Capacitor Charge Time Calculator

Calculate the charge time of your capacitor for the five multiples of the time constant and more.

Practically fully charged50 msfive time constants is the usual engineering convention — mathematically it never finishes

Time constant τ10 ms10 kΩ × 1 µF

Cutoff frequency15.9155 Hz1 ÷ 2πRC — where the output is 3 dB down and the phase shift is 45°

Charged after 10 ms3.1606 V63.212% of the supply

Discharged to1.8394 Vstarting from 5 V

Time in time constants1 τ

After 1 τ (10 ms)3.1606 V63.2% charged

After 2 τ (20 ms)4.3233 V86.5% charged

After 3 τ (30 ms)4.7511 V95.0% charged

After 4 τ (40 ms)4.9084 V98.2% charged

After 5 τ (50 ms)4.9663 V99.3% charged

Energy stored when fully charged12.5 µJ½CV² — and exactly the same amount is dissipated in the resistor getting there, whatever its value

Charging efficiency50%always exactly half, for any R and C — this is why charging a capacitor through a resistor is thermodynamically poor

At ten times the resistance100 msten times slower, and a tenth the cutoff frequency

The formula

τ = RC; V = V₀(1 − e^(−t/τ)); f_c = 1 ÷ 2πRC

Half the energy always goes to the resistor

An RC circuit charges towards the supply exponentially: 63.2% of the way after one time constant, 95% after three, 99.3% after five. It never quite arrives, which is why "fully charged" is a convention — five time constants — rather than a fact.

Here is the result that surprises people: charging a capacitor through a resistor is exactly 50% efficient, no matter what the resistance is. The capacitor ends up with ½CV², and precisely the same amount has been dissipated as heat in the resistor. Using a smaller resistor makes it happen faster but wastes exactly as much energy. Only a switching regulator, which does not dissipate the difference, beats that limit.

The same RC forms a filter, with a cutoff at 1/2πRC. At that frequency the output is 3 dB down — 70.7% in amplitude — and shifted 45° in phase. Beyond it the response falls at 6 dB per octave, which is a gentle slope: a single RC stage is a soft filter, not a wall.