RC Time Constant Calculator

Explore how a capacitor charges or discharges in an RC circuit with MiniWebtool’s RC Time Constant Calculator. Resistance, capacitance, and supply voltage determine the time constant, curves, and voltage at a chosen time.

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Help me understand MiniWebtool's RC Time Constant Calculator: https://miniwebtool.com/rc-time-constant-calculator/. What can I use it for, what inputs or settings do I need, and how do I use it and understand the output? Walk me through one simple example. Use this page as your source and answer in English.

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10 kΩ and 100 µF charging to 5 V: τ = 1 s, 3.1606 V after 1 τ

Enter the resistance, the capacitance and the supply voltage, and choose charging or discharging. The result gives the time constant and the voltage at each multiple of it.

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About RC Time Constant Calculator

The RC Time Constant Calculator computes the time constant (τ) for a resistor-capacitor (RC) circuit and provides a complete analysis of its charging or discharging behavior. Enter your resistance and capacitance values along with the supply voltage to get the time constant, voltage curve chart, time constant table showing voltages at 1τ through 5τ, cutoff frequency, and step-by-step calculation with MathJax formulas.

At a Glance

RC Time Constant Calculator computes the time constant of a resistor-capacitor circuit as tau = R x C. It also shows charging or discharging behavior, the voltage at a chosen time and the filter cutoff frequency.

RC Time Constant Calculator: features at a glance
Feature	What you get	Good for
Inputs and units	Resistance in ohms, kilohms or megohms, and capacitance in F, mF, uF, nF or pF. Enter the supply voltage, or the initial capacitor voltage when discharging.	Component values read straight from a schematic
Charging or discharging	Charging: V(t) = Vsupply x (1 - e^(-t/tau)). Discharging: V(t) = Vinitial x e^(-t/tau).	Timing and delay circuits
Voltage at a time	Enter an optional time in seconds to get the capacitor voltage at that moment.	Checking the voltage at a specific point
Time constant table	Lists the voltage at 1 to 5 time constants. After 1 tau a charging capacitor reaches about 63.2% of the supply voltage.	Estimating how long a capacitor takes to settle
Cutoff frequency	Gives the filter cutoff frequency fc = 1 / (2 x pi x R x C), the -3 dB point of an RC filter.	Designing low-pass and high-pass filters
Curve and steps	An interactive voltage curve chart and a step-by-step formula breakdown accompany the result.	Coursework and verifying hand calculations

What Is an RC Time Constant?

The RC time constant, denoted by the Greek letter τ (tau), is the product of the resistance (R) and capacitance (C) in a circuit:

$$\tau = R \times C$$

It is measured in seconds and represents a fundamental timing property of the circuit. After one time constant, a charging capacitor reaches approximately 63.2% of the supply voltage, while a discharging capacitor drops to approximately 36.8% of its initial voltage.

Charging and Discharging Formulas

Charging: When a voltage source is applied to an uncharged capacitor through a resistor, the voltage across the capacitor rises exponentially:

$$V(t) = V_{supply} \times \left(1 - e^{-t/\tau}\right)$$

Discharging: When a charged capacitor is disconnected from the voltage source and connected through a resistor, the voltage decays exponentially:

$$V(t) = V_{initial} \times e^{-t/\tau}$$

Key Time Points

1τ — 63.2% charged / 36.8% remaining
2τ — 86.5% charged / 13.5% remaining
3τ — 95.0% charged / 5.0% remaining
4τ — 98.2% charged / 1.8% remaining
5τ — 99.3% charged / 0.7% remaining (considered fully charged/discharged)

RC Filter Cutoff Frequency

The same RC combination forms a basic low-pass or high-pass filter. The cutoff frequency (−3 dB point) is:

$$f_c = \frac{1}{2\pi \tau} = \frac{1}{2\pi R C}$$

At this frequency, the output signal amplitude drops to 70.7% of the input signal.

How to Use This Calculator

Enter resistance — Input the resistance value and select the appropriate unit (Ω, kΩ, or MΩ).
Enter capacitance — Input the capacitance value and select the unit (F, mF, µF, nF, or pF).
Enter supply voltage — Enter the supply voltage (for charging) or initial capacitor voltage (for discharging).
Select mode — Choose between Charging and Discharging.
Optional: Enter time point — Enter a specific time (in seconds) to calculate the exact voltage at that moment.
Click Calculate — Review the time constant, voltage curve, time constant table, and step-by-step formulas.

Practical Applications

Timer circuits — RC timing is the basis of 555 timer circuits and many delay circuits
Filter design — RC low-pass and high-pass filters are fundamental building blocks in signal processing
Debouncing circuits — RC circuits smooth out mechanical switch bounce in digital electronics
Power supply smoothing — Capacitors in power supplies use RC charging/discharging to reduce ripple
Sensor circuits — Many sensors (e.g., touch sensors) rely on RC time constant measurement

FAQ

What is an RC time constant?

The RC time constant (τ = R × C) is measured in seconds and represents the time for a capacitor to charge to about 63.2% of the supply voltage, or discharge to about 36.8% of its initial voltage. It is the fundamental timing parameter of any resistor-capacitor circuit.

How long does it take to fully charge an RC circuit?

A capacitor is considered fully charged after 5 time constants (5τ), reaching 99.3% of the supply voltage. For many practical applications, 3τ (95%) is sufficient. The exact time depends on the resistance and capacitance values in your circuit.

What is the charging formula for an RC circuit?

The charging voltage is V(t) = V_supply × (1 − e^−t/τ), where V_supply is the source voltage, t is elapsed time, and τ = RC is the time constant. The voltage rises exponentially from 0 toward V_supply.

What is the discharging formula for an RC circuit?

The discharging voltage is V(t) = V_initial × e^−t/τ, where V_initial is the starting voltage and τ = RC is the time constant. The voltage decays exponentially from V_initial toward 0.

How is the RC time constant related to filter cutoff frequency?

The cutoff frequency of a simple RC filter is f_c = 1/(2πRC) = 1/(2πτ). At this frequency, the output signal is attenuated to 70.7% (−3 dB) of the input. This relationship makes RC circuits essential in analog filter design.

Reference this content, page, or tool as:

"RC Time Constant Calculator" at https://MiniWebtool.com/rc-time-constant-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Mar 18, 2026

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