How to Calculate Total Resistance of Resistors in Series

Resistors in series simply add: R = R₁ + R₂ + … . List the resistances separated by commas.

Explanation

Resistors joined end to end, in series, behave like one larger resistor. To find that combined resistance you just add them up.

R = R_1 + R_2 + \cdots + R_n

$R$ is the total resistance, in ohms (Ω)
$R_1, R_2, \ldots$ are the individual resistances, in ohms (Ω)

In series there is only one path for the charge, so the same current runs through every resistor. It is the voltage that gets divided: $I R_1$ across the first, $I R_2$ across the second, and so on. Those voltages have to add up to the supply voltage, which is precisely why the resistances add.

Example

The defaults are three resistors of 10, 20 and 30 Ω.

R = 10 + 20 + 30 = 60\,\Omega

The total resistance is 60 Ω, from a count of 3. Connect a 12 V supply and the current is 12 ÷ 60 = 0.2 A.

Notes

A series total is always larger than the largest resistor in the chain. Every resistor you add makes the current smaller.

Enter the values in ohms, separated by commas. Convert kilohms by multiplying by 1000 first.

Negative resistances are rejected.

One path also means one point of failure. String fairy lights in series and a single dead bulb takes out the whole set; wire them in parallel and the rest stay lit.