Parallel Resistor Calculator – Find the Total Resistance (Req)

How to Use Our Parallel Resistor Calculator

This tool is designed to handle any number of resistors in parallel. Follow these simple steps:

1. Enter Resistor Values: Input the resistance value (in Ohms, Ω) of each resistor in your parallel circuit into a separate field (R1, R2, R3, etc.).

2. Add More Resistors (If Needed): If you have more resistors than the fields shown, click the “Add Resistor” button to create additional input boxes.

3. Calculate: The calculator will automatically compute and display the total equivalent resistance of the entire circuit as you enter the values.

Input Fields Explained:

• R1, R2, R3…: The resistance value of each individual resistor in your parallel circuit. You must enter at least two values for a calculation.

Understanding Your Results

The result from the calculator is the Total Equivalent Resistance ($R\_eq$) of your circuit. This is the single resistance value that could replace all the individual parallel resistors and have the same effect on the circuit.

The most important concept to grasp is that the total resistance in a parallel circuit is always less than the value of the smallest individual resistor.

Why is Total Resistance Lower in Parallel?

Think of it like checkout lanes at a grocery store.

• Resistance is the difficulty customers have getting through a checkout lane.

• Current is the number of customers checking out per minute.

If you only have one checkout lane open (a single resistor), all customers must line up there. The overall opposition (resistance) to the flow of customers is high.

If you open five checkout lanes (five resistors in parallel), you create multiple paths for the customers. Even if some lanes are slower than others, the overall opposition drops dramatically because customers can spread out. The total “resistance” of the checkout area is now much lower than even the single fastest lane.

In an electrical circuit, connecting resistors in parallel provides multiple paths for the current to flow. More paths mean less overall opposition, hence a lower total resistance.

The Formulas for Parallel Resistance

Our calculator uses the following standard formulas:

For any number of resistors: The total resistance is the reciprocal of the sum of the reciprocals of each individual resistor.

To get the final answer, you must calculate the sum on the right and then take the reciprocal of that result.

For exactly two resistors: There is a simpler, more direct formula known as “product over sum.”

Series vs. Parallel Resistance: A Key Comparison

To fully appreciate the effect of parallel connections, it’s helpful to compare it directly with a series connection.

Frequently Asked Questions

What is the main difference between series and parallel circuits?

The key difference is the path for the current.

• Series Circuit: There is only one path. The current must flow through every component, one after another. If any component breaks, the entire circuit stops working.

• Parallel Circuit: There are multiple paths (branches). The current splits up and flows through the different branches simultaneously. If one branch breaks, the other branches can still operate. This is how the lights in your house are wired.

What if I have two identical resistors in parallel?

There’s a very useful shortcut for this common scenario: the total resistance is simply half the value of one resistor.

Concrete Example: You have two 100Ω resistors in parallel.

• Using the shortcut: $100\Omega /2=50\Omega$.

• Using the formula: $(100times100)/(100+100)=10000/200=50\Omega$.

If you have three identical resistors in parallel, the total resistance is one-third the value, and so on.

How does current behave in a parallel circuit?

The total current from the voltage source divides among the parallel branches. It does not divide equally unless all the resistors are identical. According to Ohm’s Law, current prefers the path of least resistance.

• The branch with the lowest resistance will get the most current.

• The branch with the highest resistance will get the least current. The sum of the currents in all the individual branches will equal the total current leaving the source.

How does voltage behave in a parallel circuit?

This is a defining characteristic of parallel circuits: the voltage is the same across every component in the parallel combination. If you have a 12V battery connected to three resistors in parallel, all three resistors will have the full 12V across them.

What is a practical use for parallel resistors?

One common application is to create a specific, non-standard resistance value. For example, if you need a 75Ω resistor for a project but you only have 100Ω and 300Ω resistors, you can place them in parallel: R_eq = (100 × 300) / (100 + 300) = 30000 / 400 = 75Ω Another use is as a current divider, where you intentionally split a current into precise ratios for different parts of a circuit.

What happens if one resistor in a parallel circuit burns out (opens)?

If a resistor “opens,” it means its connection is broken and its resistance becomes infinite. That entire branch is now an open circuit, and no current can flow through it. The other branches are unaffected and will continue to conduct current. However, the total resistance of the circuit will increase because there is now one less path for the current to take. This will cause the total current drawn from the source to decrease.

How do I calculate the total power dissipated in a parallel circuit?

There are two common ways:

1. Calculate total resistance ($R\_eq$) using our calculator. Then use the power formula P=V2/R_eq, where V is the voltage of the source.

2. Calculate the power of each resistor individually (P_1=V2/R_1, P_2=V2/R_2, etc.). Then, add the individual power dissipations together: $P\_Total=P\_1+P\_2+P\_3+dots$ Both methods will give you the same result.

How does adding another resistor in parallel affect the total circuit?

When you add another resistor in parallel, you are adding another path for the current. This has two main effects:

1. The total equivalent resistance decreases.

2. The total current drawn from the voltage source increases.

What if all my parallel resistors are very large?

Even if you have several large resistors, for example, three 1 MΩ (Megaohm) resistors, the parallel resistance rule still applies. The total resistance will be 1 MΩ / 3 = 333 kΩ, which is significantly smaller than 1 MΩ.

Can I use this calculator for other components like capacitors or inductors?

No. The rules for combining components in parallel are different for capacitors and inductors.

• Capacitors in Parallel: You simply add their values: $C\_Total=C\_1+C\_2+dots$ (This is like the formula for resistors in series).

• Inductors in Parallel: They follow the same reciprocal rule as resistors.

This calculator is exclusively for resistors.

Now that you’ve calculated your parallel resistance, you might want to see how it behaves in a complete circuit. Use our Ohm’s Law Calculator to find the voltage, current, and power relationships. If you need to calculate the resistance of a single-path circuit, check out our Series Resistor Calculator.