Capacitor Charge Time Calculator
Calculate charging and discharging time for RC circuits with time constant analysis
RC Circuit Parameters
Circuit resistance value
Capacitor value
Calculation Results
Key Formulas:
Time Constant: τ = R × C
Charge Percentage: % = (1 - e-t/τ) × 100
Charge Time: T = τ × ln(1/(1 - %/100))
Standard Charging Steps
| Time Constants (τ) | Charge % | Time |
|---|---|---|
| 1τ | 63.2% | - |
| 2τ | 86.5% | - |
| 3τ | 95% | - |
| 4τ | 98.2% | - |
| 5τ | 99.3% | - |
Discharge Analysis
When discharging, the capacitor follows the same time constant but in reverse. Here's the remaining charge percentage after each time constant:
| Time Constants (τ) | Remaining Charge % | Discharged % | Time |
|---|---|---|---|
| 1τ | 36.8% | 63.2% | - |
| 2τ | 13.5% | 86.5% | - |
| 3τ | 5% | 95.0% | - |
| 4τ | 1.8% | 98.2% | - |
| 5τ | 0.7% | 99.3% | - |
Quick Reference
Time Constant (τ)
τ = R × C
Time to reach 63.2% charge
Full Charge
T = 5τ (99.3%)
Considered "fully charged"
Charge Formula
% = (1 - e-t/τ) × 100
Exponential charging curve
Discharge Formula
% = e-t/τ × 100
Exponential discharge curve
Common Values
Capacitors
Resistors
Applications
Understanding Capacitor Charge Time
What is Capacitor Charge Time?
Capacitor charge time is the duration required for a capacitor to charge to a specific percentage of the applied voltage in an RC circuit. The charging follows an exponential curve, approaching full charge asymptotically.
The Time Constant (τ)
The time constant τ (tau) is the fundamental parameter of RC circuits. It represents the time needed for the capacitor to charge to 63.2% of the applied voltage, or discharge to 36.8% of its initial charge.
Why 5 Time Constants?
After 5 time constants (5τ), a capacitor reaches approximately 99.3% of full charge. This is considered "fully charged" for practical purposes, as the remaining 0.7% takes an infinitely long time to achieve due to the exponential nature of the charging curve.
Key Formulas
Time Constant
τ = R × C
Where R is resistance in ohms and C is capacitance in farads
Charging Formula
VC(t) = VS × (1 - e-t/τ)
Voltage across capacitor over time during charging
Charge Time to Percentage
t = -τ × ln(1 - %/100)
Time needed to reach a specific charge percentage
Example Calculation
Given Circuit Parameters
Resistance: 3 kΩ (3000 Ω)
Capacitance: 1000 μF (0.001 F)
Supply Voltage: 9 V
Target: 99.3% charge (full charge)
Step-by-Step Solution
Step 1: τ = R × C = 3000 × 0.001 = 3 seconds
Step 2: T = 5τ = 5 × 3 = 15 seconds
Result: The capacitor takes 15 seconds to fully charge
Verification: At t=3s, charge = 63.2% of 9V = 5.7V