Series-Parallel Circuit Calculator
Solve nested resistor networks with + and ∥
Required Parameters
Waiting for input data...
Quick Answer
Simplify nested resistor networks from the inside out. Use + for series and || (or ∥) for parallel. Example: 1k+(2.2k||4.7k) ≈ 2.5 kΩ.
How to use the series-parallel circuit calculator
- Sketch the network and mark pure series and parallel groups.
- Enter the expression using + for series and || (or ∥) for parallel.
- Use parentheses for nesting:
1k+(2.2k||4.7k)or(10||10)+4.7k. - Read Req and the simplification steps.
For a flat parallel or series list only, prefer the Parallel Resistor Calculator.
Worked example
R1 = 1 kΩ in series with (R2 = 2.2 kΩ ∥ R3 = 4.7 kΩ)
- Parallel group: (2200 × 4700) / (2200 + 4700) = 1497 Ω
- Series total: 1000 + 1497 = 2497 Ω ≈ 2.5 kΩ
Expression: 1k+(2.2k||4.7k)
Operator rules
- Parallel binds tighter than series:
1k+2.2k||4.7k→1k+(2.2k∥4.7k) - Parentheses always win
- Engineering shorthand supported:
4K7,10M,220
Related tools
- Parallel Resistor Calculator — pure parallel/series lists + missing R
- Current Divider Calculator — branch currents after you know the parallel group
- Equivalent Resistance Guide — theory and classroom method
- Series vs Parallel Circuits — definitions and comparison
Design Notes
Pure series or pure parallel lists are faster in the Parallel Resistor Calculator. Use this solver when the schematic has nested groups that cannot be entered as a single flat list.
Common Mistakes
- 1
Forgetting parentheses when series and parallel mix at the same level.
- 2
Using a single | instead of || for parallel — this tool expects || or ∥.
- 3
Trying to solve non-series-parallel (bridge) networks — those need mesh/nodal analysis.
Engineering Handbox
1. Inner parallel: (2.2k ∥ 4.7k) = 1.497 kΩ 2. Series with 1k: 1k + 1.497k = 2.497 kΩ
Knowledge Base
What is a series-parallel circuit calculator?
A tool that finds equivalent resistance for nested combination circuits — networks that mix series (+) and parallel (∥) groups. Enter an expression such as 1k+(2.2k||4.7k) and simplify from the inside out.
How do I write a parallel group?
Use || or ∥ between resistor values. Example: 2.2k||4.7k means 2.2 kΩ in parallel with 4.7 kΩ. Use parentheses for nesting: (R1||R2)+R3.
When should I use the Parallel Resistor Calculator instead?
Use the Parallel Resistor Calculator for a flat list of only parallel or only series resistors. Use this Series-Parallel Circuit Calculator when the schematic has nested groups.
Can this solve bridge circuits?
No. Wheatstone bridges and other non-series-parallel topologies need mesh or nodal analysis. This solver only handles networks that reduce by successive series and parallel combinations.
Related Engineering Tools
Parallel Resistor Calculator
Equivalent resistance for 2–10 resistors in parallel or series
Current Divider Calculator
Branch current for 2+ parallel resistors
Voltage Divider Calculator
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Ohm's Law Calculator
Solve voltage, current, resistance, or power