RC Circuit Time Constant Calculator (with Charge/Discharge Graph)

Calculate the time constant τ = R × C of an RC circuit (a resistor R and capacitor C in series). See the charging and discharging curves on a graph, plus the time to reach 63.2% charge and the practical "fully charged" time (5τ).

Last updated: 2026-09-20

What the RC time constant means

In a circuit with a resistor and a capacitor in series, connecting a supply does not raise the capacitor voltage instantly. Because the resistor limits the current, **the voltage creeps towards its target exponentially.** How quickly is captured by the time constant τ, obtained from the strikingly simple τ = R × C. With resistance in ohms and capacitance in farads, the result is in seconds.

**The time constant is the time taken to reach 63.2% of the target.** After one τ you are at 63.2%, after two at 86.5%, after three at 95.0%, and **after five τ at roughly 99.3%, which is why five time constants is taken in practice as fully charged.** Mathematically the voltage never reaches 100%, however long you wait. Enter R, C and the supply voltage and this tool computes the time constant and each of these milestones, and plots the charge and discharge curves.

How to calculate the time constant

Enter the resistance In ohms. Convert first if your value is in kilohms or megohms.
Enter the capacitance In farads. Real components are usually marked in microfarads, nanofarads or picofarads, so conversion is needed.
Enter the supply voltage This sets the target on the vertical axis of the charge curve.
Review the result and the graph You get the time constant, the time to 63.2%, the five-τ charge time, and the charge and discharge curves.

Tips for getting more out of it

Resistance can be entered in Ω/kΩ/MΩ and capacitance in F/mF/µF/nF/pF, so you can type in the numbers straight off a component's printed value (e.g. 10 kΩ, 100 µF).
The time constant τ represents how long it takes the voltage to change by 63.2%. It depends only on the R × C product, not on the supply voltage V₀.
By convention, a capacitor is considered "practically fully charged" after 5τ (about 99.3%). Use this as a rule of thumb when estimating wait times in a circuit design.
The charging and discharging curves in the graph are two sides of the same phenomenon sharing the same τ — discharge right after power-off follows the same time constant.
This calculation is also handy for estimating switching delays in digital circuits, such as a pull-up resistor paired with a decoupling capacitor.

Where this helps

Designing a timer circuit

Work back to the combination of R and C needed to trigger something after a set interval.

Dealing with switch bounce

Establish roughly what time constant is needed to absorb the chatter from a mechanical contact.

Examining a low-pass filter

The time constant relates to the cutoff frequency as f = 1/(2πRC), tying it directly to how fast the circuit responds.

Limiting inrush current at power-up

Adjusting how quickly the capacitor charges softens the current that flows in the first instants.

RC circuit terms explained

Time constant (τ): The value R × C, expressing how fast the circuit responds. **It is the time taken to reach 63.2% of the target.**
Capacitance (C): A capacitor's ability to store charge. The unit is the farad, though microfarads and picofarads are what you meet in practice.
Charge curve: The curve along which the voltage approaches its target. **It takes the form 1 − e^(−t/τ).**
Discharge curve: The curve along which stored charge drains away, decaying as e^(−t/τ).
Five time constants: The point treated in practice as fully charged. **The voltage never truly reaches 100%, but 99.3% is taken as enough.**
Cutoff frequency: The frequency at which a filter begins to attenuate the signal, related to the time constant by 1/(2πRC).

Frequently Asked Questions

The time constant τ (tau) is a measure of how long it takes a capacitor to charge or discharge, calculated as τ = R × C. After one τ, the voltage change reaches about 63.2%; after five τ, it's considered essentially complete at about 99.3%.

Substituting t = τ into the charging equation V(t) = V₀(1 − e^(−t/τ)) gives V = V₀(1 − e⁻¹). Since e⁻¹ ≈ 0.368, we get 1 − 0.368 = 0.632, or about 63.2%. This value comes directly from the mathematical properties of the exponential function.

Since τ = R × C, increasing either the resistance or the capacitance increases the time constant, making charging and discharging slower. Decreasing either one speeds them up.

It's a fundamental figure used throughout electronics: estimating the response time of decoupling capacitors and pull-up resistors in digital circuits, designing the cutoff frequency of audio low-pass/high-pass filters (fc = 1/(2πRC)), and setting the oscillation period of timer ICs like the 555 timer.

Side Note — How Far the Idea of a Time Constant Reaches

The time constant of an RC circuit is one of the first concepts taught in electrical engineering textbooks, but the underlying idea — a quantity approaching a new value at a constant proportional rate — shows up far beyond electronics. The rate at which something cools down, the rate a drug is metabolized in the body, and the rate radioactive material decays can all be described with the same exponential decay-and-approach model.

In real circuits, the charge/discharge behavior of a capacitor has long been used to build timers that switch on or off after a set delay. The famous 555 timer IC internally relies on an RC time constant to set its oscillation frequency. Because you can freely adjust the oscillation period just by changing the resistor and capacitor values, this technique is widely used in LED blinker circuits and simple clock generation.

That said, real-world circuits involve factors the ideal formula doesn't account for, such as a capacitor's leakage current, its ESR (equivalent series resistance), and capacitance drift with ambient temperature. For applications that demand precise timing, a crystal or ceramic oscillator is generally preferred over an RC oscillator. Treat the RC time constant as a useful approximation, and reach for another approach when tight precision is required.

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