Home › Physics › Resistors in Series and Parallel Calculator
Resistors in Series and Parallel Calculator
Computes the equivalent resistance of a list of resistors connected all in series (sum) and all in parallel (reciprocal of the sum of reciprocals), plus the parallel conductance.
When to use
You have two or more resistor values and need the total resistance if they are wired in series or in parallel, or want to check a parallel combination against a target value.
Do not use when: The network mixes series and parallel branches (reduce it group by group with repeated calls), the components are capacitors or inductors, or you need voltage, current or power for one resistor (use ohms-law).
Formula
series_total_ohm = R1 + R2 + …; 1 / parallel_total_ohm = 1/R1 + 1/R2 + …
Inputs
| Parameter | Type | Unit | Required | Description |
|---|---|---|---|---|
resistances_ohm | number_list | Ω | yes | Resistor values in ohms, comma-separated (1 kΩ = 1000). All values must be positive. |
Outputs
| Output | Type | Unit | Description |
|---|---|---|---|
resistor_count | integer | How many values were combined. | |
series_total_ohm | number | Ω | R1 + R2 + … (always larger than the largest resistor). |
parallel_total_ohm | number | Ω | 1 / (1/R1 + 1/R2 + …) (always smaller than the smallest resistor). |
parallel_conductance_s | number | S | Sum of conductances 1/R1 + 1/R2 + … in siemens. |
Example
100, 220 and 470 Ω: {"resistances_ohm":[100,220,470]} → {"resistor_count":3,"series_total_ohm":790,"parallel_total_ohm":59.9768,"parallel_conductance_s":0.016673}
Two 10 Ω resistors: {"resistances_ohm":[10,10]} → {"resistor_count":2,"series_total_ohm":20,"parallel_total_ohm":5}
GET https://tttkmbb.com/api/v1/calculate/resistors-series-parallel?resistances_ohm=100%2C220%2C470
Machine access
- API:
GET https://tttkmbb.com/api/v1/calculate/resistors-series-parallel(query parameters) orPOSTwith a JSON body{"inputs": {...}} - Schema: https://tttkmbb.com/api/v1/calculators/resistors-series-parallel · Markdown: https://tttkmbb.com/physics/resistors-series-parallel.md · JSON definition: https://tttkmbb.com/physics/resistors-series-parallel.json
- MCP: server
https://tttkmbb.com/mcp, toolrun_calculator with calculator_id="resistors-series-parallel" - OpenAPI operationId:
calculate_resistors_series_parallel - Freshness:
static. Authentication: none. Rate limit: fair use (see rate limits).
Sources
- HyperPhysics – Resistance and resistor combinations (reference)
- Wikipedia – Series and parallel circuits (reference)
FAQ
How do I handle a mixed circuit?
Reduce it step by step: combine each purely parallel or purely series group into one equivalent resistor, then combine the results, calling this calculator for each group.
Why is the parallel total less than the smallest resistor?
Each added parallel path lets more current flow at the same voltage, increasing total conductance; n equal resistors R in parallel give R / n.
Related calculators
- Ohm's Law Calculator — Voltage, current and power for the equivalent resistance.
- Electric Power Calculator — Power and energy drawn by the circuit.