What is the RC time constant?

The product of resistance and capacitance in seconds. After one time constant the voltage has dropped to 36.8 percent of its initial value. It determines the speed of both charging and discharging.

Why does a capacitor discharge slowly with a large resistor?

A larger resistor limits the discharge current. Less current means the charge drains from the capacitor more slowly. The time constant tau equals RC so doubling the resistance doubles the discharge time.

How do I calculate discharge time to a specific voltage?

Use t equals negative tau times the natural log of target voltage divided by initial voltage. Enter a target voltage in the calculator and it computes this automatically.

Is capacitor discharge dangerous?

Yes for large capacitors at high voltage. A 470 microfarad capacitor charged to 400V stores 37.6 joules which is potentially lethal. Always discharge capacitors safely before handling. Use a bleeder resistor.

What is the difference between discharge time and time constant?

The time constant tau is R times C and represents one exponential step to 36.8 percent. Discharge time to a specific voltage depends on the ratio of target to initial voltage and may be more or fewer time constants.

Capacitor Discharge Calculator – Time Constant, Discharge Time & Voltage Curve

V(t) = V₀ × e^−t/τ

Enter V₀, R, C, and optionally a target voltage to find discharge time.

V₀ Initial Voltage

R Resistance

C Capacitance

V_t Target Voltage (optional)

Discharge Analysis

Time Constant τ
--
τ = R × C

Initial Current

I₀ = V₀ / R

Stored Energy

E = ½CV²

After 1τ

After 3τ

After 5τ (≈0%)

Capacitor Discharge Curve

A charged capacitor discharges through a resistor following an exponential decay. The voltage drops to 36.8% after one time constant (τ = RC), to 5% after 3τ, and is considered fully discharged after 5τ (0.67%).

V₀ — Initial voltage the capacitor is charged to.
R — Discharge resistance. Larger R = slower discharge.
C — Capacitance. Larger C = more stored charge = slower discharge.
τ = RC — Time constant. After 1τ the voltage is at 36.8%. After 5τ it is effectively zero.

Capacitor Discharge Calculator

A charged capacitor stores energy in its electric field. When connected to a resistor, the stored charge flows as current, and the voltage decays exponentially toward zero. The rate of decay depends on the RC time constant — the product of resistance and capacitance. This calculator computes the time constant, discharge milestones, time to any target voltage, initial current, and stored energy.

The Discharge Equation

V(t) = V₀ × e^−t/τ

τ = R × C — time constant (seconds)
I(t) = (V₀/R) × e^−t/τ — current also decays exponentially
E = ½CV₀² — stored energy (joules)
t = −τ × ln(V_target/V₀) — time to reach target voltage

The exponential decay means the capacitor loses the same fraction of its remaining voltage each time constant. After 1τ it is at 36.8%, after 2τ at 13.5%, after 3τ at 5.0%, and after 5τ at 0.67% — considered fully discharged for practical purposes. For the relationship between charge, voltage, and capacitance, see the Capacitor Charge Calculator.

Time Constant Milestones

1τ — 36.8% of V₀ remaining. Current has dropped to 36.8% of initial.
2τ — 13.5% remaining.
3τ — 5.0% remaining. Usually safe for most digital circuits.
5τ — 0.67% remaining. Considered fully discharged.
For safety (high voltage): wait at least 5τ and verify with a meter before touching.

PSU Bleeder (400V / 10kΩ / 470µF)

τ = 10000 × 0.000470 = 4.7 s
5τ = 23.5 s to fully discharge
Time to 50V: t = −4.7 × ln(50/400) = −4.7 × (−2.08) = 9.8 s
Initial current: I = 400/10000 = 40 mA
Stored energy: E = ½ × 470µF × 400² = 37.6 J

37.6 joules at 400 V is potentially lethal. The bleeder resistor ensures the capacitor discharges safely when the PSU is unplugged. 10 kΩ gives a 4.7 second time constant — the capacitor reaches 50 V in 9.8 seconds and is below 3 V after 23.5 seconds. For the bleeder resistor design itself, see the Bleeder Resistor Calculator.

555 Timer Discharge (5V / 100kΩ / 10µF)

τ = 100000 × 0.000010 = 1.0 s
Time to 1.67V (1/3 Vcc): t = −1.0 × ln(1.67/5) = 1.10 s
This is the LOW period of a 555 astable oscillator.

In a 555 timer circuit, the capacitor charges through R_A + R_B and discharges through R_B alone. The discharge time from 2/3 Vcc to 1/3 Vcc determines the LOW output period. For the full RC timing calculation, use the RC Time Constant Calculator.

Camera Flash Tube (300V / 500Ω / 120µF)

τ = 500 × 0.000120 = 60 ms
Initial current: I = 300/500 = 600 mA
Energy: E = ½ × 120µF × 300² = 5.4 J
Time to 10V: t = −60ms × ln(10/300) = 204 ms

The flash tube presents a low resistance (simulated here as 500 Ω), so the discharge is fast — 60 ms time constant. The 5.4 joules discharge in roughly 200 ms, producing the brief intense flash. For the energy stored before firing, see the Capacitor Energy Calculator.

Safety Discharge (48V / 1MΩ / 100µF)

τ = 1000000 × 0.000100 = 100 s
5τ = 500 s = 8.3 minutes
Time to 5V: t = −100 × ln(5/48) = 226 s = 3.8 minutes

High-impedance circuits (like multimeter inputs) discharge capacitors very slowly. A 100 µF capacitor at 48 V takes over 8 minutes through a 1 MΩ path. Never rely on passive leakage for safety — always install a dedicated bleeder resistor.

Safe Discharge Practice

Always assume capacitors are charged until verified with a meter.
Use a discharge resistor — not a screwdriver. A short circuit creates an arc, welds contacts, and can shatter ceramic capacitors.
Calculate the energy (E = ½CV²) before handling. Above 1 J is painful. Above 10 J is dangerous. Above 50 J is potentially lethal.
Wait 5τ minimum after power-off, then verify with a rated meter.

Stored Energy and Danger

The energy stored in a capacitor scales with the square of the voltage. A 1000 µF capacitor at 50 V stores 1.25 J (a sharp shock). The same capacitor at 400 V stores 80 J (potentially lethal). Voltage is the dominant factor. High-voltage power supply capacitors retain lethal charges for minutes or hours after power-off without a bleeder resistor.

Frequently Asked Questions

How long does a capacitor take to fully discharge?

Theoretically infinite (exponential never reaches zero). In practice, 5 time constants reduces the voltage to 0.67% of the initial value, which is considered fully discharged. Multiply R × C × 5 for the total time.

Can I speed up discharge with a smaller resistor?

Yes. Halving the resistance halves the time constant. But the initial current doubles, which means more heat in the resistor. For high-voltage capacitors, use a resistor rated for the peak power (P = V²/R at t = 0) and use the power dissipation calculator to verify.

What is the difference between charge and discharge time?

For a simple RC circuit, both follow the same time constant τ = RC. Charging to 63.2% takes 1τ; discharging to 36.8% takes 1τ. The symmetry breaks in practical circuits where the charge and discharge paths have different resistances (e.g. 555 timer).

Is a capacitor at 50V dangerous?

Depends on the capacitance. A 10 µF at 50 V stores only 12.5 mJ (barely noticeable). A 10000 µF at 50 V stores 12.5 J (painful burn, can cause involuntary muscle contraction). Always check the stored energy, not just the voltage.

Why should I not short-circuit a capacitor to discharge it?

The instantaneous current is theoretically infinite (limited only by ESR and wire resistance). This creates a violent arc that can weld screwdriver tips, shatter ceramic capacitors, damage PCB traces, and scatter molten metal. Always use a resistor.

How does this relate to the RC Time Constant Calculator?

The RC Time Constant Calculator covers both charging and discharging with general-purpose timing analysis. This calculator focuses specifically on discharge from an initial voltage to a target voltage, with safety emphasis and stored energy analysis.

Last updated: March 2026