OctaCalc / RC Time Constant Calculator

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.

For educational and reference use only. Always verify results before use in real-world designs or safety-critical applications. For more information, see Calculation Assumptions and Disclaimer.

How to Use This RC Time Constant 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.

RC Time Constant Formula

The RC time constant defines the speed of charging or discharging:

τ = R × C

Charging voltage at time t:

V(t) = V₀ × (1 − e^(−t / RC))

Discharging voltage at time t:

V(t) = V₀ × e^(−t / RC)

τ = time constant (seconds), R = resistance (Ω), C = capacitance (F), V₀ = initial/supply voltage, t = time (seconds), e = Euler's number (≈2.718).

Example

Scenario: 10 kΩ resistor, 100 µF capacitor, 5V supply
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.