RC Time Constant Explained: How Fast Does a Capacitor Charge?
τ = R × C tells you how fast a capacitor charges: 63 % after 1 τ, over 99 % after 5 τ. Worked examples, the charging curve, uses and a free simulator.
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Put a resistor in front of a capacitor and you get a tiny timer. That simple RC circuit is behind blinking LEDs, the 555 timer, button debouncing, camera flashes and the smoothing in every power supply. One number describes how fast it works: the time constant.
Free capacitor charging simulator
Pick a resistor and a capacitor, press Charge or Discharge and watch the curve:
⚡ LOADING THE CALCULATOR…
Free, no sign-up. Prefer a bigger screen? Open the Capacitor charging calculator in the Lab →
The formula
You don't need the exponential maths for most projects. Just remember the table:
| Time | Charging (% of supply) | Discharging (% left) |
|---|---|---|
| 1 τ | 63 % | 37 % |
| 2 τ | 86 % | 14 % |
| 3 τ | 95 % | 5 % |
| 4 τ | 98 % | 2 % |
| 5 τ | 99.3 % | 0.7 % |
Worked examples
| R | C | τ = R × C | Practically full (5 τ) |
|---|---|---|---|
| 1 kΩ | 100 µF | 0.1 s | 0.5 s |
| 10 kΩ | 100 µF | 1 s | 5 s |
| 100 kΩ | 10 µF | 1 s | 5 s |
| 10 kΩ | 1 µF | 10 ms | 50 ms |
| 10 kΩ | 100 nF | 1 ms | 5 ms |
| 1 MΩ | 1 µF | 1 s | 5 s |
Notice that a big R with a small C can give the same time as a small R with a big C.
Why does it slow down?
At the start, the empty capacitor has 0 V across it, so the whole supply voltage pushes current through the resistor — charging is fast. As the capacitor fills up, its own voltage pushes back, so less voltage is left across the resistor, less current flows, and charging slows down. That gives the curve its shape: steep at first, then flattening out.
Where RC timing is used
- Blinking and timers: the 555 timer charges a capacitor through resistors and flips its output at ⅓ and ⅔ of the supply.
- Button debounce: an RC filter smooths the bouncy contacts of a push button.
- Power-on reset: a microcontroller is held in reset until an RC delay has passed.
- Filters: an RC low-pass filter lets slow signals through and blocks fast noise. Its cut-off frequency is f = 1 ÷ (2π × R × C).
- Smoothing: in a power supply, a big capacitor keeps the voltage up between the AC peaks.
Capacitors can keep their charge
A big capacitor can stay charged long after the power is off. Large capacitors in TVs, microwave ovens and power supplies can hold a dangerous voltage. Discharge them safely through a suitable resistor before touching — or leave mains equipment to professionals.
Frequently asked questions
What is the RC time constant?
It is R × C, in seconds: the time a capacitor takes to charge to about 63 % of the supply (or to discharge to about 37 %) through a resistor.
How long does a capacitor take to fully charge?
About 5 time constants (5 × R × C). After that it is above 99 % — full for practical purposes.
Why 63 percent?
Because after one time constant the charging formula gives 1 − e^(−1) ≈ 0.632, so 63.2 % of the final voltage.
How do I make an RC delay longer?
Use a bigger resistor or a bigger capacitor. Doubling either one doubles the time.
