RC time constant calculator
Work with the RC time constant: compute τ = R×C, the capacitor voltage after a time t (charging from 0, or discharging from full), or solve the R or C that gives a target time constant.
RC values
Time constant (τ)
Time constant τ
τ = R × C
Time to settle (5τ)
≈ fully charged (99.3 %)
Voltage after a time t
Capacitor voltage V(t)
V(t) = Vcc × (1 − e^(−t/τ)) — 63.21 % of Vcc
Charge/discharge reference
At 0.1τ
of final Vcc reached
At 1τ
of final Vcc reached
At 2τ
of final Vcc reached
At 3τ
of final Vcc reached
At 5τ
of final Vcc reached
Reverse — R or C for a target τ
Required R (using C above)
R = τ ÷ C
Required C (using R above)
C = τ ÷ R
About the model
The RC time constant τ = R·C is the time in seconds for the capacitor to reach 63.2 % of the supply while charging (or fall to 36.8 % while discharging). Each additional τ closes the remaining gap by the same factor: after 3τ the capacitor is at 95 %, and after 5τ it is effectively full at 99.3 %. The exponential V(t) = Vcc·(1 − e^(−t/τ)) for charging and V(t) = Vcc·e^(−t/τ) for discharge follow directly from the series-RC differential equation.
The model assumes an ideal voltage source and an unloaded capacitor — a real supply has output impedance and capacitor ESR, both of which slow the edge slightly. Capacitor tolerance (often ±20 % for electrolytics) directly scales τ, so leave margin in any timing application.
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Frequently asked questions
What is the RC time constant formula?
τ = R × C, the time in seconds for a capacitor to reach 63.2% of the supply while charging (or fall to 36.8% while discharging). The calculator's defaults of R = 10 kΩ and C = 100 nF give τ = 1 ms, and it reports 5τ ≈ fully charged at 99.3%.
How do you calculate capacitor voltage after time t?
Charging from 0 uses V(t) = Vcc × (1 − e^(−t/τ)) and discharging from full uses V(t) = Vcc × e^(−t/τ). With the default Vcc = 5 V, leave the time blank to read the state at exactly t = τ — 3.16 V (63.2%) when charging or 1.84 V (36.8%) when discharging.
How much time does a capacitor need to fully charge?
Each time constant closes the remaining gap by the same factor: 2τ reaches 86.5%, 3τ reaches 95.0% and 5τ reaches 99.3%, which is treated as effectively full. The tool lists these reference points and computes the actual time to settle as 5τ.
How do I find the R or C for a target time constant?
Use reverse mode and enter the target τ. The calculator solves R = τ ÷ C or C = τ ÷ R using the component you leave fixed, in ms or seconds, so you can pick a resistor value for a timing design quickly.
First-order RC model, ideal components. Real circuits add series resistance from the supply and capacitor tolerance shifts the timing. ICBOMS provides this tool for reference only.