Series & Parallel Circuit Calculator

Analyze series and parallel resistor networks — total resistance, current, per-resistor voltage drop, and the share of power each component dissipates.

Circuit Analysis

Analyze resistors wired in series or parallel — total resistance, current, voltage drop per element, and the share of power each component dissipates.

Topology

Source Voltage

Resistor Valuesin ohms, comma-separated

Rₜ = R₁ + R₂ + … + Rₙ

What Is Circuit Analysis?

Circuit analysis is the process of finding the voltage, current, and power at every point in a network of components. The two foundational arrangements are series, where components share a single current path, and parallel, where they share the same two nodes and therefore the same voltage. Almost every real circuit is built from combinations of these two patterns.

This series and parallel circuit calculator takes a source voltage and a list of resistor values and returns the total equivalent resistance, the total current drawn, and a per-resistor breakdown of voltage drop, current, and power dissipation — including each component's share of the total power. It is part of the Ohm's Law Calculator, so the same V = I × R relationship drives every number.

This is one mode of the full Ohm's Law Calculator — you can also jump to the voltage drop calculator or the all-in-one unit converter for related electrical work.

How Series and Parallel Circuits Work

Series resistances add

In series, the same current flows through every resistor and the voltage drops add up to the source: Rₜ = R₁ + R₂ + … . The largest resistor drops the most voltage and dissipates the most power.

Parallel resistances combine reciprocally

In parallel, every branch sees the full source voltage and the currents add: 1/Rₜ = 1/R₁ + 1/R₂ + … . The total is always smaller than the smallest branch resistor.

Series divides voltage

A series chain is a voltage divider — each resistor takes a share of the source voltage in proportion to its resistance. This is how reference voltages and bias points are set.

Parallel divides current

A parallel set is a current divider — the smallest resistor draws the most current. This is how loads share a supply and how shunts steer current around a meter.

Series & Parallel Formulas

Total resistance depends on the topology; Ohm's Law and the power equation then give current and dissipation for the whole network and each element.

Series total

Rₜ = R₁ + R₂ + … + Rₙ

Resistances add; current is the same through every element.

Parallel total

1/Rₜ = 1/R₁ + … + 1/Rₙ

Reciprocals add; voltage is the same across every element.

Per element

V = I·R · P = I²·R

Once Rₜ and total current are known, each resistor's drop and power follow from Ohm's Law.

How to Use the Circuit Analysis Calculator

1
Choose series or parallel
Pick the topology that matches your network. Series shares one current path; parallel shares two nodes.
2
Enter the source voltage
Type the supply voltage feeding the network — for example 12 V from a battery or bench supply.
3
List the resistor values
Enter the resistances separated by commas, in ohms (for example 10, 22, 47). Add as many as your circuit has.
4
Read the full breakdown
The calculator returns total resistance, total current, total power, and a per-resistor table of voltage drop, current, power, and percentage share, plus charts.

Key Circuit Concepts

Equivalent resistance

The single resistance that would draw the same current from the source as the whole network. Series adds; parallel combines reciprocally and is always less than the smallest resistor.

Voltage divider

A series pair splits the source voltage in proportion to each resistance: V₁ = V × R₁ / (R₁ + R₂). The basis of reference and bias circuits.

Current divider

A parallel pair splits the total current inversely with resistance: the smaller resistor carries the larger share. Used for shunts and load sharing.

Kirchhoff's laws

Current into a node equals current out (KCL); voltage around any loop sums to zero (KVL). They are the bookkeeping rules behind every series and parallel result.

Series & Parallel Circuits in Practice

🔋

Batteries in series

Four 1.5 V cells in series make 6 V — voltages add while capacity stays the same. This is how most battery packs raise voltage.

🔌

Batteries in parallel

Two identical packs in parallel keep the same voltage but double the capacity and current capability — common in solar and off-grid banks.

💡

LED strings

Series LEDs share one current (one resistor sets it); parallel LED branches each need their own resistor so one failure doesn't dump current into the rest.

🎛️

Voltage divider reference

Two series resistors create a precise fraction of the supply for a sensor reference or a transistor bias point.

🏠

House wiring

Household outlets are wired in parallel so every device sees the full 120/230 V and can switch on or off independently of the others.

📟

Pull-up / pull-down

A single resistor to the rail or ground sets a logic line's default state — a one-resistor series circuit analysed with the same Ohm's Law.

Best Practices for Circuit Analysis

✓Sanity-check parallel totals. The equivalent of resistors in parallel is always less than the smallest one. If your answer is larger, you've used the series formula by mistake.
✓Check each resistor's power. In series the biggest resistor runs hottest; in parallel the smallest does. Verify every element's I²R against its wattage rating, not just the total.
✓Reduce complex networks in stages. Collapse series and parallel sub-groups one at a time into equivalents until a single resistance remains, then expand back to find each branch.
✓Mind tolerance in dividers. A voltage divider's accuracy is limited by resistor tolerance. Use 1% parts where the ratio matters, and keep divider current well above any load current.
✓Account for source resistance. Real supplies and batteries have internal resistance that acts in series with your network and drops a little voltage under load.

Common Circuit-Analysis Mistakes

Adding parallel resistances directly

Parallel resistors combine reciprocally, not by simple addition. Adding them gives a total far too high and a current far too low.

Assuming equal voltage in series

Series resistors share current, not voltage — each drops a share proportional to its resistance. Only parallel elements share voltage.

Ignoring per-resistor power

A network can draw safe total power while one small resistor overheats. Always check each element's dissipation individually.

Forgetting source internal resistance

On high-current or low-voltage circuits, the battery's own resistance noticeably reduces the voltage reaching your network.

Why Circuit Analysis Matters

Series and parallel reduction is the first tool every electronics designer reaches for. It tells you how much current a circuit will draw, how voltage divides between components, and which resistor will run hottest — the answers that decide whether a design works, wastes power, or burns out.

Because real circuits are built by nesting series and parallel groups, mastering the two basic rules lets you analyse surprisingly complex networks by hand. Getting them right protects components, sets accurate reference voltages, balances loads, and underlies everything from LED arrays and battery packs to power distribution and sensor front-ends.

Built for electronics hobbyists, electrical engineering students, technicians, and makers designing resistor networks, dividers, and battery packs.

Formulas cross-checked against standard electrical engineering references — see our methodology and editorial policy. Educational only — always confirm critical designs with a licensed electrician and your local electrical code.

Circuit Analysis FAQs

In a series circuit, total resistance is the simple sum of all the resistors: Rₜ = R₁ + R₂ + … + Rₙ. For example, 10 Ω, 22 Ω, and 47 Ω in series total 79 Ω. The same current flows through every resistor, and their voltage drops add up to the source voltage.

In a parallel circuit, the reciprocals add: 1/Rₜ = 1/R₁ + 1/R₂ + … + 1/Rₙ. For two resistors this simplifies to Rₜ = (R₁ × R₂) ÷ (R₁ + R₂). The total is always smaller than the smallest individual resistor because you are adding more current paths.

In series, components share a single current path — the same current flows through each, and voltages add. In parallel, components connect across the same two nodes — they share the same voltage, and currents add. Series resistances add up; parallel resistances combine reciprocally to a smaller total.

Every branch in a parallel circuit sees the full source voltage, so the current in each branch is V ÷ R for that branch. The smallest resistance carries the most current. The branch currents add up to the total current drawn from the source — this is the current-divider principle.

In a series circuit the voltage divides in proportion to each resistance: a resistor's drop is V × (R ÷ Rₜ). The largest resistor takes the largest share of the voltage. This voltage-divider behaviour is how reference voltages and transistor bias points are created.

Adding a resistor in parallel creates another path for current, so more total current flows for the same voltage — and more current for the same voltage means less equivalent resistance. No matter how large the added resistor, it can only increase the current, so the equivalent resistance always drops below the smallest branch.

In a series circuit the largest resistor dissipates the most power, because power is I²R and the current is the same through all of them. In a parallel circuit the smallest resistor dissipates the most, because it carries the most current at the shared voltage (P = V²/R). This calculator shows each resistor's power and its percentage share.

The calculator uses exact series and parallel formulas plus Ohm's Law, so its precision far exceeds practical needs. Real circuits differ slightly because of resistor tolerance, wire and contact resistance, and the source's internal resistance — verify critical designs by measuring the assembled circuit.