RC circuit: time constant, capacitor charge time and cutoff frequency

An online tool for RC circuits: enter resistance and capacitance to get the time constant τ = R·C, the time a capacitor needs to reach any voltage, and the filter cutoff frequency. The reverse pass picks an R and C pair from the E12–E96 series for a target, and the tolerance panel shows the real spread.

How to calculate an RC circuit

Enter R and C

Pick the units or type the value in shorthand: 10k, 4u7, 100n. Ready-made circuits sit in the row below the fields.

Read τ and the cutoff

Time constant, full charge time, halfway point, stored energy and peak current all update as you type.

Check the moment that matters

Enter a time or a voltage in the row under the chart — the other field answers and the marker moves onto the curve.

Work out the charge time and pick real parts for the cutoff you need

Time constant τ

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One τ takes the cap to 63.2%

Cutoff frequency

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−3 dB point; the same for low- and high-pass

At time t

Voltage U

Full charge (5τ)

—

Halfway (0.69τ)

—

Energy at supply

—

Peak current

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Charge and discharge by τ steps 63% · 86% · 95% · 98% · 99%

Formulas what the numbers come from

Time constantτ = R · C

Voltage while chargingU(t) = U₀ · (1 − e^−t/τ)

Voltage while dischargingU(t) = U₀ · e^−t/τ

Time to reach Ut = −τ · ln(1 − U/U₀)

Cutoff frequencyf_c = 1 / (2π · R · C)

Low-pass attenuationA = −10 · lg(1 + (f/f_c)²)

Stored energyW = C · U² / 2

Peak currentI_max = U₀ / R

Figures are for an ideal first-order RC: the output is unloaded, the source has no internal resistance, and capacitor leakage and ESR are ignored.

Features

Time constant τ = R·C with units from nanoseconds to minutes

The result scales itself: 10 kΩ × 100 µF is 1 s, while 1 kΩ × 100 pF is 100 ns.

Time to any voltage, not just to 63%

Type a moment and read the voltage and current; type a voltage and read how long it takes. The two fields solve each other, and the chart marker follows a mouse, a finger or the arrow keys.

R and C picked from the E12, E24 and E96 series

Ask for 20 ms or a 1 kHz cutoff and the tool offers four pairs of real part values, each with the percentage it misses the target by.

The spread real tolerances add

A ±5% resistor and a −20…+80% electrolytic stretch τ to about one and a half times the calculated width. That is exactly why the scope disagrees with the calculator.

Gain and phase for low- and high-pass on one chart

Cutoff f = 1/(2πRC), a −20 dB per decade roll-off, −45° of phase at the cutoff and a decade-by-decade attenuation table.

Shorthand part values

Type 4u7, 2n2, 470R or 10k the way IEC 60062 marks them and the unit follows. Arrow keys walk to the neighboring value in the series.

Frequently asked questions

What is the time constant τ?

τ = R·C is the time a capacitor takes to charge to 63.2% of the supply, or to fall to 36.8% of its starting voltage. It sets the scale of the whole exponential: every point on the curve is expressed in τ.

Why is a capacitor called charged after 5τ?

At 5τ the voltage reaches 99.3% of its final value, and what is left is smaller than the noise and the part tolerance. Exact figures per step are in the "Charge and discharge by τ steps" table.

Why does the bench disagree with the calculation?

Component tolerance. A ±5% resistor together with a −20…+80% aluminum electrolytic puts the real time constant between 0.76 and 1.89 of the calculated one. Open "Component tolerance" and the tool prints both bounds for your values.

What does cutoff frequency mean, and why is it the same for both filters?

f = 1/(2πRC) is the frequency where the signal is 3 dB down, that is √2 lower in amplitude. It depends only on the product R·C; which filter you get depends on where the output is taken — across the capacitor for low-pass, across the resistor for high-pass.

How do I pick R and C for a given time?

Open "Pick R and C", enter the time constant or cutoff you want and choose a resistor series. The tool walks the E6 capacitor values and offers four pairs with their percentage error; tapping one loads it into the calculation.

Can I type 4u7 instead of 4.7 µF?

Yes. The fields read IEC 60062 marking, where the letter replaces the decimal point: 4u7 is 4.7 µF, 2n2 is 2.2 nF, 4k7 is 4.7 kΩ, 470R is 470 Ω and 1M5 is 1.5 MΩ. The unit selector follows along.

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Who is this tool for?

🔌 Electronics Enthusiasts

Published 30 Jul 2026 Updated 11 Sep 2026 Author: The Supreme