Free RC Time Constant Calculator (τ = R·C)
This RC time constant calculator finds the time constant τ of a resistor–capacitor (RC) circuit from the resistance R and capacitance C using the formula τ = R·C. Enter R in ohms and C in microfarads (µF), and the calculator converts the capacitance to farads, returns τ in both seconds and milliseconds, and reports the 5τ interval that is conventionally treated as a full charge or discharge. The time constant tells you how quickly a capacitor charges through or discharges through a resistor, which governs the timing of RC filters, timer circuits, debounce networks, and sensor sampling.
Enter resistance and capacitance to find the RC time constant τ = R·C.
τ = R·C, with R in ohms and C in farads (µF × 10⁻⁶). After one τ the capacitor reaches 63.2% of the supply voltage; after 5τ it is within ~0.7% of full charge, treated as fully charged.
Quick answer
The RC time constant is τ = R·C, where R is resistance in ohms and C is capacitance in farads, giving τ in seconds. For example, R = 1000 Ω and C = 100 µF (1×10⁻⁴ F) give τ = 1000 × 1×10⁻⁴ = 0.1 s = 100 ms. After one time constant the capacitor reaches about 63.2% of the supply voltage, and after five time constants (5τ ≈ 0.5 s here) it is considered fully charged.
Formula & method
Time constant
τ = R · C
- τ — time constant in seconds (s)
- R — resistance in ohms (Ω)
- C — capacitance in farads (F); µF × 10⁻⁶
Capacitance entered in µF is converted to farads before multiplying: C(F) = C(µF) × 10⁻⁶.
Charging / discharging and settling time
V(t) = V₀·(1 − e^(−t/τ)) • full charge ≈ 5τ
- V(t) — capacitor voltage at time t while charging
- V₀ — final (supply) voltage
- e — Euler's number ≈ 2.71828
At t = τ the capacitor reaches 63.2% of V₀; at 5τ it is within ~0.7% of V₀, the usual 'fully charged' threshold.
Examples
- Input
- R = 1000 Ω, C = 100 µF
- Result
- τ = 0.1 s = 100 ms, 5τ ≈ 0.5 s = 500 ms
- Why
- Convert capacitance: 100 µF = 100 × 10⁻⁶ = 1×10⁻⁴ F. Then τ = R·C = 1000 × 1×10⁻⁴ = 0.1 s, which is 100 ms. The full charge time is 5τ = 5 × 0.1 = 0.5 s = 500 ms.
- Input
- R = 10000 Ω, C = 47 µF
- Result
- τ = 0.47 s = 470 ms, 5τ ≈ 2.35 s = 2350 ms
- Why
- 47 µF = 47 × 10⁻⁶ = 4.7×10⁻⁵ F. τ = 10000 × 4.7×10⁻⁵ = 0.47 s = 470 ms. After 5τ = 5 × 0.47 = 2.35 s the capacitor is treated as fully charged.
- Input
- R = 470 Ω, C = 1 µF
- Result
- τ = 0.00047 s = 0.47 ms, 5τ ≈ 0.00235 s = 2.35 ms
- Why
- 1 µF = 1×10⁻⁶ F. τ = 470 × 1×10⁻⁶ = 4.7×10⁻⁴ s = 0.47 ms. The circuit settles after 5τ = 2.35 ms, fast enough for many audio and debounce applications.
- Input
- R = 2200 Ω, C = 10 µF, charging from a 5 V supply
- Result
- τ = 0.022 s = 22 ms; V(τ) ≈ 0.632 × 5 = 3.16 V
- Why
- 10 µF = 1×10⁻⁵ F, so τ = 2200 × 1×10⁻⁵ = 0.022 s = 22 ms. After one τ the capacitor reaches 63.2% of 5 V, which is about 3.16 V; after 5τ ≈ 110 ms it is essentially at 5 V.
When to use this tool
- Designing or analyzing RC low-pass and high-pass filters, where the time constant sets how fast the circuit responds and relates to the cutoff frequency f = 1/(2πτ).
- Building delay, timing, or debounce circuits and needing to know how long a capacitor takes to charge or discharge through a resistor.
- Estimating the settling time of a sample-and-hold or sensor front end, where 5τ is the practical 'fully settled' interval.
- Choosing resistor and capacitor values to hit a target charge time, by working backward from τ = R·C.
- Teaching or learning the exponential charge and discharge behavior of RC circuits and the meaning of the 63.2% and 5τ benchmarks.
Common mistakes
- Forgetting to convert microfarads to farads. C must be in farads for τ to come out in seconds, so 100 µF is 100 × 10⁻⁶ = 1×10⁻⁴ F, not 100. This calculator does the conversion for you when you enter C in µF.
- Mixing capacitance prefixes. 1 µF = 1000 nF = 1,000,000 pF. Entering a value meant for nanofarads or picofarads into the µF field will be off by a factor of 1000 or a million.
- Assuming the capacitor is fully charged after one time constant. After one τ it has only reached 63.2% of the final voltage; it takes about five time constants (5τ) to be considered fully charged or discharged.
- Using kilo-ohms or mega-ohms without converting. R must be in plain ohms here, so a 10 kΩ resistor is 10,000 Ω and a 1 MΩ resistor is 1,000,000 Ω.
- Treating τ as the period or frequency of a filter. For a simple RC low-pass filter the −3 dB cutoff is f = 1 / (2πRC) = 1 / (2πτ), which is related to τ but not equal to it.
Frequently asked questions
What is the RC time constant?
The RC time constant, written with the Greek letter tau (τ), is the product of resistance and capacitance: τ = R·C. With R in ohms and C in farads, τ comes out in seconds. It is the time it takes a capacitor charging through a resistor to reach about 63.2% of the final voltage, and it characterizes how fast the RC circuit responds.
How do I calculate the time constant of an RC circuit?
Multiply the resistance by the capacitance after putting both in base SI units. For example, with R = 1000 Ω and C = 100 µF, first convert the capacitance: 100 µF = 1×10⁻⁴ F. Then τ = 1000 × 1×10⁻⁴ = 0.1 s, or 100 ms. This calculator converts µF to farads automatically and shows τ in seconds and milliseconds.
Why is 5 time constants considered fully charged?
A capacitor charges exponentially, so it never mathematically reaches 100%, but it gets very close very quickly. After 1τ it is at 63.2%, after 3τ at 95.0%, and after 5τ at about 99.3% of the final voltage. Engineers therefore treat 5τ as the practical 'fully charged' (or fully discharged) time.
What does 63.2% have to do with the time constant?
The 63.2% figure comes directly from the charging equation V(t) = V₀(1 − e^(−t/τ)). At t = τ, the exponent is −1, so e⁻¹ ≈ 0.368 and the capacitor has reached 1 − 0.368 = 0.632, or 63.2% of the supply voltage. That is the defining property of the time constant.
How is the time constant related to a filter's cutoff frequency?
For a simple first-order RC filter, the −3 dB cutoff frequency is f = 1 / (2πRC) = 1 / (2πτ). So a larger time constant means a lower cutoff frequency and slower response, while a smaller τ gives a higher cutoff and faster response. The time constant and the cutoff frequency describe the same circuit from the time and frequency domains.
Does the time constant change if I add a second resistor or capacitor?
Yes. For resistors and capacitors in series or parallel you first combine them into a single equivalent R and C, then use τ = R·C. Capacitors in parallel add (so C increases and τ grows), while resistors in series add (R increases and τ grows). Series capacitors and parallel resistors reduce the effective value and shorten τ.
Sources & references
- RC time constant - Wikipedia
- Capacitor Charging and the RC Time Constant - HyperPhysics
- RC Charging Circuit and the RC Time Constant - Basic Electronics Tutorials
External references open in a new tab. We are independent and not affiliated with these organizations.
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