Capacitor Charge and Time Constant Calculator finds the time constant, stored charge, and transient response of an RC circuit from applied voltage, capacitance, and resistance.
Calculate RC Time Constant, Charge Time, and Stored Energy for Capacitor Circuits
This calculator finds the time constant, stored charge, and transient response of a series resistor-capacitor (RC) circuit from applied voltage, capacitance, and resistance. Electronics engineers, EE students, and hobbyists use it to size timing networks, debounce circuits, snubbers, and RC low-pass filters before building them.
How to Use
Enter Applied Voltage (V, volts), Capacitance (C, µF), and Resistance (R, ohms). The tool returns the time constant τ, stored charge and energy, charging/discharging voltage at key intervals, inrush current, and the equivalent low-pass cutoff frequency.
Formula
The time constant is the product of resistance and capacitance:
$$\tau = R \times C$$
Charging voltage rises exponentially toward the applied voltage $V_0$, and discharge is the mirror-image decay — both derived the same way in the standard RC-circuit treatment published by HyperPhysics (Georgia State University Department of Physics and Astronomy):
$$V(t) = V_0\left(1 – e^{-t/\tau}\right) \quad \text{(charging)}$$
$$V(t) = V_0\,e^{-t/\tau} \quad \text{(discharging)}$$
Stored charge and energy follow from $Q = CV$ and $E = \tfrac{1}{2}CV^2$. Converting charge to a physical electron count uses the elementary charge constant, fixed exactly under the 2019 SI redefinition and published by NIST/CODATA: $e = 1.602176634\times10^{-19}\text{ C}$, giving $N = Q/e$.
Inrush current at the instant the switch closes is $I_0 = V/R$, since an uncharged capacitor behaves as a short circuit at $t=0$. The equivalent low-pass cutoff frequency is $f_c = \dfrac{1}{2\pi RC}$, and the 10–90% rise time is $t_r = \tau \ln 9 \approx 2.2\tau$.
Common input mistake: typing capacitance in the wrong unit — a value meant as picofarads entered into a microfarad field inflates τ by a factor of a million.
A less obvious issue: at low resistance values (this tool defaults to 1 Ω), the capacitor’s own equivalent series resistance — typically 0.05–2 Ω in electrolytic parts — adds directly to R.
The calculator only uses the R you type in, so a real circuit built with an aged or leaky electrolytic can charge measurably slower than the calculated τ predicts, even with a perfectly accurate resistor in the circuit.
Reference Table
Percent of applied voltage reached at each multiple of τ, computed directly from the charging equation above (HyperPhysics, Georgia State University):
| Elapsed time | Voltage reached |
|---|---|
| 1τ | 63.2% |
| 2τ | 86.5% |
| 3τ | 95.0% |
| 4τ | 98.2% |
| 5τ | 99.3% |
| 10τ | 99.995% |
Note that a capacitor never mathematically reaches 100% — “fully charged” at 5τ is an engineering convention, not an exact value.
FAQ
What is the RC time constant used for?
It sets the speed of timing circuits, debounce networks, camera flash charging, and the roll-off frequency of RC filters. A larger τ means slower charging and a lower filter cutoff frequency.
Is a capacitor ever 100% charged?
No. The exponential curve only approaches $V_0$ asymptotically. At 5τ it reaches 99.3%, which is treated as “fully charged” for practical circuit design purposes.
Does the resistance value include the capacitor’s own internal resistance?
No — you must add it yourself. Real capacitors have equivalent series resistance (ESR), which adds to R and can dominate the result when R is small, such as 1 Ω or less.
What’s the difference between τ and the 10–90% rise time?
τ is the time to reach 63.2% of final voltage. Rise time (10–90%) is a different, commonly measured interval equal to $\tau \ln 9$, about 2.2τ — not the same number.
Why does inrush current only depend on R, not C?
At $t=0$ an uncharged capacitor has zero voltage across it, so it behaves like a short circuit. The only thing limiting current at that instant is the resistance, $I_0 = V/R$.