Capacitor Charge Time Calculator
This calculator works out how long a capacitor takes to charge in a resistor-capacitor (RC) circuit, and what voltage it reaches at any point along the way. Enter the resistance (ohms, kilohms or megaohms), the capacitance (picofarads through to farads) and the supply voltage, and it finds the RC time constant (tau), the time to reach full charge (five time constants, or 99.3% of supply voltage), and a table showing the voltage and percentage charge at each time constant from one through five. You then pick one of two modes: enter an elapsed time to see the exact voltage reached at that moment, or enter a target voltage to see how long it takes to get there. Results include the time constant, full charge time, the mode-specific voltage or time figure, charge percentage, remaining voltage, and a circuit breakdown showing every value used and the formula applied, either Vc = Vs x (1 - e^(-t/tau)) for voltage, or t = -tau x ln(1 - Vc/Vs) for time. This suits designing timing circuits, RC filters, debounce networks or power-supply smoothing, or checking how quickly a capacitor settles after power is applied. The calculator assumes an ideal circuit with constant supply voltage and no initial charge; real capacitors carry equivalent series resistance and leakage current that shift actual charge time slightly, so treat results as an engineering estimate rather than a precision measurement.
1. RC Circuit Parameters
2. Find Time or Voltage
Voltage at Each Time Constant
| Time constants | Time elapsed | Voltage (Vc) | % of Vs | Remaining |
|---|
Circuit Breakdown
Your Calculation
How Capacitor Charging Works
When a capacitor is connected in series with a resistor and a voltage source (an RC circuit), it charges exponentially rather than instantaneously. Current flows from the source, through the resistor, and into the capacitor. As the capacitor charges, the voltage across it rises and the current decreases. This produces the characteristic exponential charging curve.
The rate at which this happens is governed by the RC time constant (tau), which equals the resistance in ohms multiplied by the capacitance in farads. A larger resistance or a larger capacitance both slow the charging process.
The RC Charging Formula
The voltage across the capacitor at any time t is:
Vc(t) = Vs × (1 − e−t/τ)
Where:
- Vc(t) is the capacitor voltage at time t (volts)
- Vs is the supply voltage (volts)
- e is Euler's number (approximately 2.71828)
- t is the elapsed time (seconds)
- tau (τ) is the time constant = R × C (seconds)
To find the time required to reach a specific target voltage Vc, rearrange the equation:
t = −τ × ln(1 − Vc/Vs)
The Five Time Constants Rule
| Time constants (τ) | % of Vs reached | Remaining voltage |
|---|---|---|
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 3τ | 95.0% | 5.0% |
| 4τ | 98.2% | 1.8% |
| 5τ | 99.3% | 0.7% |
In practical electronics, a capacitor is considered fully charged after 5 time constants (5τ). At this point it holds 99.3% of the supply voltage, and the remaining charging is negligibly slow for most applications.
Worked Example
Using the default values: R = 10 kΩ, C = 100 μF, Vs = 12 V, elapsed time t = 1 s.
- Time constant: τ = 10,000 × 0.0001 = 1.000 s
- Voltage at t = 1 s: Vc = 12 × (1 − e−1/1) = 12 × (1 − 0.3679) = 12 × 0.6321 = 7.59 V
- Charge percentage: 7.59 / 12 = 63.2% (one time constant)
- Full charge (5τ): 5 × 1 = 5.000 s
These match the calculator's default output exactly.
Common Applications
RC circuits and capacitor charge time are fundamental to many electronic systems:
- Timing circuits: The 555 timer IC uses an RC network to set delay and oscillation periods
- Signal filtering: Low-pass and high-pass RC filters attenuate frequencies based on the time constant
- Power supplies: Smoothing capacitors charge and discharge at a rate determined by the load resistance and capacitance
- Debouncing: RC networks are used to smooth mechanical switch bounce in digital circuits
- Camera flash: Large capacitors store energy by charging slowly, then discharge rapidly to produce a bright flash
Unit Conversions
Resistance and capacitance are often expressed in scaled units. Common values:
- 1 kΩ = 1,000 Ω
- 1 MΩ = 1,000,000 Ω
- 1 μF = 0.000001 F = 10−6 F
- 1 nF = 0.000000001 F = 10−9 F
- 1 pF = 10−12 F
Related Calculators
- Science and Engineering Calculators: full collection
- Capacitor Energy Calculator: energy stored in a capacitor (E = ½CV²)
- Capacitor Charge and Discharge Calculator: both charge and discharge curves
- Capacitive Reactance Calculator: Xc = 1 / (2πfC)
- Ohm's Law Calculator: voltage, current, and resistance relationships
Sources and method: RC charging equation derived from Kirchhoff's voltage law applied to a series RC circuit. Time constant definition per IEC 60050-131 (International Electrotechnical Vocabulary). Formula: τ = RC; Vc(t) = Vs(1 − e−t/τ); t = −τ ln(1 − Vc/Vs).
This calculator assumes an ideal RC circuit with a constant supply voltage, zero initial charge, and ideal (lossless) components. Real-world capacitors have equivalent series resistance (ESR) and leakage current that affect actual charge time. Results are for educational and design estimation purposes.