Parallel resistor calculator

What is a parallel resistor calculator?

A parallel resistor calculator finds the single equivalent resistance that two resistors produce when they are wired in parallel. When components share the same two nodes, current can flow through either path, so the combined resistance is always smaller than either resistor on its own. This tool takes the two resistance values in ohms and instantly returns the equivalent resistance, saving you from working the fraction by hand.

Parallel connections appear everywhere in electronics, from current dividers and LED arrays to power-supply loads. Knowing the equivalent resistance lets you predict the total current drawn from a source and verify that your design stays within safe limits.

Formula

For two resistors $R_1$ and $R_2$ in parallel, the equivalent resistance is:

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

This is the product-over-sum form of the more general parallel rule $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$, which is convenient when exactly two resistors are involved.

How to use

1. Enter the resistance of the first resistor, $R_1$, in ohms.
2. Enter the resistance of the second resistor, $R_2$, in ohms.
3. Read the equivalent resistance from the result field, also in ohms.

The result appears only once both resistances are filled in and their sum is greater than zero.

Worked example

Suppose $R_1 = 4\,\Omega$ and $R_2 = 6\,\Omega$. Substituting into the formula:

$R_{eq} = \frac{4 \cdot 6}{4 + 6} = \frac{24}{10} = 2.4\,\Omega$

As a second example, two equal resistors of $R_1 = 10\,\Omega$ and $R_2 = 10\,\Omega$ give:

$R_{eq} = \frac{10 \cdot 10}{10 + 10} = \frac{100}{20} = 5\,\Omega$

Notice that in both cases the equivalent resistance is smaller than either individual resistor, which is always true for a parallel connection.

FAQ

Why is the parallel resistance always lower than the smallest resistor?

Adding a parallel path gives current another route to flow, which increases the total current for a given voltage. More current at the same voltage means lower overall resistance, so the equivalent value drops below even the smaller of the two resistors.

What happens when both resistors are equal?

When $R_1 = R_2$, the equivalent resistance is exactly half of one resistor’s value. For example, two $10\,\Omega$ resistors in parallel give $5\,\Omega$.

For related calculations, see the Ohm’s law calculator and the kilowatts to watts calculator.