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Series vs Parallel Resistors: Formula and Worked Examples
How to use
This tool calculates equivalent resistance for the same resistor list in series and in parallel. Series resistances add directly; in parallel, conductances 1/R add and the result is inverted. Inputs can be in Ω, kΩ or MΩ. For 100 Ω and 200 Ω in parallel, equivalent resistance is (100×200) ÷ (100+200) ≈ 66.6667 Ω; in series it is 300 Ω. Keep the input list in one unit: 1 kΩ equals 1,000 Ω, so convert mixed-unit values before entering them.
- Enter 1–100 positive resistor values separated by commas or spaces.
- Choose the unit shared by all values.
- Calculate both series and parallel equivalents.
How it is calculated
Example
Example: 100Ω, 220Ω and 330Ω give 650Ω in series. In parallel, 1÷(1/100+1/220+1/330) ≈ 56.90Ω, below the smallest branch resistance.
Important notes
This calculator handles all-series or all-parallel networks, not arbitrary mixed circuits. It uses nominal resistance values and does not model component tolerance, power rating or temperature effects.
Worked examples and interpreting results
Two resistors of 100 and 200 ohms give 300 ohms in series but about 66.667 ohms in parallel. Connection type changes the formula even when the component values stay the same.
| Case | Calculation | Result |
|---|---|---|
| Series connection | 100 + 200 | 300 Ω |
| Parallel connection | 1 ÷ (1 ÷ 100 + 1 ÷ 200) | 66.666667 Ω |
How to check the result
For positive resistances, the parallel equivalent is smaller than the smallest resistor, a useful quick check. A mixed series-parallel network needs each subnetwork simplified according to its own connections first.
Series and parallel resistors
Series resistance is the sum of resistor values. For parallel branches, add the reciprocal values then take the reciprocal of that total to find equivalent resistance.
- 10 Ω and 20 Ω in series: 10 + 20 = 30 Ω
- 10 Ω and 20 Ω in parallel: 1 / (1/10 + 1/20) = 6.6667 Ω
- Three 6 Ω resistors in parallel: 1 / (1/6 + 1/6 + 1/6) = 2 Ω
Important note
The parallel result is smaller than the smallest positive resistor; these formulas do not describe reactive AC impedance.
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Frequently asked questions
How do I calculate resistors in parallel?
Add the reciprocals and invert the total: 1/Req = 1/R₁ + 1/R₂ + … . For two resistors, Req = R₁R₂/(R₁+R₂).
Why is parallel resistance below the smallest resistor?
Adding a parallel path increases total conductance, so equivalent resistance decreases.
What about equal resistors?
N equal resistors R give NR in series and R/N in parallel.
Does this calculate current and power?
No. This tool focuses on equivalent resistance; use the Ohm’s law calculator for voltage/current/power relationships.
How do I calculate three equal resistors in parallel?
Three 120 Ω resistors in parallel give 120 ÷ 3 = 40 Ω. R/n applies to equal resistors; for unequal values, add reciprocals and invert the sum.
What is the equivalent resistance of 10 Ω and 20 Ω in parallel?
Parallel resistors follow 1/R = 1/R1 + 1/R2. Therefore 1/R = 1/10 + 1/20 = 0.15, so R ≈ 6.667 Ω. With positive resistors, the equivalent parallel resistance is lower than the smallest individual resistance.
How do I calculate the same two resistors in series?
Add series resistances directly: 10 Ω + 20 Ω = 30 Ω. For parallel connection, take the reciprocal of the sum of reciprocals. Convert all values into consistent units such as ohms before comparing.