Parallel Resistance Calculator
Combine up to three resistors in parallel into a single equivalent resistance, and compare it with the series total of the same resistors.
How it works
1 ÷ R_parallel = 1/R1 + 1/R2 + 1/R3 · Series: R_series = R1 + R2 + R3
Resistors in parallel share the same voltage but split the current, so their conductances (1/R) add: 1/R_total = Σ 1/Rᵢ. The equivalent resistance is therefore always smaller than the smallest single resistor, because adding another path gives current more ways to flow. For the special case of two resistors this simplifies to R1·R2 / (R1 + R2), and n equal resistors of value R give R/n. In series, by contrast, resistances simply add.
Worked example
A 100 Ω and a 220 Ω resistor in parallel: 1/R = 1/100 + 1/220 = 0.01 + 0.004545 = 0.014545, so R = 68.75 Ω — lower than either resistor. The same two in series would be 100 + 220 = 320 Ω.
Frequently asked questions
Why is parallel resistance smaller than the smallest resistor?
Each extra parallel path gives current an additional route, increasing the total conductance and so lowering the overall resistance. The combined value is always below the smallest branch — adding a resistor in parallel can only make it easier for current to flow.
What is the shortcut for two resistors in parallel?
For exactly two resistors, R_parallel = (R1·R2) ÷ (R1 + R2), the "product over sum" rule. For n identical resistors of value R, the parallel combination is simply R ÷ n.
How do parallel and series resistances differ?
In series the resistances add directly and the total is larger than any single one; in parallel the reciprocals add and the total is smaller than any single one. Series shares current, parallel shares voltage.
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This calculator is for educational purposes. Double-check important results before acting on them.