Parallel Resistance

Instantly calculate the total resistance of resistors connected in parallel. Enter 2 to 10 resistor values with this free online parallel resistance calculator.

How to Use

  1. Enter resistor values

    Input the resistance value (Ω) for each parallel resistor.

  2. Add more resistors

    Click the add button to enter additional resistor values if needed.

  3. View results

    Click Calculate to see the total equivalent resistance and total current.

What Is Parallel Resistance?

Parallel resistance is a circuit arrangement in which two or more resistors are connected side by side between the same two nodes. The same voltage appears across each resistor, while the total current splits among the branches and then recombines.

Because connecting resistors in parallel adds more paths for current to flow, the equivalent resistance (Rt) is always smaller than the smallest individual resistor. Engineers use this property to create custom intermediate values from standard parts, to spread current and reduce heating, and to match the load impedance of speakers and wiring.

Where Is It Used?

  • Current sharing and power distribution in power circuits
  • Speaker impedance matching (e.g. two 8Ω in parallel = 4Ω)
  • Building resistance values that aren't available as standard parts

Formula

The parallel equivalent resistance is the reciprocal of the sum of the reciprocals (conductances) of each resistor.

1/Rt = 1/R1 + 1/R2 + ... + 1/Rn

Here Rt is the equivalent resistance and R1-Rn are the individual resistor values (in Ω).

Worked Example (100Ω, 200Ω, 300Ω in parallel)

  • Sum of reciprocals: 1/100 + 1/200 + 1/300 = 0.01 + 0.005 + 0.003333 = 0.018333
  • Equivalent resistance: Rt = 1 / 0.018333 ≈ 54.5455Ω

For just two resistors, the product-over-sum form Rt = (R1 × R2) / (R1 + R2) is simpler. Example: 60Ω∥40Ω = 2400/100 = 24Ω.

Frequently Asked Questions

How do I calculate the equivalent resistance of parallel resistors?
Calculate it with 1/Rt = 1/R1 + 1/R2 + ... + 1/Rn. Add up the reciprocal of each resistor, then take the reciprocal of that sum. The equivalent resistance is always smaller than the smallest individual resistor.
Is there a simpler formula for two resistors?
Yes. For two resistors, the product-over-sum form Rt = (R1 × R2) / (R1 + R2) is quicker. For example, 60Ω and 40Ω in parallel give (60×40)/(60+40) = 2400/100 = 24Ω.
What happens when I connect resistors of equal value in parallel?
When you connect n resistors of equal value (R) in parallel, the equivalent resistance is R/n. For example, two 100Ω resistors in parallel give 50Ω, and four 100Ω resistors give 25Ω.
Why is parallel resistance always smaller than the smallest resistor?
Because a parallel connection adds extra paths for current to flow. More paths mean more total current, and by Ohm's law (R = V/I), for a fixed voltage more current means less resistance. That is why the equivalent resistance ends up below even the smallest branch resistor.
What is the difference between series and parallel connections?
In a series connection the resistors are in a single line, so the equivalent resistance is the sum (Rt = R1 + R2 + ...) and the same current flows through every resistor. In a parallel connection the resistors sit side by side, the equivalent resistance gets smaller, and the same voltage appears across every resistor.
How do I find the current through each resistor in a parallel circuit?
In a parallel circuit the same voltage V is across every resistor, so you find each branch current separately with Ohm's law I = V/R. The smaller-resistance branch carries more current, and the branch currents add up to the total current.
Does it still calculate if I enter only one resistor?
Yes. If you enter only one resistor, there is no parallel combination, so that value becomes the equivalent resistance (Rt) directly. To see a real parallel effect, enter two or more resistors.
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