RC time constant calculator
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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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