What the RC Time Constant Calculator does
This calculator gives the time constant of a resistor and capacitor, the time to reach any percentage of the final voltage, the charge and discharge curves, and the first-order cutoff frequency with its gain and phase. One pair of components answers two apparently different questions - how long does it take, and what does it filter - because they are the same question asked in different units.
The time constant tau = R x C is the time to get 63.2% of the way to the final voltage. After five time constants a capacitor is 99.3% charged, which is why circuits are usually called settled at 5 tau.
How to use it
- Enter the resistance and the capacitance. Shorthand is understood: 10k, 4k7, 100n, 2u2.
- Enter the supply voltage if you want the curve drawn in volts rather than as a fraction.
- Read the time constant and the cutoff frequency - they are two views of the same pair.
- Enter a percentage to find the time to reach it, which is what you need for a delay, a debounce or a power-on reset.
- Enter a target cutoff frequency to be told which capacitor to use with your resistor, or which resistor to use with your capacitor, with the nearest preferred values.
Reading the results
An RC never actually arrives. It approaches the final voltage asymptotically, so every question has to be phrased as a percentage: 63.2% at 1 tau, 95.0% at 3, 99.3% at 5.
The cutoff frequency is the -3 dB point, where the output is 0.707 of the input and the phase shift is 45 degrees. It is not a wall: an octave above it the response is only down about 7 dB, because a first-order filter rolls off at 6 dB per octave.
Charging and discharging share the same time constant only if the resistance is the same in both directions. A diode across the resistor, or a circuit that charges through one path and discharges through another, has two different time constants.
Worked example: a 10 kOhm resistor with a 100 nF capacitor
tau = 10,000 x 100e-9 = 1 ms. After 1 ms the capacitor is at 63.2% of the supply, after 3 ms at 95.0%, and after 5 ms at 99.3%. Reaching 90% takes -tau x ln(0.1) = 2.303 ms.
As a filter the same pair has fc = 1 / (2 pi x 0.001) = 159.15 Hz. At that frequency a low-pass built from it passes 0.707 of the input - exactly -3.01 dB - with 45 degrees of lag. At 1.59 kHz, ten times the cutoff, it is down about 20 dB.
Used as a switch debounce on a 5 V rail, the same 1 ms is a sensible bounce window for a tactile switch, but note that the switch shorts the capacitor when it closes: the discharge is nearly instantaneous, so the circuit is asymmetric unless a second resistor is fitted in series with the switch.
Formulas and scoring rules
- Time constant
tau = R x COhms times farads gives seconds.- Charging
v(t) = Vf x (1 - e^(-t/tau))- Discharging
v(t) = V0 x e^(-t/tau)- Time to a percentage
t = -tau x ln(1 - p)p as a fraction. 63.2% is exactly 1 tau; 90% is 2.303 tau; 99% is 4.605 tau.- Cutoff frequency
fc = 1 / (2 pi R C) = 1 / (2 pi tau)- Low-pass response
|H| = 1 / sqrt(1 + (f/fc)^2), phase = -arctan(f/fc)At fc: -3.01 dB and -45 degrees.
The same components, two jobs
A designer thinking about a delay sees tau in milliseconds; a designer thinking about noise sees fc in hertz. They are reciprocals through 2 pi, and it is often worth converting deliberately. A power-on reset with a 100 ms time constant is also a 1.6 Hz low-pass, which tells you at once that it will ignore mains hum and not much else.
Going the other way is just as useful. An anti-alias filter specified at 1 kHz is a 160 microsecond time constant, so any step at its input takes about 800 microseconds to settle - which may be longer than the time between samples.
Where the simple model stops being true
The formula assumes an ideal resistor, an ideal capacitor and a source with no impedance of its own. Real circuits add source resistance in series (which lengthens tau) and load resistance in parallel (which shortens it and lowers the final voltage).
The capacitor matters more than people expect. An electrolytic's ESR adds to R, and a Class 2 ceramic can lose most of its capacitance under DC bias - a 10 uF X5R at its rated voltage may behave as 3 uF, making a timing circuit run three times too fast. For anything where the time matters, use a film or C0G capacitor and read the bias curve.
Limitations: what the result does not prove
- It models an ideal single-pole RC. Leakage, dielectric absorption, ESR and the source's own impedance all shift the real time constant.
- Capacitor tolerance is typically 10-20%, and a Class 2 ceramic can be far further out under DC bias, so a calculated time constant is a target rather than a specification.
- The filter response shown is first order only. A cascade of two RC sections is not simply twice as steep, because each loads the other, unless they are buffered.
- For timing that must be accurate - a baud rate, a sample clock, a protection delay - a crystal, an RC oscillator with internal trimming or a timer peripheral is the right answer, not a discrete RC.
Privacy: where your data goes
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Standards and sources
- Texas Instruments - Op amps for everyone design reference - checked 19 Sep 2026
- Analog Devices - RC filter design for a precision SAR ADC front end
- Murata - MLCC DC bias characteristics
Frequently asked questions
What is an RC time constant?
tau = R x C, the time for the capacitor voltage to move 63.2% of the way to its final value. It is the natural unit of the circuit: at 3 tau it is 95% of the way there, and at 5 tau 99.3%, which is usually treated as fully settled.
How long does a capacitor take to fully charge?
Strictly, forever - the curve is exponential and never quite arrives. In practice five time constants (99.3%) is the usual definition of fully charged, and three (95%) is often enough for a logic threshold.
How do I work out the cutoff frequency of an RC filter?
fc = 1 / (2 pi R C). With 10 kOhm and 100 nF that is 159 Hz. At the cutoff the output is 0.707 of the input and lags it by 45 degrees; above it the response falls at 6 dB per octave.
What is the difference between a low-pass and a high-pass RC?
The order of the components. Take the output across the capacitor and low frequencies pass; take it across the resistor and high frequencies pass. Both have the same cutoff frequency for the same R and C, and both roll off at 6 dB per octave.
Why does my RC circuit run faster than calculated?
Usually the capacitor. Class 2 ceramics lose a large fraction of their capacitance under DC bias, and the value is not measured at your operating voltage. Electrolytics also drift with age and temperature. Use a film or C0G capacitor where the timing matters.
How do I choose R and C for a given time constant?
Any pair whose product is right will do, so choose by current and impedance. Low resistance and high capacitance is stiff and noise-immune but draws more current; high resistance and low capacitance is the opposite, and eventually leakage and the next stage's input current dominate. Keeping R between about 1 kOhm and 1 MOhm is a practical range.
What time constant do I need to debounce a switch?
Mechanical switches bounce for a few milliseconds, so 1-10 ms is the usual range - 10 kOhm with 100 nF to 1 uF. Remember that a switch shorting the capacitor discharges it instantly, so add a resistor in series with the switch if you need the delay in both directions.
Does the supply voltage change the time constant?
No. tau depends only on R and C; the voltage scales the curve but not its shape or timing. That is why an RC delay is repeatable across supply voltages, provided the threshold it drives is a fixed fraction of the supply.
Last reviewed by the A2Z.Tools team against the sources listed above.
