How to use the RC time constant calculator
- Choose Charging (capacitor starts empty and charges towards the supply through R) or Discharging (capacitor starts full and empties through R).
- Enter R, C and the supply voltage, with their units.
- Read the time constant τ and the times to reach 63%, 90%, 99% and "practically done" (5τ).
- Use the second card to find the voltage at any time t, or the time to reach a voltage — for example, how long until a capacitor reaches an Arduino's logic-high threshold.
The curve shows the selected case in orange, the opposite case dashed, a black dot at τ and a blue dot at your chosen time.
Formula
τ = R × C (ohms × farads = seconds)
Charging: V(t) = Vs × (1 − e^(−t/τ)) t = −τ × ln(1 − V/Vs)
Discharging: V(t) = Vs × e^(−t/τ) t = −τ × ln(V/Vs)
Current: I(t) = (Vs ÷ R) × e^(−t/τ)
The capacitor changes quickly at first and then slows down, because the voltage left across the resistor — and so the current — keeps shrinking.
| Time | Charging (% of Vs) | Discharging (% of Vs) |
|---|---|---|
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 2.3τ | 90.0% | 10.0% |
| 3τ | 95.0% | 5.0% |
| 4.6τ | 99.0% | 1.0% |
| 5τ | 99.3% | 0.7% |
Where RC timing is used
- Power-on delays and reset circuits — a resistor and capacitor hold a pin low for a short time after power-up.
- Switch debouncing — a small RC smooths out the bouncing of a push button before it reaches a microcontroller.
- 555 timers — the 555 timer calculator uses the same charging law; 0.693 = ln 2 is the time to charge from ⅓ to ⅔ of the supply.
- Filters — the cutoff frequency of an RC filter is fc = 1 ÷ (2πτ). See the RC filter cutoff calculator.
Common mistakes
- Wrong units. τ comes out in seconds only when R is in ohms and C in farads. 100 µF is 0.0001 F, not 100.
- Expecting "full" after 1τ. At 1τ the capacitor is only 63% charged. Use 5τ as full.
- Ignoring tolerance. Electrolytic capacitors are often ±20% off, so a "1 second" delay may be 0.8 s or 1.2 s.
- Loading the capacitor. A multimeter (often 10 MΩ input resistance) or the circuit you feed also discharges the capacitor. This matters most with large resistors.
Learn more
Find the value printed on your capacitor with the capacitor code calculator, and read capacitors explained for beginners for the theory behind charging and discharging. Looking for more hands-on ideas? Try our electronics experiments for kids or pick up an electronics kit.
