RC Time Constant Calculator
Resistance in ohms times capacitance in farads gives tau in seconds. 10 kohm with 1 uF returns 0.01 s, and a capacitor is near full charge at 5 tau.
τ (s)
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RC time constant: τ = R · C
The RC time constant τ = R · C tells you how quickly a capacitor charges or discharges through a resistor. Charging follows V(t) = Vf · (1 − e−t/τ). After 1τ the capacitor sits at 63 % of the final voltage, and by 5τ it's at 99.3 %, which is the point everyone treats as fully charged. As an example, R = 10 kΩ with C = 100 µF gives τ = 1 s, so a full charge takes roughly 5 s. That same RC pair also sets the cutoff of a first-order low-pass filter: fc = 1 / (2π · R · C).
Applications: debounce, filters, switching supplies
You'll see RC pairs doing switch debounce, where a τ around 10–50 ms smooths out mechanical bounce, plus audio filters, ripple smoothing in switching supplies, and antialiasing in front of an ADC. A smaller τ gives a faster response and pushes the cutoff frequency up.
FAQ
Why 63 % at one time constant? It falls right out of the exponential solution to the charging equation, since 1 − e−1 ≈ 0.632.
When is the capacitor "fully" charged? Strictly speaking, never. By 5τ it's within 0.7 % of the target, and that's close enough that we call it full in practice.
How do I pick R and C for a 100 Hz cutoff? Start by choosing C, say 100 nF, then solve R = 1 / (2π · fc · C) ≈ 15.9 kΩ.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.