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Series and Parallel Resistor Calculator

Enter resistor values and get the equivalent resistance in series or parallel, with the total current and power when the voltage is known.

Separate with commas or spaces. You can type 4.7e3 for 4.7 kΩ.

Enter the values to see the result here.

Formula

Rseries=R1+R2+⋯+Rn1Rparallel=1R1+1R2+⋯+1RnR_{series} = R_1 + R_2 + \dots + R_n \qquad \frac{1}{R_{parallel}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}

For two resistors in parallel this simplifies to R=R1R2/(R1+R2)R = R_1 R_2 / (R_1 + R_2). With a supply voltage VV, the total current is V/RV / R and the power is V2/RV^2 / R.

Worked example

Three resistors of 100, 220 and 470 ohms are connected in parallel across 12 V.

  • Reciprocals: 1/100+1/220+1/470=0.01+0.004545+0.002128=0.0166731/100 + 1/220 + 1/470 = 0.01 + 0.004545 + 0.002128 = 0.016673.
  • Equivalent: R=1/0.016673=60.0 ΩR = 1 / 0.016673 = 60.0\ \Omega.
  • Total current: 12/60.0=0.20012 / 60.0 = 0.200 A.
  • Total power: 122/60.0=2.4012^2 / 60.0 = 2.40 W.

In series the same three would give 100+220+470=790 Ω100 + 220 + 470 = 790\ \Omega.

Common mistakes

  • Adding resistances that are in parallel. They combine through their reciprocals.
  • Mixing units, for example kilohms and ohms. Convert everything to ohms, or type 4.7e3.
  • Forgetting a resistor’s power rating. A 1/4 W resistor cannot carry the power the circuit may put through it.
  • Reading a parallel result larger than the smallest resistor as correct. It cannot be.

Frequently asked questions

When are resistors in series and when in parallel?

In series they share one path, so the same current flows through each and the resistances add. In parallel each one connects across the same two points, so they share the voltage and the current divides between them.

Why is the parallel total smaller than any single resistor?

Each extra branch gives the current another route, which lowers the overall resistance. Two equal resistors in parallel always give half of one of them.

Can I mix series and parallel groups?

Yes. Reduce each group to one equivalent resistance first, then combine those results. For example two 100 ohm resistors in parallel (50 ohms) in series with 150 ohms give 200 ohms.

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