Series and parallel calculator

How do resistors and capacitors add up?

Combine 2 to 12 resistors or capacitors and see the equivalent value.

Combine

Connected

Resistors

Resistor 1

Resistor 1 unit
Resistor 2

Resistor 2 unit

The list can’t be shorter than 2, so none can be removed.

Total resistance

500 Ω

2 resistors in parallel: 1 kΩ and 1 kΩ

How it adds up

1/R = 1/R₁ + 1/R₂ + …
The total is always smaller than the smallest part.

Nearest E24 value

E24: 510 Ω
Next lower: 470 Ω
Next higher: 510 Ω
Difference: +2%

How to use

Choose resistors or capacitors, and whether they are connected in series or in parallel.
Type each part's value and unit. Add parts with the button, up to twelve.
Read the total, with the nearest single standard part you could use instead.

How it works

Parts in series sit one after another, so the current goes through each in turn. Parts in parallel sit side by side, so the current splits between them. Resistors in series add up, because the current has to fight through each one; in parallel they give the current more paths, so the total falls below the smallest resistor. Capacitors work the other way round: side by side their plates add up, while in series the total shrinks.

For resistors in series R = R₁ + R₂ + …, and in parallel 1/R = 1/R₁ + 1/R₂ + …. For capacitors in parallel C = C₁ + C₂ + …, and in series 1/C = 1/C₁ + 1/C₂ + …. For example, 1 kΩ and 470 Ω in parallel give 1/R = 1/1000 + 1/470, so R = 320 Ω; in series they give 1.47 kΩ. Two equal parts in parallel halve a resistance, and two equal capacitors in series halve the capacitance. The formulas are those of OpenStax University Physics, volume 2.

Real parts have tolerances, so the total is as exact as the parts. Capacitors in series also share the voltage unevenly when their values or leakage differ.

Worked example

What is the resistance of 1,000 Ω and 1,000 Ω in parallel?

Add the reciprocals: 1/R = 1/1,000 + 1/1,000.
Invert the sum to get R = 500 Ω.

The equivalent resistance is 500 Ω.

Frequently asked questions

How do I make a value I can't buy?

Combine two standard parts: in series they add up, and in parallel they come out lower than either. For example, 2.2 kΩ and 1 kΩ in series make 3.2 kΩ.

Why is the parallel resistance smaller than every resistor?

Each extra resistor opens another path for the current, so more current flows at the same voltage, which is what a lower resistance means.

Can I mix kΩ and Ω?

Yes. Each part has its own unit, and the total is shown in the unit that reads best.

Can I combine resistors and capacitors together?

No. Each calculation uses only resistors or only capacitors, all in series or all in parallel.

Does the result include component tolerances?

No. It uses the nominal values you enter. Real components can differ within their stated tolerances.