Resistors in series and parallel calculator

The formula

In series (end to end, one path):

$$R_{eq} = R_1 + R_2 + \cdots + R_n$$

In parallel (side by side, several paths):

$$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}$$

$R_{eq}$ is the single resistance that would draw the same current from the same voltage.

Where it comes from

Both rules come from Ohm’s law, $V = IR$, plus one fact about each layout.

Series. There’s only one path, so the same current $I$ flows through every resistor. The supply voltage is shared out, so the voltages add:

$$V = IR_1 + IR_2 + \cdots = I(R_1 + R_2 + \cdots)$$

Comparing with $V = IR_{eq}$ gives $R_{eq} = R_1 + R_2 + \cdots$. Each resistor’s share of the voltage is $R_k / R_{eq}$, which is the voltage divider rule.

Parallel. Every resistor sits across the same two points, so each has the same voltage $V$. The currents through the branches add up to the total:

$$I = \frac{V}{R_1} + \frac{V}{R_2} + \cdots = V\left(\frac{1}{R_1} + \frac{1}{R_2} + \cdots\right)$$

Comparing with $I = V / R_{eq}$ gives the reciprocal rule. Each branch carries a share $R_{eq} / R_k$ of the current, so the smallest resistor carries the most.

For just two resistors in parallel, the rule simplifies to “product over sum”:

$$R_{eq} = \frac{R_1 R_2}{R_1 + R_2}$$

Worked example

100 Ω, 220 Ω and 470 Ω in parallel:

$$\frac{1}{R_{eq}} = \frac{1}{100} + \frac{1}{220} + \frac{1}{470} = 0.016673\ \text{S}$$ $$R_{eq} = 59.98\ \Omega$$

The 100 Ω resistor carries $59.98/100 = 60\%$ of the current. In series, the same three would total 790 Ω.

Watch out for

• Parallel is always less than the smallest. If your parallel answer is bigger than the smallest resistor, something has gone wrong. Adding a path can only make it easier for current to flow.
• Equal resistors. $n$ equal resistors in parallel give $R/n$. Two 1 kΩ resistors make 500 Ω.
• Power ratings add too. Two ¼ W resistors in series or parallel can share ½ W, but only if they’re equal. Unequal resistors split the heat unequally.

Sources

• OpenStax, University Physics Volume 2, section 10.2 "Resistors in Series and Parallel"

Last checked November 11, 2026