How long does it take a capacitor to fully charge?

A capacitor in an RC circuit never reaches exactly 100% charge mathematically, but it is considered fully charged after 5 time constants (5tau). At 5tau the capacitor holds 99.3% of the supply voltage. The time constant tau equals R times C (resistance in ohms multiplied by capacitance in farads). For example, a 10 kilohm resistor with a 100 microfarad capacitor has tau = 1 second, and is considered fully charged after 5 seconds.

What is the RC time constant formula?

The time constant tau (in seconds) equals resistance R (in ohms) multiplied by capacitance C (in farads): tau = R x C. After one time constant the capacitor reaches 63.2% of the supply voltage. After two time constants it reaches 86.5%, and after three it reaches 95.0%. The voltage at any time t is given by Vc(t) = Vs x (1 - e^(-t/tau)), where Vs is the supply voltage and e is Euler's number (approximately 2.718).

How do I calculate the time to reach a specific voltage?

To find the time needed to charge to a target voltage Vc from a supply voltage Vs, rearrange the charging equation: t = -tau x ln(1 - Vc/Vs), where ln is the natural logarithm. The target voltage must be less than the supply voltage. For example, to charge to 8 V from a 12 V supply with tau = 1 second: t = -1 x ln(1 - 8/12) = -1 x ln(0.333) = 1.099 seconds.

Capacitor Charge Time Calculator

Calculate the time constant, charge time, and voltage at any point in an RC charging circuit. Enter the resistance and capacitance to find tau (the RC time constant), then optionally set a supply voltage and target voltage or elapsed time to see exact results.

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Standard formula RC charging equation: Vc(t) = Vs × (1 − e^−t/τ)

1. RC Circuit Parameters

Resistance (R)

kΩ

Resistance unit

Capacitance (C)

μF

Capacitance unit

Supply voltage (Vs)

2. Find Time or Voltage

What do you want to calculate?

Elapsed time (t)

Time unit

RC Circuit Results

Time Constant (τ)
-
tau = R × C

Full Charge Time (5τ)

99.3% of supply voltage

Voltage at t

Charge at 1τ

63.2%

of supply voltage

Voltage at Each Time Constant

Time constants	Time elapsed	Voltage (Vc)	% of Vs	Remaining

Circuit Breakdown

Resistance (R)-

Capacitance (C)-

Time constant (τ = RC)-

Supply voltage (Vs)-

Voltage at 1τ-

Voltage at 2τ-

Voltage at 3τ-

Full charge (5τ)-

Your Calculation

Mode-

Input value-

Result-

Formula used-

Charge percentage-

Remaining voltage-

Time to full charge (5τ)-

Summary: Enter values above to see your results.

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

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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.