What this calculator does
A capacitor charging through a resistor does not rise steadily; it approaches the supply voltage along a curve that gets flatter as it goes. The time constant, written τ and equal to resistance times capacitance, is the single number that describes how fast that happens.
After one time constant the capacitor has reached about 63 per cent of the supply. After five it is above 99 per cent, which is why five time constants is the usual rule of thumb for calling a capacitor fully charged.
The formula
Multiply resistance in ohms by capacitance in farads to get the time constant in seconds. The charging voltage is the supply times one minus e to the power of minus t over τ, and discharging is the supply times e to the power of minus t over τ.
| Term | Meaning |
|---|---|
| Time constant (τ) | Resistance times capacitance, in seconds. The time to reach about 63 per cent of the final value. |
| Exponential approach | The curve followed by charging and discharging, which gets closer to its target without ever formally arriving. |
| Five time constants | The practical rule for a full charge or discharge, at which point over 99 per cent of the change has happened. |
The inputs explained
| Field | What to enter |
|---|---|
| Resistance (Ω) | The series resistance in ohms. |
| Capacitance (µF) | The capacitance in microfarads. |
| Supply voltage (V) | The supply voltage for charging, or the starting voltage for discharging. |
| Elapsed time (s) | The elapsed time in seconds at which to evaluate the voltage. |
When to use it
Designing a timing delay
An RC pair is the simplest way to create a delay, and the time constant sets how long it lasts.
Filtering a noisy signal
The same time constant determines which frequencies pass and which are smoothed out.
Sizing a bleed resistor
A resistor across a capacitor discharges it safely, and the time constant says how long that takes.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the capacitor voltage rise over time?
The same circuit evaluated at a range of elapsed times.
| Elapsed time | Charging voltage at t | Charged fraction at t |
|---|---|---|
| 0.1 s | 0.856 V | 9.52% |
| 0.5 s | 3.541 V | 39.3% |
| 1 s | 5.689 V | 63.2% |
| 2 s | 7.782 V | 86.5% |
| 5 s | 8.939 V | 99.3% |
Questions
Why 63 per cent after one time constant?
It is what the exponential curve gives: one minus one over e, which works out at 0.632. The figure is not chosen, it falls out of the mathematics of exponential approach.
Does a capacitor ever fully charge?
Not in theory. The curve approaches the supply voltage asymptotically, getting closer forever without arriving. In practice the remaining difference becomes smaller than anything measurable after about five time constants.
What if I double the resistance?
The time constant doubles and everything takes twice as long. The same happens if the capacitance is doubled, since τ is simply their product.
Is discharging the mirror image of charging?
Yes, with the same time constant. After one τ a discharging capacitor has fallen to about 37 per cent of its starting voltage, which is the same 63 per cent change in the opposite direction.
For the stored energy involved, see the capacitor charge and energy calculator. For the frequency response of the same pair, see the low pass filter calculator.