Capacitor Discharge Calculator
Calculates the voltage, current, or RC time constant as a capacitor discharges through a resistor over time. Essential for electronics design, timing circuit analysis, and lab work.
About this calculator
When a charged capacitor discharges through a resistor, voltage and current decay exponentially with time. The governing equations are V(t) = V₀ · e^(−t / RC) for voltage and I(t) = (V₀ / R) · e^(−t / RC) for current, where R is resistance in ohms and C is capacitance in farads. The product τ = R·C is called the time constant; after one τ the voltage falls to about 36.8% of its initial value, and after 5τ it is considered fully discharged (< 1%). Energy stored in a capacitor is E = ½·C·V², so it also decays exponentially during discharge. Understanding these relationships is critical for designing filters, pulse circuits, and power supplies.
How to use
Example: V₀ = 12 V, R = 1000 Ω, C = 100 μF, t = 0.05 s. 1. Time constant: τ = R·C = 1000 × 100×10⁻⁶ = 0.1 s. 2. Voltage at t = 0.05 s: V = 12 · e^(−0.05/0.1) = 12 · e^(−0.5) ≈ 12 · 0.6065 ≈ 7.28 V. 3. Current: I = (12/1000) · e^(−0.5) ≈ 0.012 · 0.6065 ≈ 7.28 mA. 4. Select your calculation type, enter the values, and read off voltage, current, or τ instantly.
Frequently asked questions
What is the RC time constant and why does it matter?
The RC time constant τ = R·C (in seconds) determines how quickly a capacitor charges or discharges. It represents the time for voltage to fall to approximately 36.8% of its starting value during discharge. Larger resistance or capacitance means a slower decay, which is exploited in timer circuits like the 555 timer. Engineers choose R and C values deliberately to set precise timing intervals in oscillators, filters, and delay circuits.
How long does it take for a capacitor to fully discharge?
Theoretically, exponential decay never reaches exactly zero, but in practice a capacitor is considered fully discharged after 5 time constants (5τ). At that point, the remaining voltage is less than 0.7% of the initial value, which is negligible for most applications. For a 100 μF capacitor and 1 kΩ resistor, τ = 0.1 s, so full discharge takes about 0.5 s. Always verify this against your circuit's tolerance requirements.
How does capacitance value affect the discharge rate?
A larger capacitance stores more charge and therefore takes longer to discharge through the same resistance, since τ = R·C grows proportionally. Doubling the capacitance doubles the time constant and makes the voltage curve decay twice as slowly. This is why large electrolytic capacitors in power supplies can hold dangerous voltages long after being switched off. Always allow sufficient time — or use a bleed resistor — before handling high-voltage capacitor circuits.