RC Time Constant Calculator determines capacitor charge and discharge timing, plus filter cutoff frequency and stored energy, from resistance, capacitance, and applied voltage.
Calculate RC Time Constant and Transient Response for Any Resistor-Capacitor Circuit
This calculator finds how fast a capacitor charges and discharges through a resistor, along with the resulting low-pass filter cutoff frequency, stored energy, and inrush current. Electronics engineers, hobbyists, and students use it to size timing circuits, switch debounce networks, and RC filter corner frequencies.
RC Circuit Inputs and Calculated Outputs
Enter resistance (Ω, kΩ, or MΩ), capacitance (F, µF, nF, or pF), and applied DC voltage. The calculator returns the time constant, 5τ transition timing, 10–90% rise time, half-life, cutoff frequency with phase and gain, capacitor voltage at 1τ/5τ/discharge, stored energy, and initial inrush current.
RC Time Constant and Transient Response Formulas
The time constant is resistance multiplied by capacitance, per the All About Circuits DC Electronics Textbook:
$$\tau = R \times C$$
At $t = \tau$, a charging capacitor reaches 63.2% of the applied voltage; a discharging capacitor falls to 36.8% of its starting voltage:
$$V_C(t) = V\left(1 – e^{-t/\tau}\right) \text{ (charging)} \qquad V_C(t) = V \cdot e^{-t/\tau} \text{ (discharging)}$$
A capacitor is treated as fully charged or discharged at $5\tau$ (99.3%). Half the applied voltage is reached at $t_{1/2} = \tau \ln(2) \approx 0.693\tau$, and the 10–90% rise time is $t_r = \tau \ln(9) \approx 2.2\tau$ — a standard step-response result also documented in MIT’s 6.002x circuits and electronics course materials.
For the filter behavior, per the All About Circuits AC Electronics Textbook, the cutoff frequency is:
$$f_c = \frac{1}{2\pi R C}$$
At $f_c$, gain is always -3.01 dB and phase shift is always -45°, regardless of the actual R and C values used — the corner frequency moves, but those two numbers don’t.
Stored energy and initial current follow standard capacitor and Ohm’s law relations:
$$E = \frac{1}{2}CV^2 \qquad I_0 = \frac{V}{R} \qquad P_0 = I_0 \times V$$
Most common input mistake: entering resistance in ohms while capacitance is still in microfarads (or vice versa) without converting to base units — this skews τ by orders of magnitude. Example: R = 10 kΩ, C = 1 µF, V = 5 V gives $\tau = 10{,}000 \times 0.000001 = 0.01\text{ s} = 10\text{ ms}$.
Capacitor Charge and Discharge Curve
RC Time Constant Calculator FAQs
What Does the RC Time Constant Actually Measure?
It’s the time for a charging capacitor to reach 63.2% of the applied voltage, or for a discharging capacitor to fall to 36.8% of its starting voltage — not the time to fully charge or discharge.
Why Is 5τ Treated as “Fully Charged” Instead of 1τ?
At 1τ the capacitor is only 63.2% charged. The exponential curve keeps approaching 100% but never mathematically reaches it, so 5τ (99.3%) is the accepted engineering threshold for “complete.”
Why Is the Phase Shift Always Exactly -45° at the Cutoff Frequency?
At $f_c$, resistive and capacitive reactance are equal in magnitude by definition. That equality fixes the phase shift at -45° and the gain at -3.01 dB for any single-pole RC filter, regardless of the actual R and C values.
What Are the Most Common Mistakes When Calculating RC Timing?
Mixing unit prefixes (kΩ with F instead of µF); assuming 1τ means fully charged instead of 63.2%; and treating the inrush current $I_0 = V/R$ as a sustained value rather than the peak current at $t=0$, which decays exponentially afterward.
How Accurate Is the Calculated Time Constant for Real Components?
The formula assumes ideal components. Real resistors (±1–20% tolerance) and capacitors (±5–20% tolerance) mean an actual measured τ can deviate by up to roughly 30% from the calculated value.