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RC Time Constant Calculator

The time constant and cutoff frequency of a resistor and capacitor, or the part to pick for a cutoff you want.

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A resistor and a capacitor together make one of the most useful pairs in electronics: a timer, a filter, a debounce. Both behaviors come from one number, the time constant, which is just the two multiplied. This gives you the time constant and the filter cutoff of an RC pair, or works backwards to the resistor or capacitor you need for a cutoff you have in mind.

One number runs it: tau

The time constant, written tau, is the resistance times the capacitance, and it sets the pace of everything the pair does. Charge a capacitor through a resistor and after one tau it is about 63 percent of the way up; after five tau it is within a whisper of full, around 99 percent. Discharge is the mirror image. So if you want a delay or a charge time, you are really choosing a tau, and R times C is how you get it.

The same pair is a filter

Feed a signal through the same resistor and capacitor instead of a steady voltage and you have a first-order filter. Its cutoff frequency, where it begins to roll the signal off, is one over two pi tau. Low frequencies pass and high ones fade, or the reverse depending on where you take the output. That is why RC pairs are everywhere a circuit needs to smooth a signal, strip noise, or set a frequency, and why the cutoff and the time constant are two views of the same thing.

Working backwards to a part

Often you know the cutoff or the timing you want and need to pick a part. Fix one of the two, usually the capacitor since they come in fewer values, and solve for the other. This does that: give it the cutoff and the capacitor and it gives the resistor, or the cutoff and the resistor and it gives the capacitor. Then reach for the nearest standard value, which is almost always close enough, and nudge the other part if you need to land it exactly.

Tolerance is real

The math is exact; the parts are not. Resistors are often 1 or 5 percent, and capacitors are looser, with electrolytics sometimes 20 percent and drifting with temperature and age. So treat the result as the center of a spread, not a guarantee. For timing that has to be tight, use film or good ceramic capacitors and tighter resistors, or make one part adjustable and tune it. For a filter or a debounce, the usual tolerances are fine.

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