# Parallel Resistor Calculator

Created by Kenneth Alambra
Last updated: Jul 10, 2022

This parallel resistor calculator will help you determine the total resistance parallel resistors make in a circuit, also known as their equivalent resistance. You can also use this tool to find out what resistor to add to a parallel circuit to arrive at a desired equivalent resistance. Keep on reading to learn about:

• The total resistance formula for parallel resistors;
• How to calculate the equivalent resistance;
• How to calculate the resistance of a missing resistor in a parallel circuit; and
• How to use this parallel resistor calculator.

Check the capacitor code calculator to learn about another primary element of all electronic devices.

## Total resistance formula for parallel resistors

To find the total resistance across a parallel circuit of resistors, other resistive electrical components, or wires (because they have wire resistance too), we have to take the sum of the reciprocals of each resistor in the circuit and then take the reciprocal of this sum. Just like the equation for capacitors in series. In equation form, we express that like this:

$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}$

We can also further isolate the equivalent parallel resistance, $R$, to have:

$R = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}}$

where:

• $R$ is the total or equivalent parallel resistance;
• $R_1, R_2, ..., R_n$ are the resistances of the resistors 1st resistor, 2nd resistor, up to the nth resistor in the circuit.

We derived that formula from the concept that the sum of the currents passing through parallel resistors is equal to the electric current from the voltage source. We can express that in an equation form as:

$I = I_1 + I_2 + ... + I_n$

We can further expand that equation using the Ohm's Law to arrive at this relationship:

$\frac{V}{R} = \frac{V}{R_1} + \frac{V}{R_2} + ... + \frac{V}{R_n}$

Since the voltage applied through the current will be constant, each resistor will experience the same voltage and we can omit that from our equation. That will leave us with the total resistance formula for parallel resistors we see earlier.

## How to calculate the equivalent resistance of parallel resistors

Let's say we have three resistors in a parallel circuit, and these resistors have resistance values of $R_1=5\ \Omega$, $R_2=10\ \Omega$, and $R_3=20\ \Omega$. We can replace these three resistors with one resistor with a resistance value equivalent to these three altogether. We can use our total resistance formula for parallel resistors, but we can also do it step-by-step as follows:

1. Take the reciprocal of the resistance values: $\frac{1}{R_1}=\frac{1}{5}$, $\frac{1}{R_2}=\frac{1}{10}$, and $\frac{1}{R_3}=\frac{1}{20}$.

2. Add the reciprocals together: $\frac{1}{R} = \frac{1}{5} + \frac{1}{10} + \frac{1}{20}$ = $\frac{4}{20} + \frac{2}{20} + \frac{1}{20}$ = $\frac{7}{20}$

3. Get the reciprocal of their sum. $R = \frac{20}{7}\ \Omega$ = $2.8571\ \Omega$$2.9\ \Omega$

That's how to calculate the equivalent resistance of a few resistors. However, finding more resistors' equivalent or total resistance could be challenging and confusing. That is where our parallel resistor calculator comes in very handy. Let's learn how to use our tool in the next section of this text.

🙋 To find a missing resistor:

1. Take the reciprocal of your desired total equivalent resistance.
2. Subtract the reciprocals of the other resistors in the parallel circuit from the reciprocal of your desired total equivalent resistance.
3. Obtain the reciprocal of the difference to get the resistance value of the last missing resistor that you need to complete the circuit.

## How to use this parallel resistor calculator

Aside from calculating the total resistance equivalent of multiple resistors, our tool can also find the value of a "missing" resistor to complete a circuit with a particular total resistance value.

If you have to perform the same total resistance calculation we did in our example earlier, choose the Calculate equivalent resistance option for the calculator mode. Then, enter your resistors' resistance values one at a time (with a maximum of 10 resistance values), and our tool will display their equivalent resistance each time you enter a value.

On the other hand, pick Calculate missing resistor if you have a target total resistance and need another resistor together with one or more resistors to obtain that value. Enter your desired total resistance and the resistance values of your resistors in a parallel circuit. Concurrently, our calculator will automatically give you the required missing resistor you need to complete the circuit.

Kenneth Alambra
Mode
Calculate equivalent resistance
Resistor 1 (R₁)
Ω
Resistor 2 (R₂)
Ω
You can add up to 10 resistors, fields will appear as you need them.
Results
Input at least one resistor to obtain a result.
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