third resistor. It shows the inner combination, the equivalent resistance, and the working line by line. Enter a supply voltage and it also gives the total current and power drawn from the source. It treats every resistor as ideal and fixed; it does not model tolerance, temperature drift, or the internal resistance of the supply, and larger ladders need to be reduced in stages.
Choose R1 + (R2 ∥ R3) or (R1 + R2) ∥ R3 to match how your resistors are wired.
Type R1, R2 and R3 in ohms. Convert kΩ to ohms first, so 4.7 kΩ is 4700.
The optional supply voltage adds total current and power to the results.
The steps show the inner series or parallel result before the final total.
Result Equivalent resistance (Ω): 200
Inner combination (Ω): 100
Total current: 0.06 A
Total power: 0.72 W
Two equal resistors in parallel halve to 100 Ω; the series 100 Ω brings the total to 200 Ω, which draws 60 mA from 12 V.
Result Equivalent resistance (Ω): 100
Inner combination (Ω): 200
Total current: —
Total power: —
The series string adds to 200 Ω, and 200 Ω in parallel with another 200 Ω gives 100 Ω.
Series: R = Ra + Rb. Parallel: R = (Ra × Rb) ÷ (Ra + Rb). Then I = V ÷ R and P = V × I.
R1, R2, R3RVI, PThe network is reduced from the inside out. In the first layout, R2 and R3 share both nodes, so they combine by the parallel rule, and the result adds to R1 because the same current flows through it. In the second layout, R1 and R2 carry the same current and add first; that sum then sits across the same two nodes as R3 and combines with it by the parallel rule. The product-over-sum form is the two-resistor case of 1/R = 1/Ra + 1/Rb. With a voltage, Ohm's law gives the current from the source and the power is voltage times current.
Resistors are in series when the same current must pass through both with no junction between them. They are in parallel when both ends connect to the same two nodes, so they share the same voltage. Trace the wires from node to node and mark each junction before you pick a layout.
Adding a parallel path gives current another way through, so the combined opposition falls. Two equal resistors in parallel give exactly half of one; 200 Ω with 200 Ω gives 100 Ω. A parallel pair is always less than its smaller member.
A very large resistor in parallel draws almost no current, so the pair is close to the smaller value. A very small resistor in series adds almost nothing. The tool warns when two values differ by a factor of 1,000 or more, because the big one then hardly changes its branch.
The fields take ohms. Multiply kilohms by 1,000 and megohms by 1,000,000 before entering them, so 2.2 kΩ becomes 2200 and 1 MΩ becomes 1000000. The result is also in ohms.
In a parallel pair the current divides in inverse proportion to resistance: the branch through Ra carries I × Rb ÷ (Ra + Rb). With two equal resistors each branch carries half. The calculator reports the total current from the source; apply this divider rule for each branch.
It is the total dissipated by the whole network, not by each part. Work out each resistor's own current or voltage and use P = I² × R for it, then choose a rating with headroom, commonly about twice the computed dissipation.
Using this tool in an assignment, article or report? Copy a citation, or a link for your website.
Tools Directory Editorial Team. (2026, October 23). Series Parallel Combined. Tools Directory. Retrieved October 27, 2026, from https://tools.milunir.com/electronics-physics/physics-reference/series-parallel-combined/
Tools Directory Editorial Team. “Series Parallel Combined.” Tools Directory, 23 Oct. 2026, https://tools.milunir.com/electronics-physics/physics-reference/series-parallel-combined/. Accessed 27 Oct. 2026.
Tools Directory Editorial Team. “Series Parallel Combined.” Tools Directory. Last modified October 23, 2026. Accessed October 27, 2026. https://tools.milunir.com/electronics-physics/physics-reference/series-parallel-combined/.
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