RC Time Constant Calculator
The RC time constant calculator computes the characteristic time (tau) for a resistor-capacitor circuit and shows how voltage evolves during charging and discharging. The time constant tau = R x C determines how quickly a capacitor charges through a resistor when connected to a voltage source, or discharges through a resistor when the source is removed. This quantity is essential in timer design, signal filtering, power supply smoothing, and analog electronics broadly. Engineers must choose R and C values to achieve specific rise times, fall times, and filter cutoff frequencies. Enter the resistance, capacitance, supply voltage, and elapsed time to see the instantaneous voltage during charging or discharging, along with the time to reach specified charge percentages.
RC time constant formulas
tau = R * C
Charging: V(t) = Vs * (1 - e^(-t / tau))
Discharging: V(t) = V0 * e^(-t / tau)
Cutoff frequency: fc = 1 / (2 * pi * tau)
R is resistance in ohms, C is capacitance in farads, t is time in seconds, Vs is supply voltage, and V0 is initial voltage.
Voltage vs. time constant table
- At 1 tau: capacitor charged to 63.2% of supply voltage.
- At 2 tau: 86.5%
- At 3 tau: 95.0%
- At 4 tau: 98.2%
- At 5 tau: 99.3% (considered fully charged)
RC time constant: frequently asked questions
What is the RC time constant?
The RC time constant (tau) is the product of resistance (R) in ohms and capacitance (C) in farads. It represents the time for a capacitor to charge to approximately 63.2% of its supply voltage or discharge to 36.8% of its initial voltage. After 5 tau, the capacitor is considered fully charged or discharged (over 99%).
How do I calculate voltage at a specific time?
For charging: V(t) = Vs * (1 - e^(-t/tau)). For discharging: V(t) = V0 * e^(-t/tau). Where Vs is supply voltage, V0 is initial voltage, t is time in seconds, and tau = R * C. The calculator evaluates these formulas for any time you enter.
What does 5 time constants mean in practice?
Engineers commonly use 5 tau as the settling time for RC circuits. At 1 tau, a capacitor charges to 63.2%. At 2 tau: 86.5%. At 3 tau: 95.0%. At 4 tau: 98.2%. At 5 tau: 99.3%. Beyond 5 tau, the remaining change is negligible for most applications.
Where are RC circuits used?
RC circuits are used in timing circuits (555 timers), audio filters, power supply filtering, debouncing switches, analog signal processing, and setting sample rates in analog-to-digital converters. The time constant determines the cutoff frequency of RC filters.
What is the relationship between RC time constant and cutoff frequency?
The cutoff frequency of an RC filter is fc = 1 / (2 * pi * R * C) = 1 / (2 * pi * tau). At this frequency, the signal amplitude drops to 70.7% (-3 dB) of its maximum value. A larger time constant means a lower cutoff frequency and slower filtering.
Official sources
- NIST: NIST Electrical Measurements.
- IEEE Xplore: IEEE Standards and Technical References.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.