⏱️ RC Time Constant Calculator
Enter resistance and capacitance to calculate an RC circuit’s time constant (τ=RC), and find what percentage the capacitor has charged or discharged after a given elapsed time, using the standard exponential formulas.
How to use
- Enter the resistance (Ω).
- Enter the capacitance value and select its unit.
- Enter the elapsed time (seconds).
- The time constant and the charge/discharge percentage at that time are calculated automatically.
How the calculation works
This tool calculates how fast a capacitor charges and discharges through a resistor in an RC circuit. Time constant τ = R × C (seconds) Charging: V(t) = V₀ × (1 − e^(−t/τ)) Discharging: V(t) = V₀ × e^(−t/τ) The time constant is the time it takes to charge to about 63.2% of the final voltage, or to discharge to about 36.8% of the starting voltage. Enter an elapsed time to see the charge level at that moment and how much voltage would remain after discharging for the same time. Depending on the parts, τ can be anywhere from picoseconds to hours, so it is shown in s, ms, µs, ns or ps as appropriate.
Worked example
1 kΩ and 1000 µF Time constant: 1000 × 0.001 = 1 s After 1 s: charged about 63.21%, remaining after discharge about 36.79% After 3 s (3τ): charged about 95.02% After 5 s (5τ): charged about 99.33% 10 kΩ and 100 nF Time constant: 10,000 × 100 × 10⁻⁹ = 1 ms
Things to be aware of
- For delay circuits such as switch debouncing or a slow LED fade-in, choose parts by deciding how many τ the delay should be.
- An RC circuit is also a filter, with a cutoff frequency of fc = 1 ÷ (2πRC).
- Electrolytic capacitors often have a tolerance of about ±20%, so real timings can differ from the calculation.
FAQ
What is the time constant (τ)?
It’s the time for a capacitor’s voltage in an RC circuit to reach about 63.2% of its final value, calculated as τ = R × C (resistance × capacitance).
Why is the charge percentage 63.2% at t=τ?
Substituting t=τ into the charging equation V(t)=V0(1-e^(-t/τ)) gives 1-e^(-1) ≈ 0.6321 — a universal constant that follows from the exponential function.
Why is 5τ often considered "fully" charged or discharged?
At t=5τ, the charging percentage is about 99.3% and the remaining discharge is about 0.7%, which is close enough to complete for most practical purposes.