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RC Time Constant Calculator

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A resistor feeding a capacitor produces the most useful curve in electronics: an exponential approach that is 63% complete after one time constant and treated as finished after five. That one constant, tau, is simply R times C — and it sets the delay of a timer, the corner of a filter, the debounce on a switch and the rise time of a signal edge. Enter the two components and this gives tau, the whole curve, the time to any charge level you name, and the filter frequency the same pair produces.

%

Any figure below 100 — the curve never actually arrives at 100%

Try:

How to use the rc time constant calculator

  1. 1Enter the resistance and pick its unit — ohms, kilohms or megohms.
  2. 2Enter the capacitance and pick its unit; most real capacitors are microfarads or nanofarads.
  3. 3Optionally enter a percentage to find the time to reach exactly that charge level.
  4. 4Press Calculate.
  5. 5Read tau at the top, the curve in the table, and the corner frequency if the pair is being used as a filter.

Examples

A slow timing circuit

Input
10 kΩ and 100 µF
Result
τ = 1 s, effectively charged after 5 s, corner frequency 0.159 Hz

A one-second time constant is easy to observe with an LED and makes the exponential visible.

An audio-band filter

Input
1 kΩ and 100 nF
Result
τ = 100 µs, corner frequency 1.592 kHz

The same pair read as a filter rather than a timer — the constant and the corner are the same fact twice.

Time to a specific level

Input
1 MΩ and 1 µF, asking for 99%
Result
4.605 s — a little over four and a half time constants

Reaching 99% takes ln(100) time constants, which is why five is the conventional stopping point.

About the rc time constant calculator

One constant, four circuits

The reason the RC pair turns up everywhere is that a great many problems reduce to needing something to happen a little later, or needing a signal to change no faster than a certain rate. Those are the same problem, and a resistor with a capacitor solves both.

As a timer, it delays a threshold crossing: charge a capacitor through a resistor into a comparator or a logic input, and the output changes state a predictable time after the input does. As a filter, it attenuates whatever changes faster than it can follow — a low-pass if the output is taken across the capacitor, a high-pass if taken across the resistor. As a debounce, it does both at once, smoothing the millisecond chatter of a mechanical switch contact into a single clean edge.

The fourth use is the one nobody chooses: every real signal path has stray capacitance and some series resistance, so every trace is an unintended RC filter. That is why a long cable rounds off fast digital edges, and why probe capacitance changes the very waveform an oscilloscope is trying to measure.

Reading the curve properly

The table on this page lists the conventional points, and the useful thing about them is that they are proportional rather than absolute. After one time constant, 63.2% of the gap has been covered. After the next, 63.2% of what remained is covered, leaving 13.5%. The process is memoryless in the same way radioactive decay is: how far the capacitor has already charged does not affect how quickly it covers the next fraction of what is left.

That is why five time constants became the working definition of finished. It leaves 0.67% of the gap, which is below the tolerance of the components involved and below the noise on most supplies. Three constants, at 95%, is often close enough for a timer; seven, at 99.9%, is the figure to use if a measurement is about to be taken.

Discharge is the same curve upside down, and the last column of the table shows it: a capacitor that has charged to 86.5% in two time constants will fall to 13.5% of its starting voltage in the same two. In a circuit that repeatedly charges and discharges, both halves matter, and a design that allows five constants to charge but only one to discharge will drift upwards until it stops working.

Frequently asked questions

Why is the capacitor never fully charged?
Because the charging current depends on the voltage still remaining to be made up. As the capacitor fills, the difference across the resistor shrinks, so less current flows, so it fills more slowly — and the process feeds back on itself forever. Mathematically the curve approaches the supply voltage asymptotically and reaches it only at infinity. Asking this page for 100% gets an explanation rather than a number, because there genuinely is not one.
Where does the figure 63.2% come from?
It is 1 − 1/e, evaluated at one time constant. The exponential describing the charge is 1 − e^(−t/RC), and setting t equal to RC leaves 1 − e^(−1), which is 0.6321. There is nothing special about that fraction except that it is what one time constant produces, which is what makes the time constant a useful unit in the first place: the same fraction of the remaining gap is covered in every successive tau.
How does a time constant become a filter frequency?
They are two readings of the same component pair. The corner frequency is 1/(2πRC), so it is the reciprocal of tau divided by 2π — a large time constant means a low corner. Physically it is the same story: the capacitor takes time to respond, so anything changing faster than that gets attenuated. A filter with a 1 ms time constant is one that cannot follow signals much above a kilohertz.
Does the supply voltage change the timing?
No, and that surprises people. The time constant depends only on R and C, so a circuit charging towards 12 V takes exactly as long to reach 63% of 12 V as one charging towards 3 V takes to reach 63% of 3 V. What the supply voltage does change is the absolute voltage at any moment, which matters when a threshold is fixed — a comparator switching at 1.5 V is reached far sooner from a 12 V supply than from a 3 V one.
Why does my built circuit not match the calculated time?
Component tolerance, almost always the capacitor. Ceramic and film parts are usually within 5 or 10 percent, which shifts the timing by the same amount. Electrolytics are far looser — −20% to +80% is a normal specification — so a timing circuit built around one can be nearly twice as slow as calculated and still be within spec. Where timing matters, use a film capacitor, or trim the resistance against the part you actually have.

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