When a capacitor charges or discharges through a resistor, its voltage does not change in a straight line. It moves quickly at first and then more and more slowly, following an exponential curve whose speed is set by one number: the time constant τ = RC. This calculator finds τ, draws the curve, tabulates the voltage at each multiple of τ, and answers the two practical questions — what the voltage is at a given time, and how long it takes to reach a given voltage.
How to use the RC time constant calculator
- Enter the resistance (Ω, kΩ or MΩ) and the capacitance (pF to F).
- Enter the supply voltage for charging, or the capacitor’s starting voltage for discharging, and choose Charging or Discharging.
- Optionally enter a time to read the voltage at that moment.
- Optionally enter a target voltage to find how long it takes to get there.
- Read τ, the 5τ settling time, the initial current, the cutoff frequency and the curve with the 63% point marked.
RC charging and discharging formulas
The current is largest at the start, Vs/R, and decays with the same time constant. One ohm times one farad is exactly one second, so the units work out without conversion factors.
| Time | Charging (% of supply) | Discharging (% remaining) |
|---|---|---|
| 0.5τ | 39.3% | 60.7% |
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 3τ | 95.0% | 5.0% |
| 4τ | 98.2% | 1.8% |
| 5τ | 99.3% | 0.7% |
Worked example
10 kΩ and 100 µF charging from 5 V (the default)
τ = 10,000 Ω × 0.0001 F = 1 s; the capacitor is effectively full after 5τ = 5 s.
At t = 2 s: V = 5 × (1 − e−2) = 4.323 V, and the current has fallen from 500 µA to 67.67 µA.
To reach 4 V: t = −1 s × ln(1 − 4/5) = 1.609 s.
A fast discharge. Switch to discharging with 1 MΩ and 10 nF. Now τ = 10 ms, the voltage drops below 1% within 50 ms, and the same pair used as a filter has a cutoff of 15.92 Hz.
Where the time constant matters
- Delays and timers. Classic 555 timer circuits and microcontroller reset lines use an RC network to hold a pin low or high for a set time.
- Switch debouncing. A small RC filter, often 10 kΩ with 100 nF (τ = 1 ms), smooths out the bounce of a mechanical button.
- Filters. The same pair forms a low-pass filter (output across C) or high-pass filter (output across R) with a −3 dB point at 1/(2πRC).
- Power-supply bleeders. A resistor across a filter capacitor discharges it after shutdown; 5τ tells you how long to wait before the voltage is safe to touch.
Real circuits add complications: electrolytic capacitors have ±20% tolerance, the source and load add resistance, and a comparator may switch at a threshold other than 63%. Use the calculated time as a starting point and measure when it matters.
For the capacitor values themselves, see the capacitor calculator; for the impedance of a capacitor at a given frequency, the reactance and resonance calculator. The logarithms in the time formula can be explored with the logarithm calculator.
These formulas assume ideal parts and a constant source voltage. Capacitors in mains-powered equipment can hold a dangerous charge; follow your local electrical code and use a licensed electrician for installations.
Frequently asked questions
What is the RC time constant?
It is the product of resistance and capacitance, τ = R × C, measured in seconds when R is in ohms and C in farads. After one time constant a charging capacitor reaches about 63.2% of the supply voltage, and a discharging one falls to about 36.8% of its starting voltage.
How long does a capacitor take to fully charge?
In theory it never quite gets there, but after five time constants it is within 0.7% of the supply, which is treated as fully charged. A 10 kΩ resistor and 100 µF capacitor have τ = 1 s, so they charge in about 5 seconds.
How do I find the time to reach a certain voltage?
For charging, t = −τ × ln(1 − V/Vs); for discharging, t = −τ × ln(V/V0). With τ = 1 s and a 5 V supply, reaching 4 V takes −ln(0.2) ≈ 1.609 s. Enter the target voltage and the calculator does this for you.
What is the cutoff frequency of an RC filter?
fc = 1 ÷ (2πRC). At that frequency a simple RC low-pass or high-pass filter passes the signal at 70.7% of its amplitude (−3 dB). A 1 MΩ and 10 nF pair, with τ = 10 ms, has a cutoff of about 15.9 Hz.
Why is it 63.2 percent?
Because 1 − e⁻¹ = 0.632. The capacitor voltage follows an exponential, and one time constant is the point where the exponent equals −1. Each further time constant closes 63.2% of the remaining gap.