RC Circuit Time Constant Calculator

An RC circuit — a resistor and a capacitor wired together — doesn't charge or discharge instantly. It follows a smooth exponential curve, and the speed of that curve is described by a single number: the time constant, τ (tau). This calculator computes τ from your resistor and capacitor values and shows exactly how far charged (or discharged) the circuit is at 1, 2, 3, 4, and 5 multiples of τ.

The formula

τ = R × C

With resistance in ohms and capacitance in farads, τ comes out in seconds. Enter your values in whatever units are convenient — ohms, kilohms, or megohms for resistance; picofarads through farads for capacitance — and the calculator converts everything to base SI units before multiplying, then scales the result back to the most readable time unit (ns, µs, ms, s, min, or h).

For example, a 1 kΩ resistor with a 1000 µF capacitor gives τ = 1000 Ω × 0.001 F = 1 second. A 100 Ω resistor with a 470 nF capacitor — a very common combination in filters and debounce circuits — gives τ = 47 µs.

Reading the charge/discharge table

A capacitor charging through a resistor follows V(t) = Vs × (1 − e^(−t/τ)); discharging follows V(t) = Vs × e^(−t/τ). Because these are ratios, the percentage charged or discharged at any multiple of τ doesn't depend on the actual voltage or component values — only on how many τ's have elapsed. That's why the same five percentages show up in every textbook and datasheet:

Time elapsed	Charged	Discharged
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%

By convention, a circuit is treated as fully charged (or discharged) after 5τ — at that point it's within 0.7% of its final value, which is close enough for virtually every practical purpose. The table also shows the actual elapsed time at each multiple, so you can read off, for instance, exactly when a timing circuit crosses the 95% mark.

Common uses

• Timing circuits: 555 timers, debounce filters, and delay circuits are all sized around a target τ.
• Low-pass / high-pass filters: the RC time constant sets the filter's cutoff frequency (f_c = 1 / (2πτ)).
• Sensor and ADC settling: knowing how many τ's an anti-aliasing or sample-and-hold RC needs to settle to within your required accuracy.
• Power-supply decoupling: estimating how quickly a decoupling capacitor discharges once a rail drops.

Does the supply voltage matter?

No — the percentage charged or discharged at each multiple of τ is independent of voltage, resistance, and capacitance individually; it only depends on the ratio t/τ. If you need the actual voltage or current at a given time, multiply the percentage by your circuit's supply voltage or steady-state current directly.

Privacy

All calculations run entirely in your browser (or via the API, entirely on request) — no circuit values are stored or sent anywhere beyond the calculation itself.