RC Time Constant Calculator
How fast a capacitor charges or discharges through a resistor — the time constant, and the voltage at any moment.
The time constant τ is simply R × C, and it is the time to reach about 63.
How the rc time constant calculator works
The time constant τ is simply R × C, and it is the time to reach about 63.2% of the final voltage when charging, or to fall to 36.8% when discharging. Both are 1 − 1/e and 1/e respectively, which is where those odd-looking percentages come from.
The rule of thumb worth remembering is five time constants: after 5τ the capacitor is within 0.7% of its final value, which is close enough to call it settled. It is the number behind timer circuits, debounce delays and how long a power supply holds up when the mains drops.
Formula: τ = R × C; V(t) = V₀(1 − e^(−t/τ)) charging
Worked examples
| Inputs | Time constant τ | Note |
|---|---|---|
| 10 kΩ and 100 µF | 1 s | τ = 1 s, so 3.16 V after one second |
| A fast RC filter | 0.0001 s | τ = 0.1 ms, cut-off 1.6 kHz |
| A long timer | 470 s | τ = 470 s — nearly eight minutes |
FAQFrequently asked questions
What is the RC time constant?
τ = R × C, the time to charge to 63.2% of the supply or discharge to 36.8%.
Why 63.2%?
It is 1 − 1/e. The exponential curve makes those the natural landmarks rather than round numbers.
When is a capacitor fully charged?
After about five time constants it is within 0.7% of the supply, which is treated as settled.
How does this relate to filters?
The same RC pair is a low-pass filter with a −3 dB cut-off at 1 ÷ (2πτ).
How do I get a longer delay?
Increase either the resistance or the capacitance — the product is what counts.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.