RC Time Constant Calculator

Compute the time constant and cutoff frequency of an RC circuit.

Formula

τ = R × C

Inputs

Resistance (Ω)
Capacitance (µF)

What it does

The time constant τ = R × C is how long a capacitor takes to charge to about 63 % of the final voltage through a resistor. It also sets the cut-off frequency of an RC filter.

Where it's used

Delays, switch debouncing, power-on reset circuits and simple RC low-pass filters.

How to use it

Enter the resistance — prefixes work (10k).
Enter the capacitance in µF (100 nF = 0.1).
Read τ and the −3 dB cut-off frequency.

The formula explained

τ: R × C, in seconds
f_c: 1 / (2πRC) — cut-off frequency of an RC filter

Worked example

10 kΩ with a 10 µF capacitor.

Inputs:

Resistance: 10k Ω
Capacitance: 10 µF

The calculator gives:

Result: 100 ms
5τ (≈99.3% settled): 500 ms
Cutoff frequency (−3dB): 1.592 Hz

Tips and common mistakes

After about 5τ the capacitor is practically fully charged (≈99 %).
The source’s and the load’s resistance add to R.
Electrolytic capacitors have wide tolerance (often ±20 %), so timing varies.

Questions people ask

How far does the capacitor charge after each time constant?

About 63.2 % after 1τ, 86.5 % after 2τ, 95 % after 3τ, 98.2 % after 4τ and 99.3 % after 5τ. In general V = V_s × (1 − e^(−t/RC)) while charging and V = V_0 × e^(−t/RC) while discharging.

How do I make a delay of about one second?

Choose R and C so that R × C = 1 s, for example 100 kΩ and 10 µF. The delay you actually get depends on the voltage at which the next stage switches: for a threshold at 63 % of the supply it is exactly one time constant.

What is the cut-off frequency of an RC filter?

f_c = 1 / (2π × R × C). At that frequency the output is about 70.7 % of the input (−3 dB). 10 kΩ with 10 µF gives about 1.6 Hz, which suits smoothing a slowly changing signal.

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