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RC Time Constant Calculator

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.

When to use

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).

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)

Inputs

Parameter	Type	Unit	Required	Description
`resistance_ohm`	number	Ω	yes	Series resistance in ohms (1 kΩ = 1000, 1 MΩ = 1e6). Range: > 0
`capacitance_uf`	number	µF	yes	Capacitance in microfarads (1 nF = 0.001 µF, 1 pF = 1e-6 µF, 1 F = 1e6 µF). Range: > 0
`time_s`	number	s	no	Optional time after the step; enables the charge-percentage output. Range: ≥ 0

Outputs

Output	Type	Unit	Description
`time_constant_s`	number	s	τ = R × C.
`time_constant_formatted`	string		τ with an SI prefix, e.g. 100 µs.
`time_63_percent_s`	number	s	1 τ: the capacitor reaches 1 − e⁻¹ = 63.2 % of the final voltage.
`time_95_percent_s`	number	s	−ln(0.05) τ ≈ 2.996 τ.
`time_99_percent_s`	number	s	−ln(0.01) τ ≈ 4.605 τ.
`time_5_tau_s`	number	s	Conventional full-charge time 5 τ, at which 99.33 % is reached.
`cutoff_frequency_hz`	number	Hz	f_c = 1 / (2π R C), the −3 dB corner of an RC filter.
`charge_percent_after_time`	number	%	100 × (1 − e^(−t/τ)): voltage reached when charging (only when time_s is given).
`remaining_percent_after_time`	number	%	100 × e^(−t/τ): voltage left when discharging (only when time_s is given).

Example

10 kΩ and 100 µF, after 2 s: {"resistance_ohm":10000,"capacitance_uf":100,"time_s":2} → {"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}

1 kΩ and 100 nF filter: {"resistance_ohm":1000,"capacitance_uf":0.1} → {"time_constant_s":0.0001,"time_constant_formatted":"100 µs","cutoff_frequency_hz":1591.5494}

GET https://tttkmbb.com/api/v1/calculate/rc-time-constant?resistance_ohm=10000&capacitance_uf=100&time_s=2

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/rc-time-constant (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/rc-time-constant · Markdown: https://tttkmbb.com/engineering/rc-time-constant.md · JSON definition: https://tttkmbb.com/engineering/rc-time-constant.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="rc-time-constant"
OpenAPI operationId: calculate_rc_time_constant
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – RC time constant (reference)
HyperPhysics – Capacitor charging (reference)

FAQ

Why is 5 τ called fully charged?

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.

Does the cutoff frequency apply to both low-pass and high-pass?

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).

Related calculators

LC Resonance Calculator — Resonant frequency of an inductor–capacitor pair.
Capacitors in Series and Parallel Calculator — Total capacitance to use as C.
Wavelength & Frequency Calculator — Wavelength of the cutoff frequency.