Source: https://mokxi.com/learn/rc-time-constant
Updated: 2026-09-27

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# One time constant: what R times C actually means

Written by the Mokxi team, updated September 27, 2026

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A 50 Hz square wave into 10 k and 100 nF. Tau is 1 ms. Open it and look at the Scope tab.

A capacitor cannot change its voltage instantly. Its voltage only moves as charge flows onto it, and when it charges through a resistor, the current depends on how far the capacitor still has to go. So it starts fast and slows down as it fills, and the curve it follows is an exponential. The one number that describes that curve is the time constant, tau, and it is simply the resistance times the capacitance.

The circuit above is a signal generator making a 0 to 5 V square wave at 50 Hz, feeding a 10 k resistor into a 100 nF capacitor, with the scope on both ends. Tau is 10 000 ohms x 0.000 000 1 farads = 0.001 seconds, one millisecond. Each half of the square wave lasts 10 ms, ten time constants, which is plenty of time for the capacitor to charge all the way up and discharge all the way down.

Press Run and open the Scope tab along the bottom of the editor. The yellow trace is the square wave and the blue one is the capacitor: a fast rise that bends over and flattens out, then a fall that does the same thing upside down.

Want the step-by-step version? The lesson "Charging a capacitor" walks through this with checkpoints.
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## The numbers, one tau at a time

Charging from empty towards a final voltage, the capacitor covers 63.2 percent of the way in one time constant, 86.5 percent in two, 95 percent in three and 99.3 percent in five. Those come from 1 - e to the minus t over tau, and they are the same for every RC circuit ever built, which is what makes tau useful: know it and you know the whole curve.

In this circuit the capacitor tops out at 4.95 V, so one tau in, one millisecond after the rising edge, it should be at 0.632 x 4.95 = 3.13 V. The engine has it at 3.13 V. Two milliseconds in it is at 4.29 V, three milliseconds 4.71 V. Discharging is the mirror image: one tau after the falling edge it has lost 63 percent and sits at 37 percent, 1.82 V.

Five time constants is the usual answer to how long a capacitor takes to charge fully. It never gets there exactly, but after five tau it is within one percent, and nobody can tell the difference on a scope or a meter.

## Reading tau off the scope

You can measure tau rather than calculate it, which is how you find it in a circuit whose parts you do not know. In the Scope tab, switch the cursors on. Put the first time cursor on a rising edge of the yellow trace and one voltage cursor at 63 percent of the blue trace’s final value. Slide the second time cursor to where the blue trace crosses that line, and the time between the cursors is tau.

The Scope tab also prints a 10 to 90 percent rise time for each channel. For a single RC that is always 2.2 tau, because the curve takes 0.105 tau to reach 10 percent and 2.303 tau to reach 90. Divide what it prints by 2.2 and you have another estimate of tau from the same trace.

## Why it stops at 4.95 V and not 5 V

The scope’s probes are not free. Each channel is 1 megohm to ground, exactly as on a real scope, so the blue probe is a 1 M load on the capacitor, and the 10 k in front of it makes a divider: 5 V x 1 M / 1.01 M = 4.95 V. It is a one percent effect here, and it is worth noticing, because with a 1 M timing resistor instead of 10 k the probe would halve the voltage and change the time constant it was trying to measure.

## Change a value and watch the curve move

Open the circuit in the editor and change the capacitor to 1 uF. Tau is now 10 ms, the whole length of a half cycle, so the capacitor gets 63 percent of the way up before the square wave turns round and pulls it back. It never reaches the top, and the trace becomes a row of shark fins riding in the middle.

Put the capacitor back to 100 nF and raise the generator to 500 Hz. Each half cycle is now 1 ms, one tau, and you get the same shark fins for the same reason. Push it to 5 kHz and the blue trace is a small triangle sitting at 2.5 V: the capacitor is averaging the square wave. That is a low-pass filter, and its corner frequency is 1 / (2 pi R C), which is 159 Hz for these values. The button below opens a filter built to sit exactly on its corner.

## Common mistakes

Units, by a long way. 100 nF is 0.1 uF is 100 000 pF, the code printed on the part is 104, and a slip of a factor of a thousand gives a time constant a thousand times wrong. Write tau out with the powers of ten every time until it is automatic.

Electrolytic capacitors are polarized. The stripe marks the negative leg, and fitted backwards on a real bench one can heat up, bulge and vent, so check the stripe before you power anything. And timing a real circuit by its printed values: an electrolytic is often plus or minus 20 percent, so an RC delay built from one is a rough delay, not a precise one.

## Questions

What is the RC time constant?

The resistance times the capacitance, tau = R x C, in seconds when R is in ohms and C in farads. It is the time a capacitor charging through a resistor takes to cover 63 percent of the way to its final voltage. 10 k and 100 nF give 1 ms.

Why 63 percent?

Because the charging curve is 1 - e^(-t / tau), and at t = tau that is 1 - 1/e, which is 0.632. It is a property of the exponential, not of any particular part.

How long does a capacitor take to charge fully?

In theory for ever; in practice about five time constants, when it is within one percent of the final voltage. For 10 k and 100 nF that is 5 ms.

How do I pick R and C for a delay I want?

Decide the time, then pick a capacitor you have and solve R = tau / C. Keep R between about 1 k and 1 M: smaller wastes current and loads whatever drives it, larger gets swamped by leakage and by whatever you measure it with.

Related

## Keep going

PWM to an Analog Voltage With an RC Filter The 555 Monostable: One Press, One Timed Pulse Measure It: Read a Circuit With a Scope and Plotter Debouncing a Button: Why It Fires More Than Once The capacitor in the simulator Using the oscilloscope

## Build this for real

Open the editor, change a value and watch the number move with it. Nothing to install, and no account needed.

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