Capacitor Discharge Calculator

Capacitor Discharge Calculator

Compute capacitor discharge voltage over time V(t) = Vi e−t/RC, time constant τ = R·C, time to reach a target voltage/percentage, initial discharge current, and remaining vs dissipated energy. Supports Ω/kΩ/MΩ and nF/µF/mF/F.

RC Milestones (discharging)
  • 1τ → ~36.8% of Vi
  • 2τ → ~13.5%
  • 3τ → ~5.0%
  • 4τ → ~1.8%
  • 5τ → ~0.7%

Capacitor Discharge Calculator – RC Time Constant, Decay Voltage, and Time to Threshold

The capacitor discharge calculator models the exponential decay of voltage in a resistor–capacitor (RC) network after the source is removed or a discharge path is engaged. By entering the initial capacitor voltage, series resistance, and capacitance, you can evaluate the voltage at any time, compute the time required to reach a target level (absolute or percentage), and quantify remaining versus dissipated energy. The tool also provides the time constant τ = R·C and the initial discharge current. This enables precise timing analysis for analog design, power-down sequencing, debounce networks, and safety discharge paths.

Exponential Discharge: Core Equation

For a capacitor initially charged to Vi and then discharged through a resistance R, the voltage decays according to:

V(t) = Vi · e−t/(R·C)

This relation defines the characteristic decay determined by the RC time constant. The capacitor discharge calculator evaluates V(t) directly or inverts the expression to solve for the time needed to reach a target voltage Vt:

t = −R·C · ln(Vt / Vi),  for 0 < Vt ≤ Vi.

Because the approach to zero volts is asymptotic, practical engineering often targets thresholds such as 10 %, 5 %, or 1 % of Vi rather than expecting an exact zero.

Key Outputs Explained

  • Time Constant τ: The fundamental time scale for decay. After 1τ, voltage drops to ~36.8 % of its initial value. After 5τ, it falls to ~0.7 %.
  • V(t): The instantaneous capacitor voltage at the time you specify.
  • Time to Threshold: The interval required to reach a target voltage or percentage of Vi.
  • Initial Discharge Current: The magnitude at t = 0⁺ equals Vi/R and decays exponentially.
  • Energy Accounting: The initial energy is Einit = ½·C·Vi2. Remaining energy at time t is E(t) = ½·C·V(t)2, and the difference is dissipated (mostly as heat in R).

How to Use the Capacitor Discharge Calculator

  1. Enter Vi (initial capacitor voltage), R (discharge path), and C (capacitance) with appropriate units.
  2. Optionally enter a time to evaluate V(t), or select a target (percentage or voltage) to compute the required discharge time.
  3. Review outputs: time constant, V(t), time-to-target, initial current, and energy (remaining vs dissipated).

Design Applications

  • Power-down Sequencing: Ensuring a safe decay to a reference level before downstream circuits latch or reset.
  • Safety Discharge: Adding bleeder resistors to bring hazardous voltages below safe limits in a set time.
  • Debounce / Timing: Timing windows for switches or comparators that rely on exponential decay to a threshold.
  • Sample-and-Hold Decay: Estimating hold droop across leakage and intentional discharge resistance.

Worked Examples

Example A — From 5 V to 0.5 V

Vi = 5 V, R = 10 kΩ, C = 100 µF → τ = 1 s. Time to 0.5 V: t = −1·ln(0.5/5) = −ln(0.1) ≈ 2.303 s. The capacitor discharge calculator reproduces this instantly.

Example B — Percentage Threshold

With the same RC, time to 5 % of Vi is t = −τ·ln(0.05) ≈ 2.996 s. “Practically zero” (≤1 %) arrives around 4.605 τ.

Component Realism: ESR, Leakage, and Tolerance

Discharge paths in real circuits include the intended resistor and parasitics. Leakage acts like a parallel resistance that can slow or alter decay. ESR introduces additional series drop. Tolerance on R and C directly affects τ. For safety-critical timing, select tight-tolerance components, verify at temperature extremes, and allow margin above the computed time from the capacitor discharge calculator.

Bleeder Resistor Sizing

For power supplies with bulk capacitance, standards often require the voltage to fall below a specified level within a given time after unplugging. Given Vi, C, and target voltage Vt at time T, you can rearrange the decay relation to find R:

R = −T / (C · ln(Vt/Vi))

Enter candidate values into the capacitor discharge calculator to validate compliance and compute energy/power dissipation.

Comparator and Logic Thresholds

Digital inputs with Schmitt triggers change state at defined thresholds (e.g., 0.3–0.7·VDD). When discharging a timing capacitor into such an input, the switching instant occurs when V(t) crosses the threshold. The capacitor discharge calculator can compute that time precisely by setting Vt to the relevant fraction of Vi.

Energy and Thermal Considerations

The dissipated energy during discharge is converted to heat, mostly in the resistor. For large capacitances and high starting voltages, check the pulse power rating. The calculator’s energy breakdown (remaining vs dissipated) helps dimension R and ensure safe operation.

Measurement Notes

Oscilloscope probes add capacitance and resistance that slightly change τ. Use high-impedance probes (10×) for minimal loading. Compare the recorded decay curve with the predictions from the capacitor discharge calculator; small discrepancies usually indicate parasitics or tolerance.

Common Pitfalls

  • Miješanje jedinica (kΩ naspram Ω, µF naspram nF) — provjerite ulaze.
  • Ignorisanje tolerancije i temperature — τ može varirati ±25 % ili više.
  • Očekivanje “nule” bez granice — 0 V je asimptota; koristite prag (npr. 1 %).
  • Nedovoljna procena disipacije — bleeder otpornik mora izdržati impulsnu snagu.

Related Tools

Further Reading

Disclaimer: The capacitor discharge calculator provides engineering estimates. Validate results with real components and safety standards relevant to your design.