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RC Circuit Time Constant Calculator

Find an RC circuit's time constant (τ = R × C) and the percent charged or discharged at a given moment, using the standard exponential charge/discharge curve.

Time constant (τ = R × C)
1 s
Percent charged at t
63.212%
Time to ~99.3% (5 time constants)
5 s

How it works

A resistor and capacitor wired in series charge or discharge exponentially rather than instantly, with the time constant τ = R × C setting the pace — one τ after a voltage is applied, a charging capacitor has climbed to 1 − e⁻¹ (about 63.2%) of the source voltage, and a discharging one has fallen to e⁻¹ (about 36.8%) of where it started.

At any elapsed time t, the fraction complete is 1 − e^(−t/τ) while charging, or e^(−t/τ) of the starting voltage remaining while discharging — the standard first-order step response for an ideal RC circuit with a fixed applied (or fixed initial) voltage. By 5τ that fraction reaches e⁻⁵ ≈ 99.33%, the textbook rule of thumb for calling a capacitor "fully" charged or discharged.

Resistance is entered in ohms and capacitance in microfarads (µF), the unit most real capacitors are labeled in; the calculator converts capacitance to farads internally before computing τ = R × C in seconds.

FAQ

Why 5 time constants instead of a round number like 100%?

The exponential curve only approaches full charge or full discharge asymptotically — it never mathematically reaches exactly 100%. Five time constants (≈99.33%) is the widely used engineering convention for treating the transient as effectively finished.

Does this account for the capacitor's own leakage or the source's internal resistance?

No — this models the idealized RC step response taught in circuit theory: a perfect capacitor and a fixed resistance driven by a fixed voltage. Real components add small leakage and source-resistance effects this calculator doesn't include.

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