Capacitor Charge Time Calculator — RC Time Constant
Find how long a capacitor takes to charge to any target voltage through a series resistor, see the full charging curve, and read off key milestones at 1τ through 5τ.
Ω
µF
V
V
RC time constant τ = 1,000 ms
- 1
RC time constant
τ = 10,000 × 100 × 10⁻⁶ = 1τ = R × C in seconds — the characteristic speed of the RC circuit. - 2
Voltage ratio Vt ÷ Vs
3.15 ÷ 5 = 0.63 - 3
Time to target voltage
−1 × ln(1 − 0.63) × 1000 = 994.25
How does this calculator work?
An RC circuit charges a capacitor exponentially: V(t) = Vs × (1 − e^(−t/τ)) where τ = R × C. To find the time to reach any target voltage Vt use t = −τ × ln(1 − Vt/Vs). After 5τ the capacitor is at 99.3% of supply voltage. Enter R (Ω), C (µF), supply and target voltages to see the time and the full charging curve.
Formula
How this is calculated
When a capacitor C is charged through a series resistor R from a supply Vs, the voltage across the capacitor rises exponentially according to V(t) = Vs × (1 − e^(−t/τ)), where τ = R × C is the RC time constant in seconds. The voltage never quite reaches Vs — it approaches it asymptotically — but after five time constants (5τ) the capacitor is charged to 99.3% of Vs, which is considered fully charged for most practical purposes.
To find the time required to reach a specific target voltage Vt, rearrange the equation: t = −τ × ln(1 − Vt/Vs). This is valid only when Vt < Vs; attempting to charge to or beyond the supply voltage is physically impossible and yields no result. The standard milestones — 63.2% at 1τ, 86.5% at 2τ, 95.0% at 3τ and 98.2% at 4τ — derive directly from the exponential shape of the curve.
The formula assumes an ideal resistor, an ideal capacitor with no initial charge, and a perfect step-function supply voltage. Real circuits have tolerances on both R and C (typically ±1–20%), leakage currents, equivalent series resistance (ESR) in the capacitor, and stray inductance, all of which affect the actual charge time. For large time constants (τ > 1 s) the difference between component tolerance limits can matter significantly.
Frequently asked questions
After exactly one time constant τ = RC seconds, the capacitor has charged to 1 − 1/e ≈ 63.2% of the supply voltage. It is the "characteristic speed" of the RC circuit: a larger R or C means a slower charge.
After 5τ the capacitor is at 99.3% of Vs — close enough for almost all circuits. Mathematically it never reaches exactly 100%, because the exponential function never touches zero. In practice, component tolerances make the last fractions of a percent irrelevant.
The discharging curve is Vc(t) = V0 × e^(−t/τ), which is a mirror image. This calculator models charging from zero to Vs. If you need discharge time, note that the same time constant applies and the voltage falls to 36.8% at 1τ, 13.5% at 2τ, and so on.
TG we-Calculate Editorial Team. (2026). Capacitor Charge Time Calculator — RC Time Constant [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/capacitor-charge-time-calculator
TG we-Calculate Editorial Team. "Capacitor Charge Time Calculator — RC Time Constant." TG we-Calculate. 2026. https://we-calculate.com/calculator/capacitor-charge-time-calculator.
TG we-Calculate Editorial Team, "Capacitor Charge Time Calculator — RC Time Constant," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/capacitor-charge-time-calculator
@misc{wecalculate_capacitor_charge_time_calculator, title = {Capacitor Charge Time Calculator — RC Time Constant}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/capacitor-charge-time-calculator}}, year = {2026}, note = {TG we-Calculate} }
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