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Resistors in Series and Parallel Calculator

Resistors in series add up: R = R1 + R2 + R3 and so on. Resistors in parallel combine as 1 ÷ R = 1 ÷ R1 + 1 ÷ R2 + …, and the result is always smaller than the smallest resistor.

Result

In series (3 resistors)always more than the biggest one: 6 kΩ
In parallel (3 resistors)always less than the smallest one: 545.5 Ω

The formula

In series

\htmlData{sym=R_s}{R_{\mathrm{s}}} = \htmlData{sym=R_1}{R_1} + \htmlData{sym=R_2}{R_2} + \htmlData{sym=R_3}{R_3} + \cdots

In parallel

\dfrac{1}{\htmlData{sym=R_p}{R_{\mathrm{p}}}} = \dfrac{1}{\htmlData{sym=R_1}{R_1}} + \dfrac{1}{\htmlData{sym=R_2}{R_2}} + \dfrac{1}{\htmlData{sym=R_3}{R_3}} + \cdots

Parallel, for two resistors

\htmlData{sym=R_p}{R_{\mathrm{p}}} = \dfrac{\htmlData{sym=R_1}{R_1}\,\htmlData{sym=R_2}{R_2}}{\htmlData{sym=R_1}{R_1} + \htmlData{sym=R_2}{R_2}}

What each letter means

$R_{\mathrm{s}}$: Series resistance (Ω · ohm)
$R_1$: Resistance of R1 (Ω · ohm) : How strongly something opposes current.
$R_2$: Resistance of R2 (Ω · ohm) : How strongly something opposes current.
$R_3$: Resistance of R3 (Ω · ohm) : How strongly something opposes current.
$R_{\mathrm{p}}$: Parallel resistance (Ω · ohm) : What two resistors side by side add up to. Always less than the smaller one.

How it works

In series the current has to pass through every resistor one after another, so the obstacles add up and the total is more than any single resistor. In parallel the current can take several paths at once, like extra lanes on a road, so the total is less than the best single path.

Two equal resistors in parallel give half the value, and a very small resistor in parallel with a very big one is almost just the small one. You can use combinations to build a value you do not have: for example two 10 kΩ resistors in parallel make 5 kΩ.

Worked example

Three resistors, 1 kΩ, 2 kΩ and 3 kΩ. In series: 1 kΩ + 2 kΩ + 3 kΩ = 6 kΩ.
In parallel: 1 ÷ (1 ÷ 1 kΩ + 1 ÷ 2 kΩ + 1 ÷ 3 kΩ) = 545.5 Ω, less than the smallest one (1 kΩ).
A 100 Ω resistor in parallel with 1 MΩ gives 99.99 Ω: the big resistor hardly matters.

Common questions

Why is the parallel total smaller than the smallest resistor?

Adding another path always lets more current through for the same voltage, and more current for the same voltage means lower resistance. Every resistor you add in parallel can only lower the total.

How do I get a resistor value I do not have?

Combine two or more. Series adds values, so 4.7 kΩ + 330 Ω gives 5.03 kΩ. Parallel lowers them, so two 2.2 kΩ resistors make 1.1 kΩ. Check the power rating too: each resistor in a combination only takes its share of the power.

Try it live

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