How to use it
- Choose Circuit: Charging or Discharging.
- Type the Supply voltage (or starting voltage), the Resistor R and the Capacitor C.
- Type the Time t (seconds) you want to check and the Level to reach (%).
- Read Time constant τ and Voltage at time t, then look at the chart to see the curve from 0 to 5τ.
The formulas
A resistor and a capacitor in series change their voltage exponentially. The product R × C is the time constant τ: after one τ a charging capacitor has reached 63.2 % of its final voltage, and a discharging one has fallen to 36.8 % of its start.
τ = R × C
Charging: V(t) = Vs × (1 − e^(−t ÷ τ))
Discharging: V(t) = V0 × e^(−t ÷ τ)
Time to reach p %:
Charging: t = −τ × ln(1 − p)
Discharging: t = −τ × ln(p)
Low-pass cutoff: f = 1 ÷ (2π × R × C)- After 5τ the capacitor is more than 99.3 % charged, and less than 0.7 % of the starting voltage remains. Most practical timing uses 5τ as the 'done' point.
- The cutoff frequency is the point where a low-pass RC filter passes half the power, which is 0.707 of the voltage.
- The chart covers 0 to 5τ in 25 equal steps.
What this calculator does not cover
- The source resistance and the leakage of a real capacitor, which lengthen the charging time.
- Circuits with more than one resistor or capacitor, and RC filters with a load across the output.
- Pulses that start before the capacitor is empty: the starting voltage then depends on the earlier cycle.
Worked example: 10 kΩ and 100 µF charged from 5 V
τ = 10 kΩ × 100 µF = 1 s. The cutoff of a low-pass made of the same parts is 1 ÷ (2π × 1 s) = 159.2 mHz.
After 2 s the capacitor voltage is 5 V × (1 − e^(−2)) = 4.323 V.
The voltage reaches 63.2 % of the supply, 3.16 V, after one time constant. The exact time to reach 63.2 % is −1 s × ln(1 − 0.632) = 999.7 ms, because 0.368 is just above e⁻¹.
Frequently asked questions
What does the time constant tell me?
It is the time for a charging capacitor to reach about 63 % of its final voltage, or a discharging one to fall to about 37 % of its start. Five time constants is the time for it to be practically full or empty.
Why does the chart run from 0 to 5τ?
After 5τ a charging capacitor is more than 99.3 % charged and a discharging one has lost more than 99.3 % of its voltage, so the curve has effectively finished.
How is the cutoff frequency of a filter found?
Use f = 1 ÷ (2π × R × C) with the resistor and capacitor of the filter. A signal above this frequency is weakened, and one below it passes.
Can I enter the capacitance in nanofarads?
Yes. Type 100n for 100 nF or 2µ2 for 2.2 µF. The calculator converts the prefixes before the calculation, so τ comes out in seconds.
What is the difference between charging and discharging?
Charging starts from zero and approaches the supply voltage; discharging starts from the stored voltage and approaches zero. Both follow the same time constant, so the same R and C give the same speed.
Sources
Figures and text last checked on Tuesday, November 10, 2026.