{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"lc-resonance"},"result":{"entity_type":"calculator","id":"lc-resonance","calculator_id":"lc-resonance","canonical_url":"https://tttkmbb.com/engineering/lc-resonance","name":"LC Resonance Calculator","title":"LC Resonant Frequency Calculator – f = 1/(2π√LC), Solve for Inductance or Capacitance","category":"engineering","category_name":"Engineering & Automotive","tool_name":"solve_lc_resonance","featured_mcp_tool":false,"description":"Computes the resonant frequency of an inductor–capacitor circuit from L and C, or solves for the inductance or capacitance needed to resonate at a given frequency, plus the angular frequency and characteristic impedance √(L/C).","use_when":"You are designing or analysing a tuned circuit, oscillator tank, RF filter or antenna trap and know two of inductance, capacitance and frequency.","do_not_use_when":"Resistance matters (bandwidth and Q need the series/parallel resistance), or you have only R and C (use rc-time-constant).","inputs":[{"name":"inductance_uh","label":"Inductance","type":"number","unit":"µH","required":false,"exclusive_min":0,"description":"Inductance in microhenries (1 mH = 1000 µH, 1 nH = 0.001 µH). Omit to solve for it.","example":100},{"name":"capacitance_pf","label":"Capacitance","type":"number","unit":"pF","required":false,"exclusive_min":0,"description":"Capacitance in picofarads (1 nF = 1000 pF, 1 µF = 1e6 pF). Omit to solve for it.","example":100},{"name":"frequency_hz","label":"Resonant frequency","type":"number","unit":"Hz","required":false,"exclusive_min":0,"description":"Resonant frequency in hertz (1 kHz = 1000, 1 MHz = 1e6). Omit to solve for it."}],"outputs":[{"name":"solved_for","label":"Solved for","type":"string","decimals":4,"description":"Which quantity was computed: frequency_hz, inductance_uh or capacitance_pf."},{"name":"resonant_frequency_hz","label":"Resonant frequency","type":"number","unit":"Hz","decimals":4,"description":"f₀ = 1 / (2π √(L C))."},{"name":"resonant_frequency_khz","label":"Resonant frequency","type":"number","unit":"kHz","decimals":6,"description":"f₀ in kilohertz."},{"name":"resonant_frequency_mhz","label":"Resonant frequency","type":"number","unit":"MHz","decimals":6,"description":"f₀ in megahertz."},{"name":"angular_frequency_rad_s","label":"Angular frequency","type":"number","unit":"rad/s","decimals":4,"description":"ω₀ = 2π f₀ = 1 / √(L C)."},{"name":"inductance_uh","label":"Inductance","type":"number","unit":"µH","decimals":6,"description":"L = 1 / ((2π f)² C)."},{"name":"capacitance_pf","label":"Capacitance","type":"number","unit":"pF","decimals":4,"description":"C = 1 / ((2π f)² L)."},{"name":"characteristic_impedance_ohm","label":"Characteristic impedance","type":"number","unit":"Ω","decimals":4,"description":"√(L / C), the reactance of L and of C at resonance."}],"input_schema":{"type":"object","properties":{"inductance_uh":{"description":"Inductance in microhenries (1 mH = 1000 µH, 1 nH = 0.001 µH). Omit to solve for it. Unit: µH.","type":"number","exclusiveMinimum":0,"examples":[100],"x-unit":"µH"},"capacitance_pf":{"description":"Capacitance in picofarads (1 nF = 1000 pF, 1 µF = 1e6 pF). Omit to solve for it. Unit: pF.","type":"number","exclusiveMinimum":0,"examples":[100],"x-unit":"pF"},"frequency_hz":{"description":"Resonant frequency in hertz (1 kHz = 1000, 1 MHz = 1e6). Omit to solve for it. Unit: Hz.","type":"number","exclusiveMinimum":0,"x-unit":"Hz"}},"additionalProperties":false},"output_schema":{"type":"object","properties":{"solved_for":{"description":"Which quantity was computed: frequency_hz, inductance_uh or capacitance_pf.","type":"string"},"resonant_frequency_hz":{"description":"f₀ = 1 / (2π √(L C)). Unit: Hz.","type":"number","x-unit":"Hz"},"resonant_frequency_khz":{"description":"f₀ in kilohertz. Unit: kHz.","type":"number","x-unit":"kHz"},"resonant_frequency_mhz":{"description":"f₀ in megahertz. Unit: MHz.","type":"number","x-unit":"MHz"},"angular_frequency_rad_s":{"description":"ω₀ = 2π f₀ = 1 / √(L C). Unit: rad/s.","type":"number","x-unit":"rad/s"},"inductance_uh":{"description":"L = 1 / ((2π f)² C). Unit: µH.","type":"number","x-unit":"µH"},"capacitance_pf":{"description":"C = 1 / ((2π f)² L). Unit: pF.","type":"number","x-unit":"pF"},"characteristic_impedance_ohm":{"description":"√(L / C), the reactance of L and of C at resonance. Unit: Ω.","type":"number","x-unit":"Ω"}}},"formula":"resonant_frequency_hz = 1 / (2π √(L × C)) with L = inductance_uh × 1e-6 H and C = capacitance_pf × 1e-12 F; L = 1 / ((2π f)² C); C = 1 / ((2π f)² L); characteristic_impedance_ohm = √(L / C)","sources":[{"name":"Wikipedia – LC circuit","url":"https://en.wikipedia.org/wiki/LC_circuit","type":"reference","retrieved_at":"2026-09-24"},{"name":"HyperPhysics – Series resonance","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/electric/serres.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":"100 µH with 100 pF","inputs":{"inductance_uh":100,"capacitance_pf":100},"expected":{"solved_for":"frequency_hz","resonant_frequency_hz":1591549.43,"resonant_frequency_mhz":1.591549,"angular_frequency_rad_s":10000000,"characteristic_impedance_ohm":1000},"url":"https://tttkmbb.com/api/v1/calculate/lc-resonance?inductance_uh=100&capacitance_pf=100"},{"name":"Capacitor for 1 MHz with 10 µH","inputs":{"inductance_uh":10,"frequency_hz":1000000},"expected":{"solved_for":"capacitance_pf","capacitance_pf":2533.0296,"characteristic_impedance_ohm":62.8319,"resonant_frequency_khz":1000},"url":"https://tttkmbb.com/api/v1/calculate/lc-resonance?inductance_uh=10&frequency_hz=1000000"}],"faq":[{"q":"Does resistance change the resonant frequency?","a":"Only slightly for a series RLC (f₀ is unchanged); in a parallel tank with coil resistance the peak shifts down a little. Resistance mainly sets the bandwidth f₀/Q."},{"q":"Why does the same L·C product give the same frequency?","a":"Only the product L·C fixes f₀; the ratio L/C sets the characteristic impedance, which determines the voltages and currents at resonance."}],"tags":["lc resonance","resonant frequency","tank circuit","lc oscillator","inductor capacitor"],"related":[{"calculator_id":"rc-time-constant","reason":"Time constant and cutoff of an RC pair."},{"calculator_id":"wavelength-frequency","reason":"Wavelength of the resonant frequency."},{"calculator_id":"frequency","reason":"Convert between Hz, kHz, MHz and GHz."}],"links":{"html":"https://tttkmbb.com/engineering/lc-resonance","markdown":"https://tttkmbb.com/engineering/lc-resonance.md","json":"https://tttkmbb.com/engineering/lc-resonance.json","api":"https://tttkmbb.com/api/v1/calculate/lc-resonance","schema":"https://tttkmbb.com/api/v1/calculators/lc-resonance","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:59:37Z","next_actions":[{"tool":"run_calculator","calculator_id":"lc-resonance","reason":"Run LC Resonance Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/engineering/lc-resonance.md"}}