RC Time Constant Calculator
Enter the resistor and capacitor. You get the time constant, the cut-off frequency and how long it takes to reach a chosen charge.
The time constant is the time for a charging capacitor to reach about 63.2% of the supply voltage. With a supply voltage you also get the energy stored, half C times V squared.
Worked examples
One second timer
10 kilohms and 100 microfarads
1 s time constant, 1.59 Hz cut-off
RC = 10,000 x 0.0001.
Voltage after one constant
1 kilohm, 1 microfarad, 5 V, 1 ms
3.16 V
5 x (1 - e^-1).
About RC Time Constant Calculator
When a capacitor charges through a resistor, the voltage does not jump to its final value. It rises quickly at first and then more slowly. The time constant, the resistance multiplied by the capacitance, sets the pace: after one time constant the capacitor is about 63% charged, after three about 95%, and after five more than 99%. This calculator gives the time constant and a table of the first five.
The same product sets the cut-off frequency of a simple RC filter, where the output has fallen to about 71% of the input. The page gives that frequency, the time to reach any charge level you choose, the capacitor voltage after a time you enter, and the energy and charge stored when it is full. It is useful for timers, debounce circuits, smoothing filters and any design where a signal is delayed or softened by a resistor and capacitor.
How to use RC Time Constant Calculator
- Enter the resistance and the capacitance, choosing the units.
- Optionally enter the supply voltage and a time since charging began.
- Choose the charge level you want to reach, 90% by default.
- Read the time constant, cut-off frequency, charge times and stored energy.
Common uses
- Designing a simple delay or timer circuit
- Choosing parts for a low pass or high pass filter
- Setting a switch debounce time
- Estimating how quickly a smoothing capacitor charges
Frequently asked questions
What is the RC time constant?
It is the product of the resistance in ohms and the capacitance in farads, giving a time in seconds. It is the time for a charging capacitor to reach about 63.2% of the supply voltage, or for a discharging one to fall to 36.8%.
How long does a capacitor take to charge fully?
In theory it never quite finishes. After five time constants it is over 99% charged, which is usually treated as full.
How is the cut-off frequency found?
It is one divided by two pi times the resistance times the capacitance. At that frequency the filter output is about 70.7% of the input, which is minus 3 decibels.
Does the same formula apply to discharge?
Yes. A capacitor discharging through a resistor falls to 36.8% after one time constant, 13.5% after two and below 1% after five.