RC Time Constant Calculator
Calculate the RC time constant (τ), charge and discharge voltage at any time, and key milestone timings for any resistor-capacitor circuit.
How to Use This Calculator
Enter resistance in ohms, capacitance in microfarads, and supply voltage. The time constant τ and key charge milestones calculate instantly. Optionally enter a time in milliseconds to find the exact voltage at that point in the charge or discharge cycle.
Formula
The RC time constant defines the speed of charging or discharging:
Charging voltage at time t:
Discharging voltage at time t:
τ = time constant (seconds), R = resistance (Ω), C = capacitance (F), V₀ = initial/supply voltage, t = time (seconds), e = Euler's number (≈2.718).
Example
τ = 10,000 × 0.0001 = 1 second
At t = 1s (1τ): V = 5 × (1 − e⁻¹) ≈ 3.16 V
Fully charged (5τ) at t ≈ 5 seconds
Frequently Asked Questions
What is the RC time constant?
The time constant τ (tau) is the time it takes for a capacitor to charge to approximately 63.2% of the supply voltage through a resistor. After 5τ the capacitor is considered fully charged (99.3%).
Why does charging use (1 − e^−t/RC) and discharging use e^−t/RC?
During charging the voltage rises exponentially toward the supply. During discharging it falls exponentially toward zero. The exponential function e^−t/RC always represents the remaining fraction, so charging subtracts it from 1 to get the accumulated fraction.
What happens if I increase R or C?
Increasing either resistance or capacitance increases τ, making the circuit charge and discharge more slowly. This is how RC filters and timers are tuned.
What is τ used for in practice?
RC time constants appear in low-pass and high-pass filters, 555 timer circuits, debounce circuits, audio tone controls, and any application where controlled delay or smoothing is needed.