RC Circuit Calculator

This RC circuit calculator will help you calculate the characteristic frequency of the RC circuit.

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

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

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.