RC Time Constant Calculator
Find the time constant and voltage response of a resistor-capacitor circuit.
Calculate
Formulas
τ = R × CTime constant in seconds
V(t) = V0 × (1 - e-t/τ)Charging voltage at time t
RC Time Constant
After 1τ: 63.2% charged. 2τ: 86.5%. 3τ: 95.0%. 5τ: 99.3% (full). Used in filters, timing circuits, debouncing, and power supply smoothing.
What the RC Time Constant Means
When a capacitor charges or discharges through a resistor, it does so exponentially, not instantly. The time constant tau (τ) sets the speed of that process:
τ = R × Cτ is the time constant in seconds, R is resistance in ohms, and C is capacitance in farads.
After one time constant the capacitor reaches about 63% of the final voltage when charging (or falls to 37% when discharging). It is considered fully charged or discharged after about five time constants.
Worked Example
R = 10 kΩ, C = 100 µF:
τ = 10000 × 0.0001 = 1 second
The capacitor reaches 63% of supply in 1 s, and is essentially full after ~5 s.
Charge/Discharge Reference
| Time | Charging (% of final) | Discharging (% remaining) |
|---|---|---|
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 3τ | 95.0% | 5.0% |
| 5τ | 99.3% | 0.7% |
Frequently Asked Questions
Why 63%?
It comes from the exponential 1 − e⁻¹ = 0.632. The maths of charging produces this fixed fraction after exactly one time constant, regardless of the actual R and C values.
What are RC circuits used for?
Timing (delays, oscillators), filtering (smoothing noise), and debouncing switches. The time constant sets the cutoff frequency of an RC filter as well.
When is the capacitor "fully" charged?
Mathematically never, but after 5τ it is within 1% of the final value, which is treated as complete for practical purposes.