RC Time Constant Calculator
Enter R and C to get τ, the practical 5τ settle time, the voltage at any instant, and the time to any target — the exponential that governs delays and filters.
Last updated: 2026-09-28
How the calculation works
- τ = RC is the circuit's natural clock: 63.2% charged at 1τ, 86.5% at 2τ, 99.3% at 5τ.
- The exponential curve answers 'voltage after t' and its inverse 'time to reach V'.
- 5τ is the engineering 'fully settled' milestone used in debounce and delay design.
Formula
τ = R × C V(t) = V₀ × (1 − e^(−t/τ)) t(target) = −τ × ln(1 − V/V₀)
| Symbol | Meaning | Unit |
|---|---|---|
τ | Time constant | s |
t | Elapsed time | s |
Worked example
Interpreting the result
The RC exponential is everywhere: switch debounces, reset delays, LED fade, analog filtering and timing circuits all live on this curve. Design lever: pick the time constant you need and solve for R×C, then choose R to respect the currents (high R saves power but invites noise; low C costs money and space). The same τ defines the filter corner f = 1/(2πRC) — the capacitor that delays also filters.
Assumptions
- Ideal RC — no source impedance, no capacitor ESR or leakage.
- Single charging (or discharging) event from a fixed supply.
Limitations
- Electrolytic capacitor tolerance (±20%) shifts real timing — design with margin.
- Repeated switching (PWM) behavior needs the steady-state ripple analysis, not a single curve.
Frequently asked questions
What is the RC time constant?
τ = R × C seconds — the time to charge to 63.2% (or discharge to 36.8%). After 5τ the circuit is 99.3% settled, the practical 'done' milestone.
How long does a capacitor take to charge?
Mathematically never 100%; practically 5τ ≈ 99.3%. A 10 kΩ/10 µF pair: 0.5 s. Solve exact targets with t = −τ·ln(1 − V/V₀).