RC Time Constant Calculator
Calculate RC circuit time constant and capacitor charging milestones.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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The RC time constant (tau, τ) determines how quickly a capacitor charges or discharges through a resistor. This calculator finds τ and the key charging milestones.
- Enter resistance. Select the unit (Ω, kΩ, or MΩ) and enter the resistance value. This is the resistance the capacitor charges through.
- Enter capacitance. Select the unit (F, mF, µF, nF, or pF) and enter the capacitance value.
- Read the results. The time constant τ = R × C, the 5τ (full charge) time, and the percent charged at 1τ, 3τ, and 5τ.
The charging percentages are fixed by mathematics: at 1τ the capacitor is always 63.2% charged; at 3τ it is 95.0%; at 5τ it is 99.3%. These values do not change regardless of the R and C values.
About RC Time Constants
The voltage across a charging capacitor follows V(t) = Vs × (1 - e^(-t/τ)), where τ = R × C. For discharging: V(t) = V₀ × e^(-t/τ). The capacitor is considered fully charged after 5τ (99.3%). For practical purposes, 3τ (95%) is often acceptable.
RC circuits are used as low-pass filters (cutoff frequency fc = 1/(2πRC)), high-pass filters, integrators, differentiators, oscillator timing elements, and debounce circuits for switches. The 555 timer uses RC timing to set its output pulse width and frequency.
Frequently Asked Questions
What is the RC time constant and how is it calculated?
The time constant τ (tau) = R × C, where R is in ohms and C is in farads. It represents the time for the capacitor to charge to 63.2% of the supply voltage, or discharge to 36.8% of its initial voltage. For example, a 10 kΩ resistor with a 100 µF capacitor gives τ = 10,000 × 0.0001 = 1 second. The capacitor reaches 63.2% charged after 1 second, and is essentially fully charged (99.3%) after 5 seconds.
Why does it take 5 time constants to fully charge a capacitor?
The charging curve is exponential (V = Vs × (1 - e^(-t/τ))), which asymptotically approaches the supply voltage but never quite reaches it mathematically. After 5τ, the capacitor is at 99.3% — close enough for all practical purposes. After 3τ it is at 95%, and after 7τ it would be at 99.91%. Most engineering calculations use 5τ as the definition of "fully charged" as a practical rule.
How do I use an RC circuit as a low-pass filter?
A simple RC low-pass filter passes low-frequency signals while attenuating high frequencies. The cutoff frequency (where the output is 3 dB below input) is fc = 1 / (2π × R × C). Below fc, signals pass with little attenuation. Above fc, attenuation increases at -20 dB per decade. For example, a 10 kΩ resistor with 100 nF gives fc = 1/(2π × 10,000 × 1e-7) ≈ 159 Hz, filtering out signals above this frequency.
What RC values should I use for audio filtering?
For audio low-pass filtering at 20 kHz (the upper limit of human hearing), use fc = 20 kHz: R × C = 1 / (2π × 20,000) ≈ 8 µs. A 1 kΩ resistor with 8 nF or a 10 kΩ resistor with 800 pF would work. For a subsonic high-pass filter at 20 Hz: R × C = 1 / (2π × 20) ≈ 8 ms. A 100 kΩ resistor with 80 nF (use 82 nF standard value) would set this cutoff. Use the Resonant Frequency Calculator for LC filter designs at higher frequencies.