capacitor discharge calculator - Aaron Graves, PhDude Replica

Need to know how quickly a capacitor loses voltage through a resistor? Use this RC capacitor discharge calculator to estimate voltage, current, charge, and stored energy at any time point.

Initial voltage, V₀ (volts)

Resistance, R (ohms)

Capacitance, C

Time, t (seconds)

Optional target voltage, V_target (volts)

If entered, calculator also computes time required to reach this voltage.

What this capacitor discharge calculator does

This tool models an ideal RC discharge circuit, where a capacitor with initial voltage discharges through a resistor. It calculates:

RC time constant (τ = R × C)
Voltage remaining after time t
Current through the resistor after time t
Charge remaining on the capacitor
Energy remaining in the capacitor
Time to reach a specified target voltage

Core capacitor discharge equations

For a capacitor discharging through a resistor, the key relationships are exponential:

V(t) = V₀ · e^-t/(RC)

I(t) = (V₀ / R) · e^-t/(RC)

Q(t) = C · V(t)

E(t) = ½ · C · [V(t)]²

If you know a target voltage and want to solve for time, rearrange the equation:

t = -RC · ln(V_target / V₀)

Understanding the time constant (τ)

The RC time constant is the speed marker of discharge behavior:

After 1τ, voltage is about 36.8% of initial.
After 3τ, voltage is about 5%.
After 5τ, voltage is less than 1%.

This is why engineers often use “5τ” as a practical “fully discharged” guideline.

How to use the calculator

Enter starting voltage (V₀).
Enter resistor value in ohms.
Enter capacitance and choose unit (F, mF, µF, nF, pF).
Enter elapsed time in seconds.
Optionally enter a target voltage to compute discharge time to that level.
Click Calculate Discharge.

Worked example

Suppose a 1000 µF capacitor starts at 12 V and discharges through a 1 kΩ resistor.

C = 1000 µF = 0.001 F
R = 1000 Ω
τ = R×C = 1 second

At t = 2 s:

V(2) = 12·e^-2 ≈ 1.62 V
I(2) = V(2)/R ≈ 1.62 mA
Energy has dropped dramatically because energy depends on V², not just V.

Designing for a target discharge time

If you need a capacitor to drop from V₀ to V_target in a chosen time, you can solve for resistance:

R = -t / [C · ln(V_target/V₀)]

This is useful for selecting a bleeder resistor, soft-power-down behavior, and timing applications in analog electronics.

Real-world factors that affect discharge

The calculator assumes ideal components. In physical circuits, expect deviations from:

Capacitor tolerance (actual capacitance can differ from nominal)
Capacitor leakage current
ESR (equivalent series resistance)
Temperature dependence of R and C
Parasitic paths and measurement loading

Safety reminder

Large capacitors can store dangerous energy, even after power is removed. Always verify voltage with a meter and use appropriate discharge methods and protective equipment when working on high-voltage equipment.

Quick FAQ

Why never exactly 0 volts?

In the ideal math model, exponential decay approaches zero asymptotically. It gets arbitrarily close, but not exactly zero in finite time.

Can I use this for battery discharge?

Not directly. Battery discharge usually follows more complex chemistry-dependent curves, not a simple RC exponential.

What if target voltage is higher than initial voltage?

Then discharge time is effectively 0 s, because you are already at or below that threshold for discharge purposes.