Capacitor Discharge Time Calculator Formula
Understand the math behind the capacitor discharge time calculator. Each variable explained with a worked example.
Formulas Used
Time Constant (tau)
time_constant = tauTime to Target Voltage
discharge_time = tau * log(v_initial / v_target)Time to ~0 V (5 tau)
time_5tau = 5 * tauVariables
| Variable | Description | Default |
|---|---|---|
resistance | Discharge Resistance(Ω) | 10000 |
capacitance_uf | Capacitance(µF) | 100 |
v_initial | Initial Voltage(V) | 12 |
v_target | Target Voltage(V) | 1 |
c_f | Derived value= capacitance_uf / 1000000 | calculated |
tau | Derived value= resistance * c_f | calculated |
How It Works
RC Discharge Timing
tau = R x C
V(t) = V_0 x e^(-t/tau)
t = tau x ln(V_0 / V_target)
After 5 time constants, the capacitor is essentially discharged (< 1% of initial).
Worked Example
100 uF discharging through 10k from 12 V to 1 V.
resistance = 10000capacitance_uf = 100v_initial = 12v_target = 1
- 01tau = 10000 x 0.0001 = 1.0 s
- 02t = 1.0 x ln(12/1) = 1.0 x 2.485 = 2.485 s
- 035 tau = 5.0 s to fully discharge
Ready to run the numbers?
Open Capacitor Discharge Time Calculator