Combining resistors is a Class 10 and 12 physics staple and a daily task in electronics. Enter your resistor values to get the equivalent resistance when they are connected in series and in parallel.
Enter resistor values in ohms, separated by commas.
Read the series and parallel totals.
Series: Rs = R₁ + R₂ + R₃ + …
Parallel: 1/Rp = 1/R₁ + 1/R₂ + 1/R₃ + …
When several resistors are connected together, the circuit behaves as if it had one equivalent resistor. This calculator takes a list of resistor values and gives two answers: the equivalent resistance if they are all connected end to end in series, and the equivalent if they are all connected side by side in parallel. It shows the sum for series and the reciprocal sum for parallel.
Combining resistors is a standard Class 10 and Class 12 physics topic, and a practical trick in electronics when the exact value you need is not in your parts box. Two 1 kΩ resistors in parallel make 500 Ω; a 2.2 kΩ and a 330 Ω in series make 2.53 kΩ. Electricians also meet the same rules in household wiring, where appliances are connected in parallel.
1. Convert all values to the same unit, usually ohms.
2. Series: add them, Rs = R₁ + R₂ + R₃ + ….
3. Parallel: add the reciprocals, 1/Rp = 1/R₁ + 1/R₂ + 1/R₃ + ….
4. Take the reciprocal of that sum to get Rp.
5. For just two resistors in parallel, use the shortcut Rp = R₁R₂ ÷ (R₁ + R₂).
6. For n equal resistors R, series gives nR and parallel gives R ÷ n.
7. Check: the series total must exceed the largest resistor; the parallel total must be below the smallest.
In a series chain there is only one path, so the same current I flows through every resistor. By Ohm's law each one drops a voltage IR₁, IR₂ and so on. Kirchhoff's voltage law says these drops add up to the total voltage across the chain: V = IR₁ + IR₂ + … = I(R₁ + R₂ + …). Comparing with V = IRs gives Rs = R₁ + R₂ + …. The largest resistor takes the largest share of the voltage and, carrying the same current, dissipates the most power.
In parallel, every resistor is connected across the same two points, so each sees the same voltage V. Each draws its own current V ÷ Rᵢ, and Kirchhoff's current law says the total current is their sum: I = V/R₁ + V/R₂ + …. Comparing with I = V ÷ Rp gives 1/Rp = 1/R₁ + 1/R₂ + …. It is easier to think in conductance, 1/R, measured in siemens: in parallel, conductances simply add. Adding any extra path, however poor, lets more current flow and lowers the total resistance.
Real circuits often combine both. Reduce them step by step: replace each group that is clearly in series or clearly in parallel with its equivalent, redraw, and repeat. This calculator handles one group at a time, all in series or all in parallel, which is exactly what each reduction step needs. Household appliances are wired in parallel so that each gets the full 230 V and can be switched independently. Switching on more appliances lowers the total resistance and raises the total current, which is what trips an MCB when too much is running.
Tanvi is building a sensor circuit and has 220 Ω, 330 Ω and 1000 Ω resistors in her kit. She wants to see what single values she can make by connecting all three in series or all three in parallel.
Series: add them: 220 + 330 + 1000 = 1,550 Ω
Parallel: add reciprocals: 1/Rp = 1/220 + 1/330 + 1/1000 = 0.00857576 Rp = 1 ÷ 0.00857576 = 116.6078 Ω
Answer: Series 1.55 kΩ; Parallel 116.608 Ω
Adding resistances directly for a parallel connection.
Forgetting to take the final reciprocal, and reporting 1/Rp as the answer.
Mixing kΩ and Ω values in the same list.
Using the two-resistor product-over-sum shortcut for three or more resistors at once.
Treating resistors as parallel just because they are drawn side by side; they must share both end points.
Making a non-standard resistance from standard parts.
Class 10 and Class 12 numericals on equivalent resistance.
Sharing power across several resistors to stay within their ratings.
Understanding why adding appliances increases the current in household circuits.
Reducing complex networks step by step before applying Ohm's law.
What is the shortcut for two resistors in parallel?
Rp = (R₁ × R₂) ÷ (R₁ + R₂).
Why is the parallel value smaller?
Each extra path lets more current flow for the same voltage.