RC Time Constant Calculator

1. Button debouncer — 10 kΩ pulled up to 3.3 V with a 100 nF cap to ground gives τ = 1 ms. Settles in ~5 ms — long enough to ignore mechanical bounce (typically < 2 ms), short enough to feel instant to the user.
2. Audio coupling cap — 1 µF in series with a 10 kΩ input gives fc ≈ 16 Hz, comfortably below the audible band. Bumping the cap to 10 µF drops fc to 1.6 Hz for sub-bass headroom on a hi-fi input stage.
3. 555 monostable pulse — The 555's one-shot uses the same R·C product: t = 1.1 · R · C. For a 1 s output pulse with C = 10 µF, pick R ≈ 91 kΩ. The RC time constant here is exactly what sets the pulse width.

When a capacitor charges through a resistor toward a supply voltage, it follows an exponential curve: v(t) = V_s · (1 − e^−t/τ). The time constant τ = R·C is the time to reach about 63.2 % of the final voltage — a single number that captures how fast the circuit responds.

Discharging mirrors the same shape: v(t) = V₀ · e^−t/τ. After one τ the cap has dropped to 36.8 % of its starting voltage; after five τ, it's effectively zero (0.7 %). Designers usually treat 5τ as “fully charged / discharged” in practice.

The same R and C also define a first-order low-pass filter with cutoff f_c = 1 / (2π·R·C). Below f_c the cap passes signals through; above f_c, R and C divide the signal down at 20 dB/decade. Swap their positions and you get a high-pass filter with the same cutoff.

• Treat 5τ as "settled" — The error after five time constants is 0.7 %, well below the noise floor of most analog circuits. For 12-bit precision or better, allow 8–10τ.
• Target τ ≈ 1 ms for debouncing — Long enough to filter mechanical bounce (usually < 2 ms), short enough that the user can't feel the delay between press and response.
• Pick R first, then C — Resistor values span 10 Ω → 10 MΩ comfortably; capacitor selection is narrower (pF to µF in standard parts), so let R do the fine-tuning.
• Watch source impedance — The R in τ = R·C is the total path resistance — including the driver's output impedance and any series elements, not just the labelled resistor.
• Capacitor tolerance dominates — Ceramic caps swing ±10–20 %; electrolytics are worse. Don't design RC timing that needs better than ±5 % accuracy from the cap alone.
• Low-pass for noise, high-pass for DC blocking — A small RC at an ADC input cleans up sampling noise; a coupling cap in front of an amplifier blocks DC offset between stages.