Parallel Resistance Calculator
Find equivalent resistance of 2, 3, or 4 resistors in parallel.
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Formulas
1/Rt = 1/R1 + 1/R2 + 1/R3 + ...Total parallel resistance is always less than the smallest individual resistor.
Parallel Resistance
In parallel, current has multiple paths. Total resistance decreases as more resistors are added. For two equal resistors R, the parallel result is R/2. For N equal resistors: R/N.
How Parallel Resistance Works
When resistors are connected in parallel, current can flow through multiple paths at once, so the combined resistance is always lower than the smallest individual resistor. The reciprocal of the total equals the sum of the reciprocals:
1/Rt = 1/R1 + 1/R2 + 1/R3 + ...For just two resistors this simplifies to the handy product-over-sum form: Rt = (R1 × R2) / (R1 + R2).
Adding more parallel paths always reduces total resistance, because each new branch gives current another route to flow.
Worked Examples
Two 100 Ω resistors in parallel:
Rt = (100 × 100) / (100 + 100) = 50 Ω
N equal resistors in parallel give R/N — here 100/2 = 50 Ω.
100 Ω, 200 Ω, 300 Ω in parallel:
1/Rt = 1/100 + 1/200 + 1/300 = 0.0183 → Rt = 54.5 Ω
Series vs Parallel
| Property | Series | Parallel |
|---|---|---|
| Total resistance | Sum (larger) | Reciprocal sum (smaller) |
| Current | Same in all | Splits between branches |
| Voltage | Divides | Same across all |
Frequently Asked Questions
Why is parallel resistance always smaller?
Each added resistor gives current an extra path, increasing total current for the same voltage — which by Ohm's law means lower effective resistance.
What is the product-over-sum rule?
A shortcut for exactly two parallel resistors: Rt = R1·R2 / (R1+R2). It is faster than the reciprocal method but only works for two at a time.
Does this apply to impedances?
The same reciprocal rule applies to parallel impedances in AC circuits, but you must use complex arithmetic to account for phase.