How to Calculate Capacitor Charge Time
When a capacitor charges through a resistor from a DC source — a standard RC circuit — its voltage does not rise instantly or linearly. It climbs along an exponential curve that starts steep and flattens out as the capacitor approaches the supply voltage. This calculator uses the resistance, capacitance, and supply voltage you enter to find the RC time constant, the time needed to reach any target charge level, and the current flowing at the instant charging begins.
The RC charging equation
Applying Kirchhoff's voltage law to a resistor and capacitor in series with a DC source Vs gives Vs = i(t)R + Vc(t), and since the charging current is i(t) = C·dVc/dt, solving that differential equation yields the standard charging equation: Vc(t) = Vs(1 − e^(−t/RC)). The product R × C is the time constant, τ (in seconds, with R in ohms and C in farads) — it is the single number that governs how fast the whole curve moves. After one time constant the capacitor reaches 1 − e⁻¹ ≈ 63.2% of Vs; after two, ≈86.5%; after three, ≈95.0%; after five, ≈99.3%, which is why "5τ" is the standard rule of thumb for a practically fully-charged capacitor. Solving the equation for time gives the charge time to any target voltage: t = −RC × ln(1 − Vc/Vs), which this calculator applies using the target charge percentage you enter in place of Vc/Vs.
Reading the time constant and the initial current
At the instant the switch closes (t = 0), the capacitor still holds zero charge, so it behaves like a short circuit and the entire supply voltage drops across the resistor. The initial charging current is therefore simply I₀ = Vs / R — the largest current the circuit will ever see during charging. As Vc rises, less voltage remains across the resistor, so the current decays along I(t) = I₀·e^(−t/RC), reaching zero as the capacitor approaches full charge. Because charge time depends on the product R × C rather than on either component alone, the same time constant — and the same charging curve — can come from a large resistor with a small capacitor or a small resistor with a large capacitor.
Practical design notes
- Component tolerances matter: standard resistors run ±1–10% and electrolytic capacitors are often −20%/+80%, so a "5-second" charge time can vary meaningfully in a built circuit — measure key components if timing is critical.
- Electrolytic capacitors also have equivalent series resistance (ESR) and leakage current, which slightly slow real-world charging compared with the ideal formula, especially at high capacitance.
- Timing circuits (555 timers, RC delay lines, camera flash charging, debounce filters) all rely directly on this same τ = RC relationship — choose R and C together to hit a target delay rather than picking either value first.