Capacitor Charge Time Calculator
- Time constant (τ)
- 1000 ms
- 1τ (63.2%) (3.16 V)
- 999.672 ms
- 2τ (86.5%) (4.325 V)
- 2.002481 s
- 3τ (95.0%) (4.75 V)
- 2.995732 s
- 4τ (98.2%) (4.91 V)
- 4.017384 s
- 5τ (99.3%) (4.965 V)
- 4.961845 s
How to Use the Capacitor Charge Time Calculator
When a capacitor charges through a resistor from a DC supply, voltage rises exponentially rather than instantly. RC timing circuits create delays in reset sequences, soft-start power supplies, debounce networks, and camera flash triggers. Knowing how long the capacitor takes to reach a threshold voltage prevents race conditions in firmware and protects downstream components from inrush current.
The time constant is:
τ (tau) = R × C
Where R is resistance in ohms and C is capacitance in farads. After one time constant (1τ), the capacitor reaches approximately 63.2% of the supply voltage. The charging voltage at time t follows:
V(t) = Vsupply × (1 − e−t/τ)
Rearranging for time to a target percentage: t = −τ × ln(1 − fraction). Five time constants (5τ) bring the capacitor to about 99.3% — often treated as "fully charged" in practice.
Worked example: A 100 µF capacitor charges through a 10 kΩ resistor from 5 V. τ = 10,000 × 0.0001 = 1 second. At t = 1 s, V = 5 × (1 − e−1) ≈ 3.16 V (63%). To reach 95% (4.75 V): t = −1 × ln(0.05) ≈ 3.0 s (3τ). A microcontroller reset pin held low until V exceeds 4.5 V needs t = −1 × ln(0.10) ≈ 2.3 s. Choose a smaller R for faster boot or accept longer reset delay for lower inrush current.
Discharging through the same resistor follows the same τ but voltage decays toward zero. Real capacitors add ESR and leakage; high-speed designs must account for parasitic inductance. Use the RC time constant calculator for milestone tables and the inductor energy calculator for the magnetic analogue in switching converters.
Common capacitor values and 1τ with 10 kΩ
| Capacitance | τ (10 kΩ) | Typical use |
|---|---|---|
| 100 nF | 1 ms | Decoupling, fast filter |
| 1 µF | 10 ms | Bypass, short delay |
| 10 µF | 100 ms | Soft-start, audio coupling |
| 100 µF | 1 s | Power supply hold-up |
| 470 µF | 4.7 s | Bulk filtering |
| 1,000 µF | 10 s | Main rectifier cap |
Frequently asked questions
Exponential charging asymptotically approaches the supply. Each time constant adds a fixed percentage of the remaining gap, never reaching 100% in finite time.
Enter farads, or use common prefixes: microfarads (µF) and nanofarads (nF). The calculator accepts standard SI conversions.
With the same R and C, the time constant τ is identical. Discharge starts at full voltage and decays exponentially toward zero.