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Parallel Resistor Calculator

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Any group of resistors behaves, from outside, like a single resistor of some other value. Wired end to end their resistances add; wired side by side their reciprocals add, and the result is always smaller than the smallest one in the group. Enter up to ten values, choose how they are connected, and this gives the equivalent, shows how the current or the voltage divides between them, and names the single stocked part that would do the same job.

How are they wired?
Resistances in ohms
Try:

How to use the parallel resistor calculator

  1. 1Choose whether the resistors are wired in parallel or in series.
  2. 2Type each resistance in ohms — use 4700 rather than 4k7.
  3. 3Add or remove rows as needed, up to ten resistors.
  4. 4Press Calculate to see the equivalent resistance.
  5. 5Use the share table to see how much of the current or voltage each resistor takes.

Examples

Two equal resistors in parallel

Input
10 kΩ and 10 kΩ, parallel
Result
5 kΩ — exactly half

Equal values in parallel always halve, which is the one case worth memorising: N equal resistors in parallel give R divided by N.

Making an awkward value from stocked parts

Input
220 Ω and 330 Ω, parallel
Result
132 Ω

Parallel combinations are how a value that is not in any E series gets built from two that are.

A series chain

Input
1 kΩ, 2.2 kΩ and 4.7 kΩ, series
Result
7.9 kΩ, with the 4.7 kΩ taking 59.5% of the voltage

In series the largest resistor drops the most voltage, in direct proportion to its share of the total.

About the parallel resistor calculator

The two rules, and why they are different shapes

In series, the same current has to pass through every resistor in turn, because there is nowhere else for it to go. Each one drops its own voltage according to Ohm's law, and the voltages add up to the total across the chain. Divide that total voltage by the shared current and the resistances have simply added. The formula is a sum because the voltages are.

In parallel, every resistor sits across the same two nodes, so each sees the identical voltage. Each draws its own current, and the currents add. Divide the shared voltage by that summed current and what has added is the reciprocals — the conductances. This is why the parallel formula looks more complicated than the series one: it is the same simple addition, performed on the reciprocal quantity.

For exactly two resistors the reciprocal form is often written as the product over the sum, which is algebraically identical and easier to do in your head. It does not generalise to three or more without repeating it pairwise, which is why this page works from the reciprocals directly.

Reading the share table

The share column answers the question people are usually actually asking. In a series chain it shows what fraction of the applied voltage each resistor takes, which is proportional to its resistance — this is the voltage divider relationship, applied to as many elements as you like. In a parallel group it shows what fraction of the total current goes down each branch, which is inversely proportional to resistance: the smallest resistor carries the most.

That inverse relationship is what makes unequal parallel resistors worth watching. Put a 100 Ω and a 10 kΩ resistor in parallel and the small one carries 99% of the current and dissipates almost all of the heat. If the pair was chosen to share power, it has not worked. Sharing only happens between values that are close to each other.

The same reading explains why a parallel resistor is a poor way to make a big change to an existing value and a good way to make a small one. Halving a resistance means adding an equal one alongside; shaving a percent off means adding one about a hundred times larger. The share figures make the size of the intervention visible before anything is soldered.

Frequently asked questions

Why is the parallel result always smaller than the smallest resistor?
Because adding another path can only ever make it easier for current to get through, never harder. Each resistor offers its own route, and the routes are additive in conductance — the reciprocal of resistance. So the combined conductance exceeds any individual one, and the combined resistance is therefore below all of them. That gives a free sanity check on any answer: if a parallel result comes out larger than one of the inputs, something has been entered wrong.
What is the point of wiring resistors in parallel at all?
Three practical reasons. To reach a value that is not manufactured, by pairing two that are. To share power dissipation, since four 1 W resistors in parallel handle four watts where one would burn out. And to trim an existing value downward on a built board, by tacking a large resistor across one already fitted — a high value in parallel with a low one barely moves it, which makes fine adjustment possible.
How precise is the equivalent value in practice?
No better than the parts going into it, and often slightly worse. Combining two 5% resistors gives a result whose worst case is still around 5% out, because the errors can push the same way. Where a combination is being used to hit a value precisely, use 1% parts — or measure what you have, since a drawer of 5% resistors usually contains individual parts far closer to nominal than their marking promises.
Does the order of the resistors matter?
Not for the equivalent resistance, which is why this page takes an unordered list. Both formulas are commutative, so the same set of values in any arrangement gives the same total. It matters for other things the arithmetic here does not cover: where the heat is generated, which node sits at which voltage, and which resistor is easiest to reach with a probe. Those are layout questions rather than value questions.

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