RC Circuit Calculator — Time Constant, Charging & Discharging
Enter resistance and capacitance to find the RC time constant, charging/discharging voltage at any time, and the −3 dB cutoff frequency for use as a filter.
Resistance unit
Capacitance unit
V
Circuit mode
At t = τ, capacitor is at 63.2% of supply voltage
- 1
Resistance in ohms
10 kΩ × 1,000 = 10,000 Ω - 2
Capacitance in farads
100 µF × 0 = 0.0001 F - 3
Time constant τ = R × C
10,000 × 0.0001 = 1 sAfter one time constant the capacitor is at 63.2% (charging) or 36.8% (discharging) of supply voltage
How does this calculator work?
τ = R·C sets the speed of an RC circuit. Charging reaches 63.2% of supply at t = τ; discharging falls to 36.8% at t = τ. Full charge/discharge takes about 5τ. The cutoff frequency for a first-order RC filter is fc = 1/(2πRC).
Formula
How this is calculated
An RC circuit consists of a resistor (R) and a capacitor (C) in series. The time constant τ = RC (in seconds when R is in ohms and C in farads) governs how quickly the capacitor charges or discharges. At t = τ the capacitor has reached 63.2% of the supply voltage when charging, or has fallen to 36.8% when discharging — both are e⁻¹ ≈ 36.8% away from the final state. After 5τ the capacitor is within ~1% of its final value and is considered fully charged or discharged for most practical purposes.
The charging voltage follows V(t) = Vs · (1 − e^(−t/τ)) and the discharging voltage V(t) = V₀ · e^(−t/τ), where Vs and V₀ are the supply and initial voltages respectively. These exponential curves arise from the differential equation describing current through a resistor and charge on a capacitor: I = C · dV/dt and V_R = I·R, which combine to give a first-order linear ODE.
RC circuits also act as first-order filters. The cutoff (−3 dB) frequency is fc = 1/(2πRC): signals below fc pass with little attenuation (low-pass configuration when the output is taken across C), while frequencies above fc are attenuated at −20 dB/decade. By choosing R and C, engineers set the corner frequency of audio equalizers, anti-aliasing filters, signal smoothing circuits, and timer circuits (555 timer, etc.). This calculator assumes ideal components with no parasitic inductance or resistance.
Frequently asked questions
τ is not the time to full charge — it is the time constant. After 1τ the capacitor is at 63.2%, after 2τ at 86.5%, after 3τ at 95.0%, after 4τ at 98.2%, and after 5τ at 99.3%. Engineers use 5τ as the practical "fully charged" threshold, though the exponential never actually reaches 100%.
Rearrange fc = 1/(2πRC) to get RC = 1/(2π·fc). Pick a convenient capacitor value from standard ranges (e.g. 100 nF) and compute R = 1/(2π·fc·C), then choose the nearest standard resistor (E12 or E24 series). Online and this calculator's τ output let you verify the result.
Yes. For an audio low-pass filter (e.g. before a speaker or ADC) use the cutoff frequency output to set fc. A common choice for a simple 20 kHz filter is R = 8 kΩ, C = 1 nF → fc ≈ 19.9 kHz. The real circuit will also have load impedance effects not modelled here.
Also known as
TG we-Calculate Editorial Team. (2026). RC Circuit Calculator — Time Constant, Charging & Discharging [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rc-circuit-calculator
TG we-Calculate Editorial Team. "RC Circuit Calculator — Time Constant, Charging & Discharging." TG we-Calculate. 2026. https://we-calculate.com/calculator/rc-circuit-calculator.
TG we-Calculate Editorial Team, "RC Circuit Calculator — Time Constant, Charging & Discharging," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rc-circuit-calculator
@misc{wecalculate_rc_circuit_calculator, title = {RC Circuit Calculator — Time Constant, Charging & Discharging}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rc-circuit-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?