capacitance discharge calculator

How capacitor discharge works

In a simple resistor-capacitor (RC) circuit, a charged capacitor releases energy through the resistor over time. The voltage does not drop linearly; it drops exponentially. That means the voltage falls quickly at first and then more slowly as it approaches zero.

The core equation is: V(t) = V₀ × e^-t/(RC)

• V(t) = capacitor voltage after time t
• V₀ = initial voltage at t = 0
• R = resistance in ohms (Ω)
• C = capacitance in farads (F)
• RC = time constant, often written as τ (tau)

Why the time constant matters

The time constant τ = RC tells you how quickly discharge happens:

• After 1τ, voltage is about 36.8% of V₀
• After 2τ, voltage is about 13.5% of V₀
• After 3τ, voltage is about 5.0% of V₀
• After 5τ, voltage is below 1% and often treated as “fully discharged” in many practical designs

This behavior is critical when designing power supplies, timing circuits, startup delays, and safety bleed resistors.

What this calculator gives you

1) Voltage after a chosen time

Enter C, R, V₀, and time t to get the remaining capacitor voltage.

2) Charge and energy remaining

The calculator also computes:

• Charge: Q(t) = C × V(t)
• Stored Energy: E(t) = ½ × C × V(t)²

This is useful when checking whether a capacitor still holds enough energy to damage components or create a safety hazard.

3) Time to reach a target voltage

If you enter a target voltage, time is calculated with: t = -RC × ln(Vtarget / V₀). This is especially useful when you want to know how long to wait before touching or servicing a circuit.

Example use case

Suppose you have a 100 µF capacitor charged to 12 V, discharging through a 10 kΩ resistor:

• C = 100 µF = 100 × 10⁻⁶ F
• R = 10,000 Ω
• τ = RC = 1 second

After 1 second, voltage is 12 × e⁻¹ ≈ 4.41 V. After 5 seconds (5τ), it drops near 0.08 V. That gives a quick feel for how resistor and capacitor values control decay speed.

Common mistakes to avoid

• Unit mismatch: µF and mF are very different (1 mF = 1000 µF).
• Wrong resistor unit: 10 kΩ is not 10 Ω.
• Target voltage above V₀: impossible for passive discharge.
• Ignoring safety: large capacitors can retain dangerous energy.

Safety reminder

Even when voltage seems low, high-capacitance and high-voltage capacitors can deliver high current. Always follow proper discharge procedures and verify with a meter before handling hardware.

Related terms and applications

If you are studying or designing with RC networks, you will often see these topics:

• RC time constant calculator
• capacitor discharge time calculator
• exponential decay in electronics
• bleeder resistor sizing
• energy in capacitors
• transient analysis in first-order circuits

This capacitance discharge calculator is a practical starting point for all of those analyses.