Parallel and Series Resistor Calculator

Parallel and Series Resistor Calculator supports engineering calculations with transparent assumptions, practical result interpretation, and links to next-step technical resources.

Formula & Circuit

Formula

1/RT = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

Parallel resistors share the same voltage; total resistance decreases as branches increase.

Equivalent Circuit

Branch Contribution

Enter resistor values to visualize contribution.

Inputs & Outputs

Optional Source Voltage

Result Format

Total Resistance

Source Current

Source Power

Series vs Parallel Fundamentals

Choose topology by what stays constant in the network. In series, current is common and voltage divides. In parallel, voltage is common and current divides by branch conductance.

Series Rule

RT = R1 + R2 + ... + Rn

Current is equal in all branches; voltage drop is proportional to resistance.

Parallel Rule

1 / RT = 1 / R1 + 1 / R2 + ... + 1 / Rn

Voltage is equal in all branches; current split follows conductance.

Quick Network Examples

Practical reference values for rapid estimation before fine tuning resistor selections.

Topology	Network	Equivalent	Engineering Note
Series	100 Ω + 220 Ω + 470 Ω	790 Ω	Series total always increases with additional resistors.
Parallel	100 Ω \|\| 220 Ω \|\| 470 Ω	≈ 59.49 Ω	Parallel total is always below the smallest branch resistor.
Parallel with dominant branch	100 Ω \|\| 10 kΩ	≈ 99.01 Ω	A very large branch contributes little to total conductance.

Topology Selection Matrix

Use objective-driven rules to choose topology and validate operating margins.

Scenario	Preferred Topology	Reason	Critical Checks
Sensor pull-up / pull-down networks	Series + reference branch	Predictable node bias and controlled current draw.	Input leakage, threshold margin, startup state
Current sharing / load balancing	Parallel branches	Distribute current and reduce equivalent resistance.	Tolerance mismatch, thermal runaway, branch derating
Attenuation chains and resistor ladders	Series network	Set deterministic drops across each stage.	Power dissipation per stage, noise coupling, fault mode