What is the RC time constant?

The RC time constant (τ, tau) is the product of resistance and capacitance: τ = R × C. It represents the time for the capacitor to charge to 63.2% (or discharge to 36.8%) of its final value. It's measured in seconds when R is in Ohms and C is in Farads.

How long does a capacitor take to fully charge in an RC circuit?

A capacitor is considered fully charged after 5 time constants (5τ). At 5τ, the capacitor reaches 99.3% of the supply voltage. For a circuit with τ = 0.1s, full charge takes approximately 0.5 seconds.

How do I calculate RC cutoff frequency?

The cutoff frequency of an RC filter is fc = 1 / (2π × R × C). For R = 10kΩ and C = 10μF: fc = 1 / (2π × 10,000 × 0.00001) ≈ 1.59 Hz. At this frequency, the output signal is reduced to 70.7% of the input (−3 dB).

What is the difference between RC low-pass and high-pass filters?

In an RC low-pass filter, the output is measured across the capacitor — it passes low frequencies and blocks high ones. In an RC high-pass filter, the output is across the resistor — it passes high frequencies and blocks low ones. Both use the same cutoff frequency formula fc = 1/(2πRC).

What is the voltage across a charging capacitor at time t?

For a charging capacitor: Vc(t) = Vs × (1 − e^(−t/τ)), where Vs is the supply voltage and τ = RC. For discharging: Vc(t) = V0 × e^(−t/τ), where V0 is the initial voltage. Enter time t in our calculator to find the voltage at any moment.

RC Circuit Calculator

Our free RC circuit calculator computes all key parameters of resistor-capacitor circuits: time constant (τ = RC), cutoff frequency (fc = 1/2πRC), charging and discharging voltage curves, and the time to reach any charge percentage. Use it for filter design, timing circuits, and capacitor charging analysis.

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Calculation Mode

Resistance (R)

Capacitance (C)

Supply Voltage (Vs)

Time (t)

timer Time Constant (τ = RC)

100 ms

= 0.100 s

Cutoff Frequency (fc) 1.59 Hz

At 1τ 63.2% charged

At 3τ 95.0% charged

At 5τ (full) 500 ms

Voltage at t —

Charge Curve

01τ2τ3τ4τ5τ

Input Values

Calculation Mode

Time Constant & Frequency

Charging Voltage at Time t

Discharging Voltage at Time t

Resistance (R)

Capacitance (C)

Time (t)

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RC Circuit: R=10kΩ, C=10μF

Time constant τ: 0.100 s
Cutoff frequency fc: 1.59 Hz
63.2% charged at: t = 0.1 s
Fully charged (5τ): t = 0.5 s

Use this as an RC low-pass filter to block signals above 1.59 Hz, or as a timing circuit with ~100 ms delay.

lightbulb Tips

•τ = R × C — one time constant = 63.2% charge
•Fully charged at 5τ (99.3%)
•fc = 1 / (2πRC) — the -3 dB cutoff
•Larger C or R → slower response, lower fc

electric_bolt RC Quick Reference

Charge at nτ

1τ 63.21%

2τ 86.47%

3τ 95.02%

5τ 99.33% ≈ full

Common Formulas

τ R × C

f_c 1 / (2πRC)

Vc charging Vs(1−e^−t/τ)

Vc discharging V0·e^−t/τ

How to Use This Calculator

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Select Mode

Choose: time constant, charging, or discharging calculation.

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Enter R and C

Input resistance (Ω) and capacitance (F).

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View Results

Get time constant, cutoff frequency, and charge curves.

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Check Voltage at t

Enter a specific time to find capacitor voltage.

The Formula

The time constant τ = RC defines how fast the capacitor charges or discharges. After 1τ, the capacitor reaches 63.2% of full charge. After 5τ it's considered fully charged (99.3%). The cutoff frequency fc marks where the filter's output falls to 70.7% (−3 dB) of its input.

τ = R × C

lightbulb Variables Explained

τ (tau) Time constant in seconds
R Resistance in Ohms (Ω)
C Capacitance in Farads (F)
fc Cutoff frequency: fc = 1 / (2π × R × C)
Vc(t) Capacitor voltage during charging: Vs × (1 − e^(−t/τ))

tips_and_updates Pro Tips

After 1τ: capacitor is 63.2% charged

After 3τ: 95% charged — usable for most applications

After 5τ: 99.3% charged — considered fully charged

Cutoff frequency is where signal is attenuated by −3 dB (70.7% amplitude)

Low-pass RC filter: output across capacitor; high-pass: output across resistor

Larger τ means slower charging and lower cutoff frequency

RC Circuit Calculator — Time Constant, Frequency & Charging

Calculate RC circuit time constant (τ), cutoff frequency (fc), and capacitor charging/discharging curves with our free RC circuit calculator. Enter resistance and capacitance values to get instant results.

RC Time Constant Calculator

The RC time constant τ = R × C determines how fast a capacitor charges. At t=1τ, the capacitor reaches 63.2% of supply voltage. At t=5τ, it reaches 99.3% and is considered fully charged. For R=10kΩ and C=10μF, τ = 0.1 seconds.

RC Filter Cutoff Frequency Calculator

The cutoff frequency of an RC filter is fc = 1/(2π × R × C). This is the frequency at which the filter's output drops to −3 dB (70.7% of input). Below fc, a low-pass RC filter passes the signal; above fc, it attenuates it.

Capacitor Charging & Discharging Calculator

During charging: Vc(t) = Vs × (1 − e^(−t/τ)). During discharging: Vc(t) = V0 × e^(−t/τ). Enter your supply voltage, initial voltage, resistance, capacitance, and time to find the exact capacitor voltage at any point.

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