🧮 Series & Parallel Resistor Calculator
Add as many resistors as you like and see the series and parallel equivalent resistance at once. Everything runs in your browser — no data leaves this page.
What is a Series & Parallel Resistor Calculator?
Resistors can be wired in a circuit in two fundamental ways: in series and in parallel. This series and parallel resistor calculator computes the series equivalent resistance and the parallel equivalent resistance for every resistor you add — at the same time. Add as many resistor rows as you need, enter each value in Ω, kΩ or MΩ, and the tool instantly formats the results to the most readable unit. Every calculation happens in your browser; no data is ever sent to a server.
Series resistance formula
When resistors are connected in series (end to end), the current flows through a single path and passes through every resistor. The equivalent resistance is therefore the sum of all resistances: Rseries = R1 + R2 + R3 + … In a series connection the total resistance is always larger than the largest single resistor. For example, 1 kΩ, 2 kΩ and 3 kΩ in series give 1 + 2 + 3 = 6 kΩ.
Parallel resistance formula and equivalent resistance
When resistors are connected in parallel (side by side), the current is given more than one path. The reciprocal of the equivalent resistance equals the sum of the reciprocals of each resistor: 1/Rparallel = 1/R1 + 1/R2 + 1/R3 + … So the equivalent resistance is Rparallel = 1 / (1/R1 + 1/R2 + …). Using the same example, 1 kΩ, 2 kΩ and 3 kΩ in parallel give 1/R = 1/1000 + 1/2000 + 1/3000 ≈ 0.001833, so R ≈ 545 Ω. As you can see, the parallel result is smaller than even the smallest resistor in the circuit (1 kΩ).
Why is parallel resistance always smaller than the smallest?
Every resistor you add in parallel opens a new path for the current. More paths make it easier for current to flow, so the total conductance rises while the equivalent resistance falls. That is why the parallel equivalent resistance is mathematically always smaller than the smallest resistor. A handy shortcut: two equal resistors in parallel halve the value (for example two 10 kΩ → 5 kΩ); for n equal resistors the result is R/n.
Practical tips
- Make a non-standard value: if the resistance you need is not in stock, combine the standard (E12/E24) resistors you have in series or parallel to get close to the target. Use series to go up and parallel to go down.
- Power sharing: putting resistors in parallel spreads the dissipated power across several components. To avoid exceeding a single resistor's power rating, it is common to parallel two resistors so they share the heat load.
- Mixed circuits: for circuits that contain both series and parallel sections, first reduce each parallel group to a single equivalent, then add the results in series.
Frequently Asked Questions
What are the series and parallel resistor formulas?
For resistors in series the equivalent resistance is the sum of all resistors: R = R1 + R2 + R3 + … For resistors in parallel the reciprocals add up: 1/R = 1/R1 + 1/R2 + 1/R3 + …, so the equivalent resistance is R = 1 / (1/R1 + 1/R2 + …).
Why is parallel resistance always smaller than the smallest resistor?
A parallel connection gives the current more than one path, so the total conductance increases and the equivalent resistance drops. Because every added path makes it easier for current to flow, the result is always smaller than even the smallest resistor in the circuit.
What happens if I put two equal resistors in parallel?
Two equal resistors in parallel give exactly half their value. For example, two 10 kΩ resistors in parallel result in 5 kΩ. For n equal resistors in parallel the result is R/n.
How do I make a non-standard resistor value?
You can build a value you do not have in stock by combining standard resistors in series or parallel. Use series (addition) for a larger value and parallel for a smaller one. Try different combinations in this calculator to get close to your target value.