How do you calculate resistors in parallel?
Add the reciprocals and take the reciprocal of the sum: 1/R = 1/R1 + 1/R2 + … For two resistors that simplifies to R1 × R2 ÷ (R1 + R2), so 10 kΩ in parallel with 4.7 kΩ is 3.197 kΩ.
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Series and parallel resistor calculator
Add up to eight resistors in parallel or in series with this parallel resistor calculator and see how the current or voltage divides between them. Or enter an existing resistor and a lower target to get the value to add in parallel, rounded to E24 and E96.
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Examples
Ω
Ω
Ω
V
Optional: shows the current and power in each resistor.
Parallel resistance
3.197 kΩ
- Total conductance
- 312.8 µS
- Smallest resistor
- 4.7 kΩ the total is always below it
If every part has the same tolerance (say ±1 %), the combination is within the same percentage, in parallel or in series.
How the current divides
| Part | Resistor | Share of current |
|---|---|---|
| R1 | 10 kΩ | 32 % |
| R2 | 4.7 kΩ | 68 % |
What is the parallel resistor formula?
Use 1/R = 1/R1 + 1/R2 + … + 1/Rn. For two resistors this is R1 × R2 ÷ (R1 + R2): 10 kΩ in parallel with 4.7 kΩ gives 10 × 4.7 ÷ 14.7 = 3.197 kΩ. The total is always below the smallest resistor. In series, simply add the values.
Resistors in parallel formula and the series rule
Resistors in series share one current, so their resistances add. Resistors in parallel share one voltage, so their conductances (1/R) add.
Series: R = R1 + R2 + … + Rn Parallel: 1/R = 1/R1 + 1/R2 + … + 1/Rn
- R
- equivalent resistance of the network in Ω
- R1 … Rn
- the individual resistances in Ω
Two resistors in parallel, and the resistor Rx that brings an existing R down to a target Rt:
R = R1 × R2 ÷ (R1 + R2) Rx = R × Rt ÷ (R − Rt)
With a voltage V across a parallel network, each branch carries Ik = V ÷ Rk and dissipates V² ÷ Rk. With V across a series string, the current is V ÷ R and each resistor drops Vk = V × Rk ÷ R.
Worked examples
Example 1: 1 Ω, 2 Ω and 2 Ω in parallel across 3 V (OpenStax Example 10.3)
1/R = 1/1 + 1/2 + 1/2 = 2 S, so R = 500 mΩ. The source supplies 3 ÷ 0.5 = 6 A: 3 A through the 1 Ω resistor and 1.5 A through each 2 Ω. The 1 Ω part dissipates 9 W and each 2 Ω part 4.5 W, 18 W in all.
Example 2: four 20 Ω and one 10 Ω in series across 9 V (OpenStax Example 10.2)
R = 4 × 20 + 10 = 90 Ω, so I = 9 ÷ 90 = 100 mA. Each 20 Ω resistor drops 2 V and dissipates 200 mW; the 10 Ω drops 1 V.
Example 3: trimming 1 kΩ down to 800 Ω
Rx = 1000 × 800 ÷ (1000 − 800) = 4 kΩ. The nearest E24 value, 3.9 kΩ, gives 795.9 Ω (-0.51 %); the nearest E96 value, 4.02 kΩ, gives 800.8 Ω (+0.10 %), well inside a 1 % part’s tolerance.
Two resistors in parallel: common value pairs
R1 × R2 ÷ (R1 + R2) for common resistor values. The diagonal is half the value.
| R1 \ R2 | 100 Ω | 220 Ω | 470 Ω | 1 kΩ | 2.2 kΩ | 4.7 kΩ | 10 kΩ |
|---|---|---|---|---|---|---|---|
| 100 Ω | 50 Ω | 68.8 Ω | 82.5 Ω | 90.9 Ω | 95.7 Ω | 97.9 Ω | 99 Ω |
| 220 Ω | 68.8 Ω | 110 Ω | 150 Ω | 180 Ω | 200 Ω | 210 Ω | 215 Ω |
| 470 Ω | 82.5 Ω | 150 Ω | 235 Ω | 320 Ω | 387 Ω | 427 Ω | 449 Ω |
| 1 kΩ | 90.9 Ω | 180 Ω | 320 Ω | 500 Ω | 688 Ω | 825 Ω | 909 Ω |
| 2.2 kΩ | 95.7 Ω | 200 Ω | 387 Ω | 688 Ω | 1.1 kΩ | 1.5 kΩ | 1.8 kΩ |
| 4.7 kΩ | 97.9 Ω | 210 Ω | 427 Ω | 825 Ω | 1.5 kΩ | 2.35 kΩ | 3.2 kΩ |
| 10 kΩ | 99 Ω | 215 Ω | 449 Ω | 909 Ω | 1.8 kΩ | 3.2 kΩ | 5 kΩ |
Parallel resistor to lower a 10 kΩ
The exact value to add across a 10 kΩ resistor for each target, the nearest E24 part and the result it gives.
| Target | Exact partner | Nearest E24 | Result | Error |
|---|---|---|---|---|
| 9.1 kΩ | 101.1 kΩ | 100 kΩ | 9.091 kΩ | -0.10 % |
| 8.2 kΩ | 45.56 kΩ | 47 kΩ | 8.246 kΩ | +0.56 % |
| 7.5 kΩ | 30 kΩ | 30 kΩ | 7.5 kΩ | +0.00 % |
| 6.8 kΩ | 21.25 kΩ | 22 kΩ | 6.875 kΩ | +1.10 % |
| 5.6 kΩ | 12.73 kΩ | 13 kΩ | 5.652 kΩ | +0.93 % |
| 4.7 kΩ | 8.868 kΩ | 9.1 kΩ | 4.764 kΩ | +1.37 % |
| 3.3 kΩ | 4.925 kΩ | 5.1 kΩ | 3.377 kΩ | +2.35 % |
| 2.2 kΩ | 2.821 kΩ | 2.7 kΩ | 2.126 kΩ | -3.36 % |
| 1 kΩ | 1.111 kΩ | 1.1 kΩ | 991 Ω | -0.90 % |
Using parallel and series resistors in practice
Combining two resistors is the usual way to reach a value that is not in the series you stock, or to share power: two equal resistors in parallel each carry half the current and half the power, so the pair handles twice what one part could. Tolerances do not get worse: the combination of ±1 % parts is still within ±1 %. Mind the layout, though: in a low-value current-sense network the copper between parallel parts adds resistance of its own, so place them symmetrically and take the sense connections from the resistor pads. Finally, a resistor more than about 100 times larger than the one it is across changes the total by under 1 %, less than the tolerance of either part, so it is rarely worth adding.
Glossary
- Equivalent resistance
- The single resistance that draws the same current from the same voltage as the whole network.
- Parallel
- Parts connected across the same two nodes, so they share one voltage and split the current.
- Series
- Parts connected end to end, so they share one current and split the voltage.
- Conductance
- The reciprocal of resistance, in siemens (S). Conductances in parallel add.
- Current divider
- Parallel resistors splitting a current in inverse proportion to their resistance.
- E24 and E96
- IEC 60063 standard value series with 24 and 96 values per decade, for 5 % and 1 % parts.
- Tolerance
- How far a part’s real value may be from its marked value, for example ±1 %.
Related guides
- Standard resistor values: E12, E24 and E96 tables.
- Current divider calculator: branch currents in more detail.
- Ohm's law calculator: voltage, current and power for the total.
- Learn: series and parallel: why the formulas work.
Frequently asked questions
What is 10 kΩ in parallel with 10 kΩ?
5 kΩ. Any number n of equal resistors in parallel gives R ÷ n, so four 100 Ω resistors in parallel make 25 Ω.
How many resistors can this parallel resistance calculator take?
Up to eight, in parallel or in series. Enter the voltage across them and it also works as a parallel circuit calculator, with the current and power in each branch.
Can this parallel and series resistor calculator handle a mixed network?
Not in one pass: each run is all parallel or all series. For a mixed network, work out the total resistance in stages, reducing one parallel or series group at a time.
Is the parallel resistance always less than the smallest resistor?
Yes. Every resistor you add in parallel gives the current another path, so the total is always below the smallest one. Adding a much larger resistor lowers it only slightly.
What resistor do I put in parallel to get a lower value?
Rx = R × Rt ÷ (R − Rt), where R is the existing resistor and Rt the target. To bring 1 kΩ down to 800 Ω you need 4 kΩ; the nearest E96 value, 4.02 kΩ, gives 800.8 Ω.
How does current divide between parallel resistors?
In inverse proportion to resistance, because each has the same voltage across it: I = V ÷ R for each branch. In OpenStax's example, 3 V across 1 Ω, 2 Ω and 2 Ω drives 3 A, 1.5 A and 1.5 A.
What is the tolerance of resistors in parallel or series?
If every part has the same tolerance, the combination has that tolerance too, in the worst case: two ±1 % resistors in parallel or in series make a ±1 % result. Random errors partly cancel, so the typical error is smaller.
Do resistors in parallel share the power?
Each dissipates V² ÷ R, so equal resistors share it equally and two equal 1/4 W parts in parallel can carry 1/2 W between them. With unequal values the smaller resistor takes more of the power, so check each part on its own.
How do you calculate resistors in series?
Add them: R = R1 + R2 + … The same current flows through each, and the voltage divides in proportion to resistance. Four 20 Ω and one 10 Ω in series make 90 Ω. The Series tab above works as a series resistor calculator for up to eight parts.
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