RC Circuit Calculator — Time Constant and Cutoff
Works out the time constant of a resistor and capacitor, how long it takes to charge or discharge, and the frequency at which the same pair acts as a filter.
Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
The formula
τ = R × C f_c = 1 ÷ (2πRC) V(t) = V₀ × (1 − e^(−t/τ))
The time constant is the only number an RC circuit really has. Everything else is that one figure read differently: charge time is a multiple of it, and cutoff frequency is its reciprocal scaled by 2π. Which of the two you care about depends on whether you are timing something or filtering something.
What to watch out for
The same circuit does two jobs and the literature describes them differently:
- As a timer, the number that matters is τ = RC. After one τ the capacitor is 63.2% charged, after five it is 99.3% — close enough that everyone calls it done.
- As a filter, the number is the cutoff frequency, where the output has dropped 3 dB. It is simply 1 ÷ 2πτ.
Whether it is a low-pass or a high-pass filter depends only on where you take the output — across the capacitor for low-pass, across the resistor for high-pass. The cutoff frequency is the same either way.
Frequently Asked Questions
What is the time constant of an RC circuit?
Resistance times capacitance. A 10 kΩ resistor with a 0.1 µF capacitor gives 1 ms. Use ohms and farads and the answer comes out in seconds.
How long does a capacitor take to fully charge?
About five time constants. It never mathematically reaches the supply voltage, but after 5τ it is at 99.3%, which is indistinguishable from full in any real circuit.
What is the cutoff frequency of an RC filter?
1 ÷ (2πRC). A 10 kΩ and 0.1 µF pair turns over at about 159 Hz. Below cutoff a low-pass filter passes the signal; above it, the output falls at 20 dB per decade.