Series and Parallel Resistor Calculator
Combine as many resistors as you like and get the equivalent resistance, plus the nearest E12 standard value so you know what you can actually buy. Type values in ohms or with a k or M suffix, separated by commas: 220, 330, 470 or 4.7k, 10k.
Last updated: June 2026
Enter two or more resistor values above, separated by commas.
Series: R = R1 + R2 + ... · parallel: R = 1 ÷ (1/R1 + 1/R2 + ...)
Combining resistors
Resistors in series simply add up, because the current has to pass through every one of them in turn. Resistors in parallel behave the opposite way: each extra resistor opens another path for the current, so the combination always ends up lower than the smallest single resistor in the set. That last point catches people out, because intuition says adding a component should add resistance. Put a 220 and a 330 side by side and you get 132 ohms, less than either.
The two formulas
In series, add the values: R equals R1 plus R2 and so on. In parallel, add the reciprocals and invert the total: R equals 1 divided by the sum of 1 over each resistor. For exactly two resistors in parallel there is a shortcut worth memorising, the product over the sum: R equals R1 times R2, divided by R1 plus R2. Two equal resistors in parallel always give exactly half the value, which is the quickest sanity check there is.
Why your answer is not a real resistor
Parallel combinations rarely land on a value you can buy. The calculator therefore also gives the nearest E12 value, the twelve-step series that general-purpose 10 percent resistors are made in: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68 and 82, repeated in every decade. Tighter 5 percent parts come from E24, which fills in twelve further values between those, so the calculator reports that one as well whenever it differs. If the nearest standard part is close enough for your tolerance budget, use it. If it is not, a series or parallel pair is exactly how you reach an odd value from parts you already own.
Worked example
Take 220, 330 and 470 ohms. In series they total 1.02 kilohms, and the nearest E12 value is a plain 1 kilohm resistor, which is within 2 percent and almost certainly close enough. In parallel the same three give 103.06 ohms, comfortably below the 220 that is smallest in the set, and the nearest E12 value is 100 ohms. Note how the series answer is dominated by the largest resistor while the parallel answer is dominated by the smallest.
A note from my own bench: two identical resistors in parallel halve the resistance but also double the power the pair can absorb, which is the cheap way out when the only 100 ohm part in the drawer is a quarter-watt and the circuit wants half a watt. I also reach for two 10k in series far more often than I hunt for a single 20k, simply because 10k is the value I keep in quantity.
Common pairs in series and parallel
| Resistors | In series | In parallel |
|---|---|---|
| 100 + 100 | 200 Ω | 50 Ω |
| 220 + 330 | 550 Ω | 132 Ω |
| 1k + 2.2k | 3.2 kΩ | 687.5 Ω |
| 4.7k + 4.7k | 9.4 kΩ | 2.35 kΩ |
| 10k + 10k | 20 kΩ | 5 kΩ |
Every parallel figure is below the smaller of the pair, and equal pairs land on exactly half.
Frequently Asked Questions
How do I calculate resistors in series and parallel?
In series you add the values straight up, so 220 plus 330 plus 470 gives 1,020 ohms. In parallel you add the reciprocals and invert the result, so the same three resistors give 103.06 ohms. For just two resistors in parallel the product over the sum is quicker: multiply the two values and divide by their total. Two identical resistors in parallel always come to exactly half of one of them, which is the fastest way to check you have not slipped a decimal.
Why is parallel resistance always lower than the smallest resistor?
Because every resistor you add in parallel gives the current another route. More routes means less total opposition, so the combined resistance falls. Even adding a very large resistor alongside a small one nudges the total slightly below the small one, since a little extra current now bypasses it. This is why the parallel answer is dominated by the smallest value in the set, while the series answer is dominated by the largest.
Why do capacitors combine the opposite way round?
Because capacitance measures stored charge per volt rather than opposition to current. Putting capacitors side by side in parallel gives more plate area, so the capacitances simply add. Putting them in series makes every capacitor in the chain carry the same charge while their voltages add up, and because capacitance is charge per volt, the total falls, so you add the reciprocals exactly the way you would for parallel resistors. If you are used to resistor rules, remember that the capacitor formulas are swapped, not different.
Why is my calculated value not a standard resistor value?
The spacing of a standard series is chosen so that parts of a given tolerance cover the whole range without leaving gaps, which is why the steps look uneven rather than evenly spread. Combinations almost never land on one of them, and that is precisely when building the value yourself pays off: 220 plus 330 in series gives 550, and two 470s in parallel give 235, neither of which you can buy as a single resistor. The calculator shows the closest E12 and E24 values so you can judge whether an off-the-shelf part is near enough before reaching for two.
How much power does each resistor in the network dissipate?
It depends on the arrangement, and the calculator does not work it out for you. In series every resistor carries the same current, so the largest value dissipates the most power: use P equals I squared times R for each one. In parallel every resistor sees the same voltage, so the smallest value dissipates the most: use P equals V squared divided by R. Check the worst case against the part rating, because a quarter-watt resistor in the wrong spot of an otherwise correct network is a common failure.
Methodology and sources
This tool combines any number of resistors in either arrangement and reports the equivalent resistance together with the nearest standard part, so the answer is something you can actually source.
- Method: Series: R = R1 + R2 + ... Parallel: R = 1 ÷ (1/R1 + 1/R2 + ...). The nearest standard value is found by normalising the result into a single decade and picking the closest entry, done against both E12 and E24 so the tighter series is reported whenever it differs. Input accepts plain ohms, a k (kilo) or M (mega) suffix, or the infix style printed on datasheets such as 4k7 and 470R, separated by commas or spaces. A lowercase m is rejected rather than guessed at, because it conventionally means milli. Results below one ohm are shown in milliohms.
- Standards and sources: The series and parallel relations follow directly from Ohm's law and Kirchhoff's laws. The E12 preferred-value series is defined in IEC 60063, the international standard for preferred number series in resistors and capacitors.
- Assumptions and limits: Assumes ideal resistors: tolerance, temperature coefficient and lead resistance are ignored, so a network of 5 percent parts will not measure exactly the calculated figure. Power dissipation per resistor is not computed, and neither is the effect of a load placed across the network. Values must be greater than zero.
Reviewed and maintained by Rick Oosterling, a maker who builds and repairs 12 V, solar and small electronics projects on the bench. Last reviewed: June 2026. This is a design aid; confirm part ratings and tolerances against the datasheet before committing a build.