π Parallel Resistor Calculator
Calculate total resistance of resistors in parallel: 1/Rt = 1/R1+1/R2+...
Result
How to Use This Calculator
This calculator finds the equivalent resistance of resistors in parallel. Enter two or more resistor values and it combines them into a single equivalent resistance.
Enter the first resistor value in ohms in the R1 field.
Enter the second in R2. Click the add button for a third, fourth, or more resistors.
Click Calculate. The equivalent resistance appears in ohms.
Notice the result is always smaller than your smallest resistor. If it is not, check your entries.
Resistors in Parallel
In parallel, every resistor sees the same voltage, and the total current is the sum of the branch currents. Conductance, the reciprocal of resistance, is what actually adds: each branch contributes its own 1/R to the total. Flip the sum back and you get the equivalent resistance. The two-resistor shortcut, product over sum, is worth memorizing since pairs are the most common case.
The intuition is plumbing: one pipe carries some water, and adding a second pipe in parallel always lets more water through. Electrically, more paths mean less total resistance. This is the opposite of series, where each resistor adds another obstacle in the single path.
Worked Example
Where This Comes Up
Parallel resistance is the math behind household wiring, car headlights that stay bright independently, and combining standard resistor values to hit a nonstandard target. Need 3 Ξ© but only stock 12 Ξ© and 4 Ξ©? Parallel them. Audio speaker wiring uses it too: two 8 Ξ© speakers in parallel present 4 Ξ© to the amplifier, which changes how much power the amp delivers.
The classic blunder is adding parallel resistors like series ones. If your parallel total comes out bigger than the parts, you added instead of using reciprocals. For exactly two resistors, the product-over-sum form is faster and less error-prone than the reciprocal dance.
Frequently Asked Questions
Why is the total less than the smallest resistor?
Each added resistor opens another path for current. More paths mean more total current at the same voltage, which is exactly what a smaller equivalent resistance means.
What if all the resistors are equal?
Divide by the count: n equal resistors R give R/n. Two 10 Ξ© resistors in parallel make 5 Ξ©, and four make 2.5 Ξ©.
What happens if one resistor burns out?
In parallel, the rest keep working: the total becomes the parallel combination of the survivors. This is why your kitchen lights stay on when one bulb dies.
Are house circuits series or parallel?
Parallel. Every outlet and light gets the full mains voltage independently, and each draws only its own current.
Can I combine series and parallel in one circuit?
Yes. Reduce each parallel group to its equivalent resistance first, then add the series parts. Work from the inside out.