Capacitor Discharge Calculator

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Work out how fast a capacitor loses voltage through a resistor. You can either find the time to reach a chosen voltage, or find the voltage after a set time.

Uses V(t) = V0 x e-t/(R x C)
Time constant: tau = R x C
In time mode, if Vt is blank, percent remaining is used (V(t)/V0 x 100).
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How this calculator works

This calculator models an ideal capacitor discharging through a resistor. It uses the standard exponential discharge equation for an RC circuit.

Step 1: Convert units

The calculator converts your inputs into base units:

  • Resistance R is converted to ohms.
  • Capacitance C is converted to farads.
  • Time t is converted to seconds (only used in “Find voltage after a time” mode).

Step 2: Compute the time constant

It calculates the RC time constant:

tau = R x C

Step 3: Choose what you want to solve for

Mode A: Find time to reach a voltage

If you choose “Find time to reach a voltage”, you provide a starting voltage V0 and either:

  • a target voltage Vt (must be less than or equal to V0), or
  • a target percent remaining (in Advanced options), which means V(t) / V0 x 100.

The model equation is:

V(t) = V0 x e^(-t / tau)

Solving for time gives:

t = -tau x ln(Vt / V0)

You can use either of these equivalent equations to find the discharge time:

  • t = −τ × ln(Vtarget / V₀)
  • t = RC × ln(V₀ / Vtarget)

Here, τ = RC, V₀ is the initial voltage, and Vtarget is the target voltage (called Vt above). These forms apply when 0 < Vtarget ≤ V₀. Reversing the voltage ratio changes the sign of its logarithm, so the minus sign in the first equation gives the same answer as the second equation. Both give a positive time when the target voltage is lower than the initial voltage, and zero time when the voltages are equal.

If you use percent remaining p (0 to 100), it uses Vt / V0 = p / 100, so:

t = -tau x ln(p / 100)

If you enter Vt = 0 V, the ideal model never reaches exactly 0 V. It approaches 0 V as time increases.

Mode B: Find voltage after a time

If you choose “Find voltage after a time”, you provide a starting voltage V0 and a time t. The calculator returns:

  • V(t) using V(t) = V0 x e^(-t / tau)
  • Percent remaining using 100 x V(t) / V0

Important limits

  • This is an ideal first order RC model. It ignores capacitor ESR/ESL, inductance, and non-linear components.
  • Real circuits can discharge faster if there are extra discharge paths (load resistance, leakage, measurement equipment).
  • Results are most accurate when the discharge resistor dominates other resistances in the circuit.

Resistor power and energy

The added results use the same starting voltage, resistance and capacitance as the discharge calculation. No extra inputs are needed.

Starting power = V0 squared / R
Starting current = V0 / R
Initial stored energy = 0.5 x C x V0 squared

Use volts, ohms and farads for watts, amps and joules. For example, 100 V, 10 kOhm and 1000 uF give 1 W starting power, 0.01 A starting current and 5 J stored energy. These starting quantities are the same in both modes. A partial discharge releases only part of the stored energy.

The ideal model assumes the source is disconnected and all discharged energy goes into the resistor. A wattage comparison alone cannot establish that a real resistor is suitable; its voltage limit, pulse capability, repetition and operating conditions also matter. This calculation does not establish that a capacitor is safe to handle.

Methodology

This calculator models an ideal RC discharge. It assumes a capacitor starts at V0 and discharges through a constant resistance R.

Inputs and unit handling

  • Resistance units are converted to ohms (ohm, kOhm, MOhm).
  • Capacitance units are converted to farads (pF, nF, uF, mF, F).
  • Time units are converted to seconds (ns, us, ms, s, min, hr).

Core quantities

  • Time constant: tau = R x C.
  • Discharge voltage: V(t) = V0 x e^(-t / tau).
  • Voltage ratio: V(t) / V0 = e^(-t / tau).
  • Current ratio (ideal): I(t) / I0 = e^(-t / tau). This matches the voltage ratio because I(t) = V(t) / R.

Mode 1: Find time to reach a voltage

If you enter a target voltage Vt, the calculator solves for time using:

  • t = -tau x ln(Vt / V0)

Constraints:

  • Vt must be 0 or greater.
  • Vt must be less than or equal to V0.
  • If Vt is 0 V, ideal exponential decay approaches 0 V but does not reach exactly 0 V in finite time. Use a small threshold instead (for example 1% remaining).

Mode 1 alternative: Target percent remaining

If target voltage is blank and you enter a target percent remaining p, the calculator uses the ratio p/100:

  • t = -tau x ln(p / 100)

Constraints:

  • p must be greater than 0 and less than 100.

Mode 2: Find voltage after a time

If you enter time t, the calculator computes:

  • V(t) = V0 x e^(-t / tau)
  • Percent remaining = 100 x (V(t) / V0)

Reference points shown in results

  • At 1 x tau: about 36.8% remaining.
  • At 3 x tau: about 5.0% remaining.
  • At 5 x tau: about 0.7% remaining.

Numerical notes

  • The exponential function is bounded for extreme inputs to avoid overflow in the browser.

Limitations

  • This is an ideal RC model. It ignores capacitor leakage, ESR, dielectric absorption, temperature drift, and any non-linear load effects.
  • Real circuits can deviate, especially at very small currents or very long discharge times.

Sources

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