Series & Parallel Resistance Calculator

Calculate total resistance for any combination of resistors in series or parallel. Add up to 6 resistors, enter an optional supply voltage, and see the total resistance plus the current through every resistor on a live animated circuit diagram.

What is Series & Parallel Resistance Calculator?

Real circuits rarely use just one resistor — components are combined in series (end-to-end, one path for current) or in parallel (side-by-side, multiple paths for current) to reach a target resistance, split a voltage, or divide a current. Knowing how to combine resistor values is one of the most fundamental skills in circuit design, and it's needed constantly whether you're building an LED current-limiting network, a voltage divider, or a sensor bias network.

This calculator handles both configurations for up to six resistors at once. Switch between series and parallel to instantly see how the total resistance changes, and optionally enter a supply voltage to see the actual current flowing through each resistor, visualized live on an animated circuit diagram where faster-moving dots mean higher current.

Formula

Series: Rtotal = R1 + R2 + R3 + ... + Rn

Parallel: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

Current (if voltage is known): I = V / R (Ohm's Law), applied to the total circuit and to each individual branch in parallel.

How to Calculate

Choose whether your resistors are connected in series or parallel.
Enter each resistor's value in ohms — add more resistors with the + button, up to 6 total.
Optionally enter the supply voltage if you want to see the current through the circuit.
Read the total resistance from the result panel.
If a voltage was entered, check the total current and, for parallel circuits, the current through each individual branch.

Example

Three resistors of 100Ω, 220Ω, and 330Ω are combined in series: total resistance = 100 + 220 + 330 = 650Ω. The same three resistors combined in parallel instead: 1/Rtotal = 1/100 + 1/220 + 1/330 ≈ 0.01818, giving Rtotal ≈ 55Ω — much lower than even the smallest individual resistor.

Key Benefits

Handles both series and parallel configurations in a single tool
Supports up to 6 resistors at once, added or removed on the fly
Shows the actual current through every resistor once a supply voltage is entered
Animated circuit diagram makes the difference between series and parallel intuitive at a glance
Works for any resistance unit or scale — just enter values in ohms

Common Mistakes to Avoid

Adding resistances directly for a parallel circuit — parallel resistance always requires the reciprocal formula, never simple addition.
Forgetting that total parallel resistance is always smaller than the smallest individual resistor, and treating a small combined result as an error.
Assuming current is equal across all branches in a parallel circuit — it only is if every resistor has the same value.
Mixing up which resistors are actually in series versus parallel in a more complex network before applying either formula.

Pro Tips

For two resistors in parallel only, a shortcut formula works: Rtotal = (R1 × R2) / (R1 + R2).
If all resistors in a parallel group have the same value R, the total is simply R divided by the number of resistors.
For series circuits, the largest resistor value dominates the total — for parallel circuits, the smallest resistor value dominates.
Break complex networks into series and parallel sub-groups, solve each with this calculator, then combine the results.

Key Terms Explained

Series circuit: A circuit where components are connected end-to-end, forming a single path for current to flow.
Parallel circuit: A circuit where components are connected across the same two points, forming multiple paths for current.
Equivalent resistance: A single resistance value that has the same effect on a circuit as a combination of multiple resistors.
Conductance: The reciprocal of resistance (1/R), which adds directly for parallel components — the reason the parallel formula uses reciprocals.

Common Use Cases

Combining standard resistor values to approximate a non-standard target resistance
Designing an LED current-limiting resistor network for multiple LEDs
Calculating the equivalent resistance of a sensor or potentiometer network
Verifying how current splits across parallel branches in a power distribution circuit
Checking series resistor chains used in voltage-divider or bias networks

Frequently Asked Questions

What is the formula for resistors in series?

For resistors in series, the total resistance is simply the sum of every resistor: Rtotal = R1 + R2 + R3 + ... Adding more resistors in series always increases the total resistance, and the same current flows through every resistor in the chain.

What is the formula for resistors in parallel?

For resistors in parallel, you add the reciprocals of each resistance and then take the reciprocal of that sum: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... Adding more resistors in parallel always decreases the total resistance, and the total resistance is always smaller than the smallest individual resistor.

Why is the total resistance in parallel always less than the smallest resistor?

Each parallel branch gives current an additional path, so adding a branch always increases the total conductance (1/R) of the network — and more conductance means less resistance. This is why a parallel combination of two 100Ω resistors gives exactly 50Ω, not 200Ω: you've effectively doubled the cross-sectional 'width' available for current to flow.

How is current split between resistors in a parallel circuit?

In a parallel circuit, every branch has the same voltage across it (the supply voltage), so the current through each branch is simply that voltage divided by that branch's own resistance (Ohm's Law: I = V/R). A branch with a smaller resistance always carries more current than a branch with a larger resistance.

Do I need to enter a supply voltage to use this calculator?

No — the total resistance is calculated from the resistor values alone. The supply voltage is optional and only needed if you also want to see the current through the circuit and through each individual branch, using Ohm's Law.

Can I mix series and parallel resistors in one circuit?

This calculator handles a single combination — either all-series or all-parallel — for up to 6 resistors at once. For a more complex network with both series and parallel sections, break the circuit into smaller groups: calculate each parallel group's equivalent resistance first, then add those equivalent values in series with any remaining series resistors.