Free calculator
RC time constant calculator
A capacitor charging through a resistor fills fast at first, then slower and slower. The time constant, τ = R × C, sets the pace: type a resistance and a capacitance to get τ, how long until it's full, and the voltage at any moment.
10k = 10,000 Ω.
µ or u = micro, n = nano, p = pico.
Time constant, τ = R × C
- Fully charged (5τ)
- 5 s
- Cutoff, f = 1 ÷ (2πRC)
- 0.159 Hz
| After | Time | Charged | Left (discharging) |
|---|---|---|---|
| 1τ | 1 s | 63.2% | 36.8% |
| 2τ | 2 s | 86.5% | 13.5% |
| 3τ | 3 s | 95.0% | 5.0% |
| 4τ | 4 s | 98.2% | 1.8% |
| 5τ | 5 s | 99.3% | 0.7% |
The voltage at any moment
20m = 20 ms.
Capacitor voltage
- That's
- 1.00 τ
The formulas
Charging from 0 V towards a supply Vs, and discharging from Vs:
Each time constant closes about 63% of the gap that's left: 63% after 1τ, 86% after 2τ, 95% after 3τ, and over 99% after 5τ.
A worked example
A 10 kΩ resistor charging a 100 µF capacitor from 5 V:
After one second it's at about 5 × 0.63 = 3.2 V, and after five seconds it's effectively full.
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
“RC charging” is lesson 2 of 5 in Capacitor Caves, Electronics World 3. Free with an account. Lessons unlock in order, so you’ll do the 16 before it first.
Or start from the very first lesson, no account neededThe ideas behind it
- RC time constant explainedτ = R × C: how long a capacitor takes to charge through a resistor, and the 63% rule.
- Capacitor discharge explainedFast at first, then slower: the 37% rule, the formula, and how long a capacitor takes to empty.
- Low-pass filter explainedA resistor and a capacitor that pass the bass and fade the treble, and where the cutoff sits.
- How does a capacitor work?Two plates and a gap: how a capacitor stores charge and energy, and why it blocks steady DC.
Questions people ask
What is the RC time constant?
τ = R × C, in seconds when R is in ohms and C in farads. After one τ a charging capacitor reaches about 63% of the supply; a discharging one falls to about 37%.
How long does a capacitor take to charge fully?
About five time constants: after 5τ it's over 99% charged, close enough to full for almost any circuit. In theory it only approaches the supply and never quite gets there.
How is the time constant related to cutoff frequency?
An RC low-pass filter's cutoff is f = 1 ÷ (2π × R × C). Signals well below it pass, and signals well above it are cut down.
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