🔌 Parallel Resistor Calculator
1/Rt = 1/R1 + 1/R2 + … — Always less than smallest resistor.
Total Resistance (Rt)
How to Use This Calculator
Enter the resistance of each parallel branch in the input fields, adding more branches with the "Add Resistor" button if needed. The total equivalent resistance is always less than the smallest individual resistor you enter.
Enter R1 in ohms. Enter R2 in ohms in the second field.
Click "Add Resistor" if your circuit has three or more parallel branches.
Click Calculate to get the total parallel resistance.
Use the result with Ohm's Law: divide the supply voltage by Rt to get total current, or calculate individual branch currents as I_n = V / R_n.
Parallel Resistance Formula
In a parallel circuit every branch has the same voltage across it. More branches mean more current paths, which lowers the total resistance. The total current is the sum of all individual branch currents. Smaller resistors carry more current; larger resistors carry less. The total resistance is always less than the smallest individual value.
Worked Examples
Where This Comes Up in Real Life
The house wiring in your home connects all sockets and lights in parallel, not in series. This means every appliance gets the full mains voltage (230 V in the UK, 120 V in the US), regardless of how many other appliances are running. If the sockets were in series, turning on one appliance would change the voltage seen by every other one.
When you need a resistance value that is not available in standard component ranges, you can get close by combining two resistors in parallel. For example, standard E12 values do not include 66.7 Ω, but putting two 100 Ω resistors in parallel gives exactly that. Similarly, connecting a 10 kΩ resistor in parallel with a 100 kΩ gives Rt = (10,000 × 100,000) / (110,000) = 9,090 Ω, close to the 9.1 kΩ E96 series value.
Frequently Asked Questions
How do parallel resistors combine?
1/Rt = 1/R1 + 1/R2 + … Total resistance is always less than the smallest individual resistor.
Two equal resistors in parallel?
Rt = R/2. Two 100Ω resistors in parallel give 50Ω.
What is current in parallel?
Total current splits: I_n = V/R_n. Smaller resistors carry more current.
Why use parallel resistors?
To decrease total resistance, provide multiple current paths, or when you need the same voltage across each component.
Quick formula for 2 resistors?
Rt = (R1 × R2)/(R1 + R2). This is the "product over sum" formula.