Use this calculator to determine the total resistance of a network. This calculator can give results for series, parallel, and any combination of the two. A schematic is automatically drawn as resistors are added to the network as a visual aid.

Complicated resistor networks can often be simplified into a single equivalent resistor value. Two equations used in the simplification process are the resistors in series equation and the resistors in parallel equation.

### Resistors in Series

Resistors are in series when chained together in a single line. The current flowing is common to all resistors in this chain. This is because the current flowing through the first resistor has one path through each of the following resistors in the chain. The total resistance of must equal the sum of each resistor’s value used in the chain.

$$R_{\text{equiv}} = R_1 + R_2 + R_3 + \ldots R_n$$We can consider this entire chain of resistors as a single resistor with a value of $R_{\text{equiv}}$.

### Resistors in Parallel

Resistors are in parallel when they share the same two nodes. The voltage drop across each resistor in this configuration is common. The current now has multiple paths and may not be the same for each resistor. The total resistance of resistors in parallel is the sum of the reciprocal of each resistor’s value used.

$$\frac{1}{R_{\text{equiv}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots \frac{1}{R_n}$$We can consider these parallel resistors as a single resistor with a value of $R_{\text{equiv}}$

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