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Calculator

RC Time Constant Calculator

Time constant, cutoff frequency and capacitor voltage over time.

kΩ
µF
V
ms

Result

Time constant (τ)
100 ms
Cutoff frequency
1.592 Hz
Charging after 100 ms
3.161 V (63.2 %)
Discharging after 100 ms
1.839 V
Time to 90%
230.3 ms
Time to 99%
460.5 ms
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How it works

When a capacitor charges through a resistor, its voltage does not jump — it climbs along a curve. The time constant τ = R × C describes how quickly. After one τ the capacitor reaches 63.2% of the supply; after about five τ it is effectively full.

The same R and C form a first-order low-pass filter with a cutoff frequency of 1 / (2πRC). RC circuits are used to debounce buttons, smooth PWM into an analog level, filter ADC noise and delay a reset signal.

Formula

Time constantτ = R × C
ChargingVc(t) = Vs × (1 − e^(−t/τ))
DischargingVc(t) = Vs × e^(−t/τ)
Cutoff frequencyfc = 1 / (2π × R × C)

Worked example. 10 kΩ and 10 µF give τ = 100 ms and fc = 1.59 Hz. After 100 ms the capacitor reaches 63.2% of 5 V = 3.16 V.

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Frequently asked questions

How long does a capacitor take to fully charge?

Never fully in theory, but after 5τ it is at 99.3% — good enough for most purposes.

How do I choose R and C to debounce a button?

Mechanical buttons bounce for about 1–10 ms, so target a τ of 1–5 ms, for example 10 kΩ with 470 nF. Software debouncing is often simpler.

How do I smooth PWM into a DC voltage?

Use an RC low-pass with a cutoff far below the PWM frequency — at least 10× lower. A 1 kHz PWM needs a cutoff under 100 Hz, so 10 kΩ with 1 µF (about 16 Hz) works well, at the cost of a slower response.

Is the units shortcut right: kΩ × µF = ms?

Yes. 1 kΩ × 1 µF = 1,000 Ω × 0.000001 F = 0.001 s = 1 ms. This calculator uses kΩ, µF and ms for convenience.

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