What this calculator finds

It computes the circuit time constant (τ), the capacitor’s maximum charge (Q), and the capacitor voltage V_c(t) at time t. Both the charging and discharging curves are described by the time constant.

Why it matters

• Designing RC low-pass/high-pass filter cutoff frequencies (1/2πRC)
• Reset delays, debouncing and timing in digital circuits
• Estimating settling time of sample-and-hold ADC inputs

RC Circuit Formulas

The time constant τ is the product of resistance and capacitance and is the time to reach about 63.2% of the final value. The charging voltage follows an exponential curve asymptoting to the source voltage V.

How the formula works

• A larger R or C gives a larger τ, so the capacitor charges more slowly.
• Each τ closes ~63.2% of the remaining gap; after 5τ the capacitor is considered ~99.3% charged.
• During discharge V_c(t) = V₀·e^(−t/τ), an exponential decay.

Cutoff frequency

The −3 dB cutoff of an RC filter is f_c = 1/(2πRC) = 1/(2πτ). A larger τ shifts the passband to lower frequencies.

Worked example

For R = 10 kΩ, C = 100 µF and V = 5 V, τ = 10×10³ × 100×10⁻⁶ = 1 s. Maximum charge Q = C·V = 100×10⁻⁶ × 5 = 500 µC. At t = 1 s, V_c = 5 × (1 − e⁻¹) ≈ 3.16 V — about 63.2% of the final value.

Practical tips

• Pick R and C from the required delay/settling time, then consider leakage current and load capacitance.
• For input debouncing, make τ long enough relative to the bounce duration.
• A large capacitor ESR makes the charge curve deviate from the ideal exponential.

Limitations & cautions

• Assumes ideal R and C, ignoring leakage, ESR and inductance.
• Connecting a capacitor directly to a source causes a large inrush current — consider series resistance.
• At high frequency, wiring inductance and parasitics dominate and the first-order model becomes inaccurate.