SizingKitElectronics · timing
RC time constant calculator
Multiply a resistance by a capacitance and this returns the time constant and the corner frequency of the same network side by side, the 10-to-90 rise time, the peak current at the instant of the step and the energy the resistor turns into heat getting there. It also solves the curve in both directions — time to reach any percentage, or the percentage reached after any time — and prints an eight-row table of the exponential you can put on paper. Free, no signup, and those eight rows are generated from the exponential rather than copied off a chart.
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- No signup
- Tau and corner frequency
- Any percentage, either way
- Printable curve
The two parts, and the step across them
The resistance is everything in the charging path — the series resistor, the source impedance driving it, and the switch or output stage on the end of it. Leave any of those out and the measured time runs long.
The whole path, not only the resistor you drew.
The value at your working voltage, which is not the value on the label for a class 2 ceramic.
Sets the voltages and the currents, never the timing.
Default 20% — IEC 60062 tolerance letter M (±20%) — the code an aluminum electrolytic usually carries. Letter J is ±5% and K is ±10%. Class 1 ceramics reach ±1% and hold it over temperature; class 2 ceramics such as X7R meet their tolerance only at 25 °C with no bias, and lose capacitance with both.
TIME CONSTANT τ
10.0000 ms
THE SAME NETWORK AS A CORNER
15.9155 Hz
| Settled to 99.326% at 5τ | 50.0000 ms |
|---|---|
| Rise time, 10% to 90% — τ × ln 9 | 21.9722 ms |
| Rise time × corner frequency | 0.3497 |
| Current at the instant of the step, V ÷ R | 500.00 µA |
| Energy in the capacitor when charged, ½CV² | 12.5 µJ |
| Energy the resistor turns to heat getting there | 12.5 µJ |
| τ across a ±20% capacitor | 8.0000 ms to 12.0000 ms |
The two energy rows are equal and that is exact, not a coincidence: charging a capacitor through a resistor from a fixed source always dumps as much energy into the resistor as it stores in the capacitor, whatever the resistance is. Making the resistor smaller makes it hotter faster; it does not make the charge cheaper. That is why a switching regulator exists.
Any point on the curve, either direction
Percentages here are of the step, measured from where the curve started. Charging 90% and discharging to 10% are the same instant on the same curve.
The same exponential, mirrored.
63.21% is one τ by definition — the rest is arithmetic on the same curve.
Measured from the instant of the step.
TIME TO GET THERE
23.0259 ms
2.3026 time constants, at 4.5000 V
WHERE IT HAS GOT TO
91.792%
4.5896 V of 5 V, with 8.208% of the step still to go.
The curve, in time constants
The same eight rows for every RC network there has ever been — the percentages depend on nothing but the exponential. The two right-hand columns are yours.
| Multiple | Charged to | Discharged to | Elapsed | Charging voltage |
|---|---|---|---|---|
| 0τ | 0.000% | 100.000% | 0.0000 µs | 0.0000 V |
| 1τ | 63.212% | 36.788% | 10.0000 ms | 3.1606 V |
| 2τ | 86.466% | 13.534% | 20.0000 ms | 4.3233 V |
| 3τ | 95.021% | 4.979% | 30.0000 ms | 4.7511 V |
| 4τ | 98.168% | 1.832% | 40.0000 ms | 4.9084 V |
| 5τ | 99.326% | 0.674% | 50.0000 ms | 4.9663 V |
| 6τ | 99.752% | 0.248% | 60.0000 ms | 4.9876 V |
| 7τ | 99.909% | 0.091% | 70.0000 ms | 4.9954 V |
generated from v(t) = V(1 − e^(−t/RC)), the solution of the RC step response — not a transcribed chart. Five time constants is a convention, not a standard: no document fixes it, and it survives because the 0.674% left unresolved at that point is already smaller than the ±20% the capacitor itself is guaranteed to. Waiting for a sixth constant measures something the parts do not promise.
How to work out when an RC network has actually arrived
Two components, one product, and three questions that fall out of it: how long, how far, and at what frequency.
Add up the whole resistance in the path
The time constant is set by everything the charging current flows through, not by the resistor on the schematic: the source impedance of whatever drives the node, the on-resistance of the switch or output stage, and the series resistor together. A 10 kΩ resistor driven by a 1 kΩ source is an 11 kΩ network and runs 10% slow, which is exactly the size of discrepancy people chase on a scope for an afternoon.
Use the capacitance at your working voltage
A class 2 ceramic marked 1 µF can be half that with a few volts of DC bias across it, and an aluminum electrolytic is guaranteed only to a ±20% window in the first place. Put the honest figure in, then set the tolerance field to what the part actually carries and read the band the time constant lies in — a 1% resistor beside a 20% capacitor buys you nothing.
Ask the curve the question you actually have
If it is a reset line or an ADC settling into a sample, you want the time to reach a percentage. If it is a debounce or a supervisory delay, you want the percentage reached after a fixed time. Both are on the same curve and both are here, and the answer prints in time constants as well as in seconds so you can sanity-check it against the table below.
Technical specifications
| Table generation | The eight tau rows come from v(t) = V(1 − e^(−t/RC)) evaluated in the page, not from a transcribed chart — 1τ is 63.212%, 3τ is 95.021%, 5τ is 99.326% |
|---|---|
| Five tau | A convention, not a standard. It survives because the 0.674% left unresolved is already inside a ±20% capacitor's own tolerance |
| Rise time relation | 10% to 90% is τ × ln 9 = 2.1972 τ, and rise time × corner frequency is ln 9 ÷ 2π = 0.3497 — the origin of the 0.35 rule of thumb |
| Corner frequency | 1 ÷ 2πRC, the −3 dB point of the same network read as a first-order filter, printed beside the time constant rather than on another page |
| Energy identity | Charging through a resistor stores ½CV² in the capacitor and dissipates exactly ½CV² in the resistor, whatever the resistance is |
| Component ranges | 1 mΩ to 1 TΩ and 1 fF to 100 F, which spans a gate-drive network at one end and a supercapacitor backup at the other |
| Percentage range | 0.0001% to 99.9999%. 100% is refused: the exponential approaches its end value asymptotically and never reaches it |
| Privacy | Nothing you type is transmitted; the exponential is evaluated in the page on each keystroke |
Frequently asked questions
Why is 63.2% the number everyone quotes for one time constant?
Because 1 − 1/e is 0.63212, and e is what falls out of the differential equation rather than anything anyone chose. The current into a capacitor is proportional to the voltage still missing, which makes the rate of change proportional to what remains — the definition of exponential decay. One time constant is simply the time at which the exponent reaches −1, so the figure is a property of the mathematics and is identical for every RC network in existence.
Is five time constants a standard?
No, it is a working convention with a good reason behind it. At 5τ the step is 99.326% resolved and 0.674% remains, which is already well inside the ±20% tolerance an aluminum electrolytic carries — so waiting for a sixth constant is measuring precision the parts never promised. Where a real specification exists, such as an ADC settling to within one least significant bit, the required number of constants comes out of the resolution instead: 12 bits needs 12 × ln 2 = 8.32τ, 16 bits 11.09τ.
How does the time constant relate to the cutoff frequency?
They are the same network described in two domains, related by fc = 1 ÷ 2πτ. A 10 kΩ and 1 µF pair is a 10 ms constant and a 15.92 Hz corner at once, and which one you quote depends only on whether you are looking at a step or a spectrum. The 2π is the part people drop: 1/τ is the angular frequency in radians per second, and dividing by 2π converts it to hertz.
My measured charge time is longer than the calculator says. Why?
The most common cause is resistance you did not count — the output impedance of the driving stage, a switch's on-resistance or a current-limited supply all add to R. The next most common is the capacitor being smaller than its label under bias, which makes the network faster rather than slower, so a slow result usually points at resistance. A distant third is scope loading: a 10 MΩ probe on a 1 MΩ network is a real 9% error, and a 1× probe with 1 MΩ input halves the network entirely.
Does the supply voltage change the timing?
Not at all. The time constant is R times C and contains no voltage term, so a 5 V step and a 24 V step through the same network take exactly the same time to reach the same percentage. What the voltage changes is the current at the instant of the step, which is V ÷ R and is the figure that decides whether the driving stage can actually deliver it, and the energy the resistor has to absorb.
How much energy does charging a capacitor waste?
Exactly as much as it stores — ½CV² into the capacitor and ½CV² into the resistor — and the resistance does not change that ratio, only how fast the loss happens. It is a surprising result that follows directly from integrating the resistor's dissipation over the whole charge. It is also the reason a large bulk capacitor charged through a resistor is a heat problem rather than an efficiency one, and why anything that cares about efficiency uses an inductor and a switch instead.
Can I use this for an RL circuit?
The shape of the curve is identical but the constant is not: for an inductor and a resistor the time constant is L ÷ R rather than R × C, so a larger resistance makes an RL network faster and an RC network slower. Every percentage in the table below still applies, since both are first-order systems governed by the same exponential — only the product that sets the timescale differs.
About the exponential, the settling convention, and the part that dominates the error
An RC network is the simplest system in electronics with a memory, and the reason it behaves the way it does is a single sentence: the current that charges the capacitor is proportional to the voltage still missing. That makes the rate of change proportional to what remains, which is the definition of exponential approach, and it is why every percentage in the table on this page is a property of mathematics rather than of any particular pair of components. The product R × C sets only the timescale. Change both parts by a factor of ten in opposite directions and nothing about the shape moves.
The same product is also a frequency, and treating those as separate subjects is the single most common way of misunderstanding a first-order network. A 1 ms constant is a 159 Hz corner; a debounce network that settles comfortably in a millisecond is also a filter that has thrown away everything above a few hundred hertz, which is the point of it. That equivalence has a useful corollary in the rise time: 10% to 90% takes ln 9 constants, so multiplying a rise time by the corner frequency always gives ln 9 ÷ 2π = 0.3497 — the origin of the “0.35 divided by the bandwidth” rule every scope manual quotes without deriving. Read the same network at a frequency rather than at an instant and the impedance calculator gives it a magnitude and a phase.
What decides the accuracy of a real timing network is almost never the arithmetic. It is the capacitor: an aluminum electrolytic carries the IEC 60062 letter M, ±20%, and loses capacitance as it ages and as it warms; a class 2 ceramic such as X7R meets its tolerance only at 25 °C with no DC bias and can lose half its value with a few volts across it. Against that, resistor tolerance is noise — which is why this page prints the band the time constant lies in rather than a single figure, and why a precision delay uses a crystal and a counter instead of an RC pair. The resistor color code calculator handles the other half of the network, and where the RC is charging through a divider rather than a single resistor, the voltage divider calculator works out the Thevenin resistance that actually sets the constant. On the supply side, the battery capacity calculator covers the far end of the same time axis, where storage is measured in hours rather than microseconds.
Where the curve is evaluated
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
The tau table is generated in the page from the exponential itself, so it is correct offline and cannot go stale — there is no chart file behind it to get out of step with the arithmetic.