RC Discharge Time Calculator
Calculate the discharge time of a capacitor through a resistor for any target voltage.
Includes the time constant tau, half-life, and 5-tau rule.
RC Discharge Time
When a charged capacitor is connected across a resistor, the stored charge bleeds out through the resistor and the voltage decays exponentially. This is a first-order linear circuit and one of the cornerstone results in electronics.
Formula
V(t) = V₀ × e^(−t/τ)
Solving for t:
t = −τ × ln(V/V₀)
Where:
- V₀ = initial voltage (volts)
- V = target voltage at time t (volts)
- τ = R × C = the time constant (seconds)
- R = resistance in ohms
- C = capacitance in farads
The Time Constant τ
τ is the time it takes the voltage to fall to 1/e ≈ 36.8% of its starting value. It is the single number that characterizes the speed of the entire decay.
Decay Reference Table
| Multiples of τ | V / V₀ | % Discharged |
|---|---|---|
| 1τ | 36.8% | 63.2% |
| 2τ | 13.5% | 86.5% |
| 3τ | 5.0% | 95.0% |
| 4τ | 1.8% | 98.2% |
| 5τ | 0.7% | 99.3% |
The “5-tau rule” is the engineering rule of thumb that capacitors are considered fully discharged after 5 time constants.
Worked Example
A 470 µF capacitor is charged to 12 V and discharged through a 10 kΩ resistor.
- τ = 10 000 × 470 × 10⁻⁶ = 4.7 s
- Time to reach 1 V: t = −4.7 × ln(1/12) = 4.7 × 2.485 ≈ 11.7 s
- Time to reach 0.1 V: t ≈ 22.5 s ≈ 4.8τ
Common Use Cases
| Application | Why RC discharge matters |
|---|---|
| Power supply bleed resistors | Safe handling after disconnect |
| Camera flash | Strobe duration tuning |
| Filter circuits | Cutoff frequency f = 1 / (2πRC) |
| Timing circuits | 555 timer, debounce, delay |
| ESD protection | Charge dissipation paths |
Relationship to Half-Life
The voltage half-life is t₁/₂ = τ × ln 2 ≈ 0.693 × τ. This is mathematically identical to the half-life concept used in radioactive decay — only the variable being tracked changes.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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