{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"resistors-series-parallel"},"result":{"entity_type":"calculator","id":"resistors-series-parallel","calculator_id":"resistors-series-parallel","canonical_url":"https://tttkmbb.com/physics/resistors-series-parallel","name":"Resistors in Series and Parallel Calculator","title":"Series and Parallel Resistor Calculator – Equivalent Resistance of a List of Resistors","category":"physics","category_name":"Physics","tool_name":"calculate_resistors_series_parallel","featured_mcp_tool":false,"description":"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.","use_when":"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).","inputs":[{"name":"resistances_ohm","label":"Resistances","type":"number_list","unit":"Ω","required":true,"description":"Resistor values in ohms, comma-separated (1 kΩ = 1000). All values must be positive.","example":[100,220,470]}],"outputs":[{"name":"resistor_count","label":"Number of resistors","type":"integer","decimals":4,"description":"How many values were combined."},{"name":"series_total_ohm","label":"Series total","type":"number","unit":"Ω","decimals":4,"description":"R1 + R2 + … (always larger than the largest resistor)."},{"name":"parallel_total_ohm","label":"Parallel total","type":"number","unit":"Ω","decimals":4,"description":"1 / (1/R1 + 1/R2 + …) (always smaller than the smallest resistor)."},{"name":"parallel_conductance_s","label":"Parallel conductance","type":"number","unit":"S","decimals":6,"description":"Sum of conductances 1/R1 + 1/R2 + … in siemens."}],"input_schema":{"type":"object","properties":{"resistances_ohm":{"description":"Resistor values in ohms, comma-separated (1 kΩ = 1000). All values must be positive. Unit: Ω.","type":"array","items":{"type":"number"},"minItems":1,"examples":[[100,220,470]],"x-unit":"Ω"}},"additionalProperties":false,"required":["resistances_ohm"]},"output_schema":{"type":"object","properties":{"resistor_count":{"description":"How many values were combined.","type":"integer"},"series_total_ohm":{"description":"R1 + R2 + … (always larger than the largest resistor). Unit: Ω.","type":"number","x-unit":"Ω"},"parallel_total_ohm":{"description":"1 / (1/R1 + 1/R2 + …) (always smaller than the smallest resistor). Unit: Ω.","type":"number","x-unit":"Ω"},"parallel_conductance_s":{"description":"Sum of conductances 1/R1 + 1/R2 + … in siemens. Unit: S.","type":"number","x-unit":"S"}}},"formula":"series_total_ohm = R1 + R2 + …; 1 / parallel_total_ohm = 1/R1 + 1/R2 + …","sources":[{"name":"HyperPhysics – Resistance and resistor combinations","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wikipedia – Series and parallel circuits","url":"https://en.wikipedia.org/wiki/Series_and_parallel_circuits","type":"reference","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"100, 220 and 470 Ω","inputs":{"resistances_ohm":[100,220,470]},"expected":{"resistor_count":3,"series_total_ohm":790,"parallel_total_ohm":59.9768,"parallel_conductance_s":0.016673},"url":"https://tttkmbb.com/api/v1/calculate/resistors-series-parallel?resistances_ohm=100%2C220%2C470"},{"name":"Two 10 Ω resistors","inputs":{"resistances_ohm":[10,10]},"expected":{"resistor_count":2,"series_total_ohm":20,"parallel_total_ohm":5},"url":"https://tttkmbb.com/api/v1/calculate/resistors-series-parallel?resistances_ohm=10%2C10"}],"faq":[{"q":"How do I handle a mixed circuit?","a":"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."},{"q":"Why is the parallel total less than the smallest resistor?","a":"Each added parallel path lets more current flow at the same voltage, increasing total conductance; n equal resistors R in parallel give R / n."}],"tags":["resistors in series","resistors in parallel","equivalent resistance","total resistance","resistor network"],"related":[{"calculator_id":"ohms-law","reason":"Voltage, current and power for the equivalent resistance."},{"calculator_id":"electric-power","reason":"Power and energy drawn by the circuit."}],"links":{"html":"https://tttkmbb.com/physics/resistors-series-parallel","markdown":"https://tttkmbb.com/physics/resistors-series-parallel.md","json":"https://tttkmbb.com/physics/resistors-series-parallel.json","api":"https://tttkmbb.com/api/v1/calculate/resistors-series-parallel","schema":"https://tttkmbb.com/api/v1/calculators/resistors-series-parallel","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:31:10Z"}