RC Time Constant Calculator
Find τ = R × C, the 63.2% charge point, and the ~5τ time a capacitor needs to charge or discharge.
Reaches 63.2% of the source in one τ; treated as fully charged (~99.3%) after 5τ ≈ 5 s.
Fraction of the source voltage as the capacitor charges. It reaches 63.2% at one τ and about 99.3% by 5τ, where it is considered fully charged.
The RC time constant is τ = R × C. With a 10 kΩ resistor and a 100 µF capacitor, τ = 10 000 × 0.0001 = 1 second. After one time constant a charging capacitor reaches 63.2% of the supply voltage, and it is treated as fully charged after about 5τ — here, 5 seconds.
What the RC time constant is
The time constant, written with the Greek letter τ (tau), sets how quickly a capacitor charges or discharges through a resistor. It is simply the resistance multiplied by the capacitance: a bigger resistor limits current, and a bigger capacitor stores more charge, so either one makes the circuit respond more slowly. One τ is the time to reach 63.2% of the way to the final voltage — not the time to finish.
R in ohms and C in farads give τ in seconds — 1 Ω × 1 F = 1 s
Charging voltage over time; at t = τ the exponential term leaves 1 − e⁻¹ ≈ 0.632
Worked example
Take a 10 kΩ resistor in series with a 100 µF capacitor across a supply.
- 1 Convert the resistance to ohms. 10 kΩ = 10 000 Ω.
- 2 Convert the capacitance to farads. 100 µF = 100 × 10⁻⁶ = 0.0001 F.
- 3 Multiply R by C. τ = 10 000 × 0.0001 = 1 s — the time constant.
- 4 Find the 63.2% point. After one τ (1 s) the capacitor charges to 63.2% of the supply voltage.
- 5 Estimate the full-charge time at 5τ. 5 × 1 s = 5 s to reach about 99.3%, which counts as fully charged.
Charge and discharge at each time constant
Percentages are of the source voltage. Charging follows 1 − e⁻ⁿ; discharging follows e⁻ⁿ. Both use the same τ.
| Elapsed time | Charging (% of source) | Discharging (% of source) |
|---|---|---|
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 3τ | 95.0% | 5.0% |
| 4τ | 98.2% | 1.8% |
| 5τ | 99.3% | 0.7% |
Reading the results
Charging vs. discharging. Charging climbs along 1 − e^(−t/τ) toward the supply, while discharging decays along e^(−t/τ) toward zero. The shapes mirror each other and share the same τ, so a capacitor takes as long to empty as it does to fill.
Why ~5τ counts as “done.” The exponential never mathematically reaches 100%, but by 5τ it is within 0.7% of the target. Engineers therefore treat about five time constants as fully charged or fully discharged for practical purposes.
Filters and timing. The same τ sets the corner frequency of an RC filter, f = 1 ÷ (2π × τ), and the delay in timing or debounce circuits. Increase R or C to slow the response and lower the cutoff; decrease them to speed it up.