RC Time Constant Calculator
Time constant, charge and discharge curves and cutoff frequency for any resistor and capacitor.
The RC Time Constant Calculator runs entirely in your browser. Component values are calculated on your device.
Decode a capacitor marking
About RC Time Constant Calculator
A resistor and a capacitor in series have one number that governs everything they do together: the time constant, tau, which is simply R times C. After one tau a charging capacitor has reached 63.2 per cent of the supply, after five it is at 99.3 and treated as settled. The same pair is also a first-order filter, with a corner frequency of 1/(2πRC), which is why a debounce that settles in five milliseconds is also a low-pass at about 32 hertz. This calculator gives all of it, and works backwards too — name a time constant and it sizes the resistor or the capacitor. Values can be typed the way they appear on a schematic: 4k7, 100n, 2µ2.
Features
- Time constant, five-tau settling time and −3 dB cutoff frequency
- Solves for the resistor or the capacitor when the time constant is the target
- Charge and discharge percentages at one through five time constants
- Time to reach any threshold voltage, charging or discharging
- Stored charge and energy at a given supply voltage
- Accepts engineering notation such as 4k7 and 100n, and SI unit suffixes
- Results auto-scaled to sensible units, from picofarads to farads
How to use the RC Time Constant Calculator
- Enter the resistor and capacitor values, in any notation
- Read the time constant, the settling time and the cutoff frequency
- Set a supply and a threshold voltage to time a charge or discharge
- Or switch mode to size a component for a time constant you need
Example
Input
R = 10k, C = 100n
Output
tau 1 ms · settles in 5 ms · cutoff 159.2 Hz
The classic debounce network: a millisecond time constant, settled well inside a keypress.
Common errors & troubleshooting
- The time constant is a thousand times out. — A prefix has gone missing. 100n and 100u differ by a factor of a thousand — the tool echoes the value it parsed under each field so you can check what it read.
- The capacitor never quite reaches the supply voltage. — It never does. The curve is exponential, so it approaches the supply asymptotically; five time constants gets to 99.3 per cent, which is why that is the conventional settling point.
- The real circuit is slower than the calculation. — Add the source impedance. The driving stage's output resistance is in series with your resistor, and on a slow one that can dominate the time constant.
- An electrolytic capacitor gives timings that drift. — Their tolerance is often −20 to +80 per cent and they age. For timing that has to hold, use film or C0G ceramic, and design so the tolerance does not matter.
Frequently asked questions
- What is the RC time constant formula?
- Tau equals R times C, with resistance in ohms and capacitance in farads, giving a time in seconds. 10 kΩ with 100 nF gives 0.001 seconds, or one millisecond.
- Why is 63.2% the figure quoted for one time constant?
- Because charging follows 1 − e^(−t/τ), and at t = τ that works out to 0.632. The number falls out of the exponential rather than being chosen — the same reason discharge lands on 36.8 per cent.
- How long does a capacitor take to fully charge?
- Strictly, forever, since the curve is asymptotic. In practice five time constants reaches 99.3 per cent and is treated as fully charged in nearly every design.
- How is the cutoff frequency related to the time constant?
- It is 1/(2πτ). A one-millisecond time constant is a 159 Hz corner, so a timing choice and a filtering choice are the same decision made twice.
- How do I pick an RC value for switch debouncing?
- Aim for a time constant a few times longer than the bounce, typically 1 to 10 ms, and check the settling time is still shorter than the fastest press you need to catch. This tool sizes the components for a target directly.
Related tools
All ArrayKit tools