{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"capacitors-series-parallel"},"result":{"entity_type":"calculator","id":"capacitors-series-parallel","calculator_id":"capacitors-series-parallel","canonical_url":"https://tttkmbb.com/engineering/capacitors-series-parallel","name":"Capacitors in Series and Parallel Calculator","title":"Series and Parallel Capacitor Calculator – Total Capacitance of a List of Capacitors","category":"engineering","category_name":"Engineering & Automotive","tool_name":"calculate_capacitors_series_parallel","featured_mcp_tool":false,"description":"Computes the total capacitance of a list of capacitors connected all in parallel (sum) and all in series (reciprocal of the sum of reciprocals), and optionally the energy stored at a given voltage.","use_when":"You have two or more capacitor values and need the equivalent capacitance for a parallel or a series connection.","do_not_use_when":"The network mixes series and parallel groups (reduce it group by group), the components are resistors (use resistors-series-parallel), or you need charging time (use rc-time-constant).","inputs":[{"name":"capacitances_uf","label":"Capacitances","type":"number_list","unit":"µF","required":true,"description":"Capacitor values in microfarads, comma-separated (1 nF = 0.001 µF, 1 pF = 1e-6 µF). All values must be positive.","example":[10,22,47]},{"name":"voltage_v","label":"Applied voltage","type":"number","unit":"V","required":false,"min":0,"description":"Optional voltage across the combination; enables the stored-energy outputs (E = ½ C V²).","example":12}],"outputs":[{"name":"capacitor_count","label":"Number of capacitors","type":"integer","decimals":4,"description":"How many values were combined."},{"name":"parallel_total_uf","label":"Parallel total","type":"number","unit":"µF","decimals":6,"description":"C1 + C2 + … (always larger than the largest capacitor)."},{"name":"series_total_uf","label":"Series total","type":"number","unit":"µF","decimals":6,"description":"1 / (1/C1 + 1/C2 + …) (always smaller than the smallest capacitor)."},{"name":"parallel_total_nf","label":"Parallel total","type":"number","unit":"nF","decimals":3,"description":"Parallel total in nanofarads."},{"name":"series_total_nf","label":"Series total","type":"number","unit":"nF","decimals":3,"description":"Series total in nanofarads."},{"name":"energy_parallel_j","label":"Energy stored (parallel)","type":"number","unit":"J","decimals":6,"description":"½ × parallel_total × V² (only when voltage_v is given)."},{"name":"energy_series_j","label":"Energy stored (series)","type":"number","unit":"J","decimals":6,"description":"½ × series_total × V² (only when voltage_v is given)."}],"input_schema":{"type":"object","properties":{"capacitances_uf":{"description":"Capacitor values in microfarads, comma-separated (1 nF = 0.001 µF, 1 pF = 1e-6 µF). All values must be positive. Unit: µF.","type":"array","items":{"type":"number"},"minItems":1,"examples":[[10,22,47]],"x-unit":"µF"},"voltage_v":{"description":"Optional voltage across the combination; enables the stored-energy outputs (E = ½ C V²). Unit: V.","type":"number","minimum":0,"examples":[12],"x-unit":"V"}},"additionalProperties":false,"required":["capacitances_uf"]},"output_schema":{"type":"object","properties":{"capacitor_count":{"description":"How many values were combined.","type":"integer"},"parallel_total_uf":{"description":"C1 + C2 + … (always larger than the largest capacitor). Unit: µF.","type":"number","x-unit":"µF"},"series_total_uf":{"description":"1 / (1/C1 + 1/C2 + …) (always smaller than the smallest capacitor). Unit: µF.","type":"number","x-unit":"µF"},"parallel_total_nf":{"description":"Parallel total in nanofarads. Unit: nF.","type":"number","x-unit":"nF"},"series_total_nf":{"description":"Series total in nanofarads. Unit: nF.","type":"number","x-unit":"nF"},"energy_parallel_j":{"description":"½ × parallel_total × V² (only when voltage_v is given). Unit: J.","type":"number","x-unit":"J"},"energy_series_j":{"description":"½ × series_total × V² (only when voltage_v is given). Unit: J.","type":"number","x-unit":"J"}}},"formula":"parallel_total_uf = C1 + C2 + …; 1 / series_total_uf = 1/C1 + 1/C2 + …; energy_j = ½ × C_farad × voltage_v²","method":"Capacitors combine the opposite way to resistors: parallel adds plate area (capacitances add), series adds plate separation (reciprocals add). In series each capacitor carries the same charge, so the smallest one sees the largest share of the voltage.","sources":[{"name":"Wikipedia – Series and parallel circuits – capacitors","url":"https://en.wikipedia.org/wiki/Series_and_parallel_circuits#Capacitors","type":"reference","retrieved_at":"2026-09-24"},{"name":"HyperPhysics – Capacitance","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capac.html","type":"reference","retrieved_at":"2026-09-24"}],"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":"10, 22 and 47 µF at 12 V","inputs":{"capacitances_uf":[10,22,47],"voltage_v":12},"expected":{"capacitor_count":3,"parallel_total_uf":79,"series_total_uf":5.99768,"parallel_total_nf":79000,"energy_parallel_j":0.005688,"energy_series_j":0.000432},"url":"https://tttkmbb.com/api/v1/calculate/capacitors-series-parallel?capacitances_uf=10%2C22%2C47&voltage_v=12"},{"name":"Two 100 nF capacitors","inputs":{"capacitances_uf":[0.1,0.1]},"expected":{"capacitor_count":2,"parallel_total_uf":0.2,"series_total_uf":0.05,"series_total_nf":50},"url":"https://tttkmbb.com/api/v1/calculate/capacitors-series-parallel?capacitances_uf=0.1%2C0.1"}],"faq":[{"q":"Why put capacitors in series at all?","a":"To raise the voltage rating (the applied voltage divides across them) or to obtain a small, non-standard value. Balancing resistors are usually needed so the voltage shares equally."},{"q":"Do the units matter?","a":"Any unit works as long as all values use it; the calculator assumes microfarads and also reports nanofarads. Energy needs farads, which is handled internally."}],"tags":["capacitors in series","capacitors in parallel","total capacitance","equivalent capacitance","capacitor network"],"related":[{"calculator_id":"resistors-series-parallel","reason":"The mirror-image rules for resistors."},{"calculator_id":"rc-time-constant","reason":"Charging time of the resulting capacitance through a resistor."},{"calculator_id":"lc-resonance","reason":"Resonant frequency with an inductor."}],"links":{"html":"https://tttkmbb.com/engineering/capacitors-series-parallel","markdown":"https://tttkmbb.com/engineering/capacitors-series-parallel.md","json":"https://tttkmbb.com/engineering/capacitors-series-parallel.json","api":"https://tttkmbb.com/api/v1/calculate/capacitors-series-parallel","schema":"https://tttkmbb.com/api/v1/calculators/capacitors-series-parallel","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:45:20Z"}