RC Time Constant Calculator - Tau, Cutoff Frequency and Charge Time for RC and RL Circuits
RC Time Constant Calculator
How fast does a capacitor or inductor charge?
RC and RL
Switch between a resistor-capacitor and a resistor-inductor circuit. The time constant is R times C, or L divided by R.
Cutoff Frequency
The -3 dB point of the matching low-pass or high-pass filter is 1 divided by 2 pi tau.
Charge Times
See how long it takes to reach 63.2, 90, 95 and 99 percent, and how charged it is after any time you choose.
Private
Nothing you enter is stored.
What the Time Constant Means
When a capacitor charges through a resistor, the voltage does not jump to its final value. It approaches it exponentially: after one time constant (tau equals resistance times capacitance) it has covered 63.2 percent of the distance, after two about 86.5 percent, after three about 95 percent, and after five more than 99 percent. Discharging is the mirror image. An inductor behaves the same way for current, with tau equal to inductance divided by resistance.
The same constant sets the cutoff frequency of simple RC and RL filters, 1 over 2 pi tau, where the output has fallen to about 70.7 percent (-3 dB). A 10 kilohm resistor and a 100 nF capacitor, for example, give tau of 1 millisecond and a cutoff near 159 Hz. It is also used to choose debounce delays, timing circuits and snubbers. Real capacitors have wide tolerances, often 10 to 20 percent, so allow for that.
Key Takeaways
- 5 tau is "done": After five time constants a circuit is within 1 percent of its final value.
- Units: Use the unit menus so that ohms, farads and henries are converted for you.
- Related calculators: See also the Resistor Calculator and the Ohm's Law Calculator.