{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"rc-time-constant"},"result":{"entity_type":"calculator","id":"rc-time-constant","calculator_id":"rc-time-constant","canonical_url":"https://tttkmbb.com/engineering/rc-time-constant","name":"RC Time Constant Calculator","title":"RC Time Constant Calculator – τ = R·C, Charge Times to 63/95/99 % and Cutoff Frequency","category":"engineering","category_name":"Engineering & Automotive","tool_name":"calculate_rc_time_constant","featured_mcp_tool":false,"description":"Computes the time constant τ = R·C of a resistor–capacitor circuit, the times to reach 63.2 %, 95 % and 99 % of the final voltage (and the 5τ 'full charge' convention), the −3 dB cutoff frequency 1/(2πRC), and optionally the charge level after a given time.","use_when":"You need how fast a capacitor charges or discharges through a resistor, or the corner frequency of a simple RC low-pass/high-pass filter.","do_not_use_when":"The circuit contains an inductor (use lc-resonance), the capacitor is driven by a constant-current source, or you only need the combined value of several capacitors (use capacitors-series-parallel).","inputs":[{"name":"resistance_ohm","label":"Resistance","type":"number","unit":"Ω","required":true,"exclusive_min":0,"description":"Series resistance in ohms (1 kΩ = 1000, 1 MΩ = 1e6).","example":10000},{"name":"capacitance_uf","label":"Capacitance","type":"number","unit":"µF","required":true,"exclusive_min":0,"description":"Capacitance in microfarads (1 nF = 0.001 µF, 1 pF = 1e-6 µF, 1 F = 1e6 µF).","example":100},{"name":"time_s","label":"Elapsed time","type":"number","unit":"s","required":false,"min":0,"description":"Optional time after the step; enables the charge-percentage output.","example":2}],"outputs":[{"name":"time_constant_s","label":"Time constant τ","type":"number","unit":"s","decimals":9,"description":"τ = R × C."},{"name":"time_constant_formatted","label":"Time constant","type":"string","decimals":4,"description":"τ with an SI prefix, e.g. 100 µs."},{"name":"time_63_percent_s","label":"Time to 63.2 %","type":"number","unit":"s","decimals":9,"description":"1 τ: the capacitor reaches 1 − e⁻¹ = 63.2 % of the final voltage."},{"name":"time_95_percent_s","label":"Time to 95 %","type":"number","unit":"s","decimals":9,"description":"−ln(0.05) τ ≈ 2.996 τ."},{"name":"time_99_percent_s","label":"Time to 99 %","type":"number","unit":"s","decimals":9,"description":"−ln(0.01) τ ≈ 4.605 τ."},{"name":"time_5_tau_s","label":"5 τ (99.3 %, 'fully charged')","type":"number","unit":"s","decimals":9,"description":"Conventional full-charge time 5 τ, at which 99.33 % is reached."},{"name":"cutoff_frequency_hz","label":"Cutoff frequency","type":"number","unit":"Hz","decimals":4,"description":"f_c = 1 / (2π R C), the −3 dB corner of an RC filter."},{"name":"charge_percent_after_time","label":"Charge after time_s","type":"number","unit":"%","decimals":2,"description":"100 × (1 − e^(−t/τ)): voltage reached when charging (only when time_s is given)."},{"name":"remaining_percent_after_time","label":"Remaining after time_s","type":"number","unit":"%","decimals":2,"description":"100 × e^(−t/τ): voltage left when discharging (only when time_s is given)."}],"input_schema":{"type":"object","properties":{"resistance_ohm":{"description":"Series resistance in ohms (1 kΩ = 1000, 1 MΩ = 1e6). 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Unit: s.","type":"number","x-unit":"s"},"time_99_percent_s":{"description":"−ln(0.01) τ ≈ 4.605 τ. Unit: s.","type":"number","x-unit":"s"},"time_5_tau_s":{"description":"Conventional full-charge time 5 τ, at which 99.33 % is reached. Unit: s.","type":"number","x-unit":"s"},"cutoff_frequency_hz":{"description":"f_c = 1 / (2π R C), the −3 dB corner of an RC filter. Unit: Hz.","type":"number","x-unit":"Hz"},"charge_percent_after_time":{"description":"100 × (1 − e^(−t/τ)): voltage reached when charging (only when time_s is given). Unit: %.","type":"number","x-unit":"%"},"remaining_percent_after_time":{"description":"100 × e^(−t/τ): voltage left when discharging (only when time_s is given). Unit: %.","type":"number","x-unit":"%"}}},"formula":"τ = resistance_ohm × capacitance_uf × 1e-6; t(p) = −τ × ln(1 − p); cutoff_frequency_hz = 1 / (2π τ); charging V(t)/V₀ = 1 − e^(−t/τ); discharging V(t)/V₀ = e^(−t/τ)","sources":[{"name":"Wikipedia – RC time constant","url":"https://en.wikipedia.org/wiki/RC_time_constant","type":"reference","retrieved_at":"2026-09-24"},{"name":"HyperPhysics – Capacitor charging","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capchg.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 kΩ and 100 µF, after 2 s","inputs":{"resistance_ohm":10000,"capacitance_uf":100,"time_s":2},"expected":{"time_constant_s":1,"time_constant_formatted":"1 s","time_63_percent_s":1,"time_95_percent_s":2.995732,"time_99_percent_s":4.60517,"time_5_tau_s":5,"cutoff_frequency_hz":0.1592,"charge_percent_after_time":86.47,"remaining_percent_after_time":13.53},"url":"https://tttkmbb.com/api/v1/calculate/rc-time-constant?resistance_ohm=10000&capacitance_uf=100&time_s=2"},{"name":"1 kΩ and 100 nF filter","inputs":{"resistance_ohm":1000,"capacitance_uf":0.1},"expected":{"time_constant_s":0.0001,"time_constant_formatted":"100 µs","cutoff_frequency_hz":1591.5494},"url":"https://tttkmbb.com/api/v1/calculate/rc-time-constant?resistance_ohm=1000&capacitance_uf=0.1"}],"faq":[{"q":"Why is 5 τ called fully charged?","a":"Charging is exponential and never strictly completes; at 5 τ the capacitor holds 99.3 % of the final voltage, which is treated as complete in practice."},{"q":"Does the cutoff frequency apply to both low-pass and high-pass?","a":"Yes. The same RC pair gives a −3 dB point at 1/(2πRC) whether the output is taken across the capacitor (low-pass) or the resistor (high-pass)."}],"tags":["rc time constant","capacitor charge time","rc filter cutoff frequency","tau","rc circuit"],"related":[{"calculator_id":"lc-resonance","reason":"Resonant frequency of an inductor–capacitor pair."},{"calculator_id":"capacitors-series-parallel","reason":"Total capacitance to use as C."},{"calculator_id":"wavelength-frequency","reason":"Wavelength of the cutoff frequency."}],"links":{"html":"https://tttkmbb.com/engineering/rc-time-constant","markdown":"https://tttkmbb.com/engineering/rc-time-constant.md","json":"https://tttkmbb.com/engineering/rc-time-constant.json","api":"https://tttkmbb.com/api/v1/calculate/rc-time-constant","schema":"https://tttkmbb.com/api/v1/calculators/rc-time-constant","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:44:54Z"}