Series and Parallel Resistor Calculator
Series and Parallel Resistor Calculator
Total resistance of up to six resistors in series or in parallel, with the voltage across and current through each one, the power every resistor has to get rid of, and the nearest single standard value to the combination.
Resistors in series or parallel
100 Ω, 220 Ω and 330 Ω in series across 12 V, ¼ W parts
Series and parallel
- Series
- one current through all of them; the voltages add to the supply, so each takes Vs × Rn ÷ Rtotal
- Parallel
- one voltage across all of them; the currents add, so each takes Itotal × Rtotal ÷ Rn
- P
- I² × R in series, V² ÷ R in parallel — the smallest parallel resistor always gets the most
Worked example
100 Ω, 220 Ω and 330 Ω in series across 12 V, ¼ W parts
R = 100 + 220 + 330 = 650 Ω
I = 12 ÷ 650 = 18.46 mA, the same through all three
Voltages: 1.846 V, 4.062 V and 6.092 V — they add back to 12 V
Powers: 34.08 mW, 74.98 mW and 112.5 mW; the 330 Ω works hardest but is well inside ¼ W
Nearest single standard value: 649 Ω (E96, +0.15%) or 680 Ω (E24, -4.41%)
The same three in parallel would be 56.9 Ω — smaller than the 100 Ω, and that one would then dissipate 1.44 W, far too much for a ¼ W part
Hitting an awkward value with two E24 resistors in parallel
| Target | Nearest single E24 | Error | Best E24 pair in parallel | Gives | Error |
|---|---|---|---|---|---|
| 665 Ω | 680 Ω | +2.26% | 680 Ω ∥ 30 kΩ | 664.9 Ω | -0.01% |
| 1.58 kΩ | 1.6 kΩ | +1.27% | 2.2 kΩ ∥ 5.6 kΩ | 1.579 kΩ | -0.03% |
| 2.37 kΩ | 2.4 kΩ | +1.27% | 2.4 kΩ ∥ 200 kΩ | 2.372 kΩ | +0.07% |
| 8.25 kΩ | 8.2 kΩ | -0.61% | 11 kΩ ∥ 33 kΩ | 8.25 kΩ | +0.00% |
| 12.4 kΩ | 12 kΩ | -3.23% | 13 kΩ ∥ 270 kΩ | 12.4 kΩ | +0.02% |
| 49.9 kΩ | 51 kΩ | +2.20% | 51 kΩ ∥ 2.4 MΩ | 49.94 kΩ | +0.08% |
Adding resistors up
Series is the easy one. Put resistors end to end and the same current has to fight its way through all of them, so the resistances add: 100 + 220 + 330 = 650 Ω. Because the current is common, the voltage across each one is in proportion to its resistance — that is all a voltage divider is, and the voltage divider calculator does the two-resistor case with a load on the output. The powers add too, and the largest resistor gets the most: in the worked example the 330 Ω part takes 112.5 mW of the 221.5 mW total.
Parallel adds conductances, not resistances. Each resistor offers the current its own path, so the paths add: 1/Rtotal = 1/R₁ + 1/R₂ + … For two resistors that rearranges to the shortcut everyone memorises, R₁R₂ ÷ (R₁ + R₂) — sometimes written as “product over sum” — and for two equal resistors it collapses to half of one of them. The shortcut only works for two at a time, but you can apply it repeatedly.
Parallel is always smaller than the smallest. The same three resistors in parallel come to 56.9 Ω — below the 100 Ω, not between the values. That has to be true: adding another path can only let more current through, and more current at the same voltage means less resistance. The bound at the other end is just as useful: n equal resistors in parallel give exactly R ÷ n, so a parallel combination can never be smaller than the smallest member divided by the number of resistors. If your answer falls outside that window, you have added resistances instead of conductances.
Watch the power when you parallel things up. In parallel every resistor sees the full voltage, so the smallest one works hardest: 100 Ω across 12 V is 1.44 W, six times a ¼ W part’s rating. This page flags any resistor at or over the rating you enter. Going the other way, paralleling identical resistors is the standard trick for sharing heat: four 1 kΩ ¼ W parts in parallel make a 250 Ω 1 W resistor, and four in series make a 4 kΩ 1 W one.
Getting to an awkward value. Combining resistors is usually not about textbook exercises; it is about hitting a value nobody sells. The table above searches every pair of E24 values for the best parallel combination of six awkward targets: a single ±5% value can be 3.23% away, while the best pair gets within 0.08%. Two cautions. First, tolerance does not improve: two ±5% resistors in parallel are still a ±5% combination, so if you need the accuracy, buy a ±1% part. Second, the total above is compared with the nearest single E24 and E96 value for you — if a stock part is within your tolerance, use it and fit one component instead of two.
To read the values off the parts you already have, use the resistor colour code calculator or the SMD resistor code calculator; for the current and power in any one of them, the Ohm’s law calculator.
Frequently asked questions
How do you calculate resistors in series?
Add them: Rtotal = R1 + R2 + R3. 100 Ω, 220 Ω and 330 Ω in series make 650 Ω, and the same current flows through all three.
How do you calculate resistors in parallel?
Add the reciprocals and invert: 1/Rtotal = 1/R1 + 1/R2 + … The same three resistors in parallel make 56.9 Ω. For just two, R1 × R2 ÷ (R1 + R2) is quicker.
Is parallel resistance always less than the smallest resistor?
Yes. Every extra path lets more current through at the same voltage, which means less resistance. It can never fall below the smallest resistor divided by the number of resistors.
What do two equal resistors in parallel make?
Half of one of them: two 1 kΩ resistors in parallel are 500 Ω. Three make a third, and n make R ÷ n — which is also how you spread dissipation over more parts.
Which resistor gets hot in a parallel circuit?
The smallest, because they all see the same voltage and P = V² ÷ R. 100 Ω across 12 V dissipates 1.44 W, while 330 Ω across the same 12 V dissipates 436.4 mW.
How do I make a resistor value I do not have?
Put two in parallel or in series and check the total against your tolerance. The table on this page shows the best E24 pairs for six common awkward targets; all of them get within 0.1%, though the tolerance of the parts themselves does not improve.
Related calculators
References
- Horowitz P, Hill W. The Art of Electronics, 3rd ed. Cambridge University Press, 2015. Chapter 1 (resistors in series and parallel, reactance, resonance, zener regulators) and Chapter 9 (voltage regulators).
- IEC 60063:2015. Preferred number series for resistors and capacitors (the E6, E12, E24, E48, E96 and E192 series). International Electrotechnical Commission.