RC Time Constant Calculator
Enter R, C and source voltage to get the time constant, charge milestones, cut-off frequency and capacitor energy.
Step-by-step
- Enter valid values to begin.
Ideal capacitor (no leakage or ESR) and ideal resistor driven by a constant source with a perfect switch. Real electrolytic capacitors have wide tolerance (often −20/+80% or ±20%) and leakage that stretches discharge times, and ceramics lose capacitance with DC bias. The 1.5× voltage-rating margin is a derating practice, not a standard. Rise time 2.2τ applies to a full step response from 0 to the final value.
RC Time Constant: The Curve Behind Every Timer and Filter
Core Engineering Principles
A capacitor charges through a resistor at a rate proportional to the voltage still missing. That one fact gives the exponential curve, and the only number that matters is τ = R × C. After one time constant the capacitor has covered 63.2% of the journey, after two 86.5%, after three 95.0%, after four 98.2% and after five 99.3%. We call five time constants “fully charged” in practice, but remember the curve never actually arrives. The same curve describes discharge, with the voltage falling to 36.8% after one τ.
The same τ sets the frequency behaviour. Take the output across the capacitor and you have a low-pass filter with a −3 dB point at fc = 1 / (2πRC); take it across the resistor and you have a high-pass with the same corner. The step response and the frequency response are two views of one product. Real capacitors depart from the ideal. An aluminium electrolytic can be 20% off in value and leaks, so a long delay built on one drifts with temperature and age. For a timing circuit we use film or C0G ceramics, and we keep the resistor well below the capacitor’s leakage resistance.
fc = 1 / (2πRC) • tr = 2.2τ • E = ½CV²
NEC & Standard References
IEC 60384-1 is the generic specification for fixed capacitors in electronic equipment; its sectional parts cover specific types such as aluminium electrolytics and ceramics. IEC 60063 provides the preferred values for R and C. IEEE Std 100 defines time constant and cut-off frequency. A voltage rating of at least 1.5× the working voltage is derating practice used here as a warning, not a standard requirement.1. τ = 10,000 × 100 × 10−6 = 1.000 s.
2. Voltage at 1τ to 5τ: 7.585 V, 10.376 V, 11.403 V, 11.780 V and 11.919 V.
3. Time to reach 6 V: t = −1 × ln(1 − 6/12) = 0.693 s.
4. fc = 1 / (2π × 1) = 0.159 Hz, and rise time = 2.2 s.
5. Stored energy = ½ × 100 µF × 12² = 7.2 mJ. The resistor burns the same 7.2 mJ while charging, whatever its value.
6. Rating check: 1.5 × 12 = 18 V, so 25 V passes.
- The cap is not at 5τ the moment you think. A logic input with a threshold near 70% of the rail sees “high” at about 1.2τ, so timers depend on the threshold, not just τ.
- Inrush through a small R is large. Peak current is Vs/R at the first instant; switch contacts and supply limits must survive it.
- Stored energy bites. A large capacitor on a high-voltage rail can hold a lethal charge long after power-off; bleed it and measure before touching.
- Leakage ruins long delays. Beyond a few seconds, use a larger C with a smaller R rather than a huge R.