RC Time Constant Calculator
Calculate RC time constant (tau), 63%, 90%, 99% charge/discharge times, and cutoff frequency.
How it works
An RC circuit composed of a resistor (R) and a capacitor (C) has a characteristic time constant denoted by the Greek letter tau (τ).
The time constant dictates how quickly the capacitor charges or discharges through the resistor:
τ = R × C
During charging from 0 V to supply voltage V, the capacitor voltage follows V(t) = V × (1 - e^(-t/τ)):
- 63.2% charge (or 63.2% discharged): reached at 1.0τ (t = τ)
- 90.0% charge (or 90.0% discharged): reached at 2.3τ (t = ln(10) × τ ≈ 2.303τ)
- 99.0% charge (or 99.0% discharged): reached at 4.6τ (t = ln(100) × τ ≈ 4.605τ)
- 99.3% charge: practical steady state reached at 5.0τ
In an RC low-pass or high-pass filter, the cutoff frequency (fc, or -3 dB point) is:
fc = 1 / (2π × R × C)
Worked example
If you have a 10 kΩ resistor and a 1 μF capacitor in series:
τ = 10,000 Ω × 0.000001 F = 0.01 seconds (10 ms)
Charging and discharging milestones for this circuit:
- 63.2% voltage: 1τ = 10.0 ms
- 90.0% voltage: 2.3τ ≈ 23.03 ms
- 99.0% voltage: 4.6τ ≈ 46.05 ms
- 5τ (steady state): 50.0 ms
The cutoff frequency for this filter is:
fc = 1 / (2π × 10,000 × 0.000001) ≈ 15.92 Hz
Frequently Asked Questions
What are the key charge and discharge times (63%, 90%, 99%)?
Capacitor voltage follows an exponential curve: 1τ reaches 63.2%, 2.3τ reaches 90.0%, 4.6τ reaches 99.0%, and 5τ reaches 99.3% (practical full charge or discharge).
Is there an LC time constant?
No. An RC circuit has τ = R × C and an RL circuit has τ = L / R. An ideal LC circuit does not dissipate energy in resistance and does not have an exponential time constant; instead, it has a resonant frequency f = 1 / (2π√(LC)) where energy oscillates between the inductor and capacitor. To calculate resonant tank frequencies, visit our LC Resonance Calculator.
Why use the cutoff frequency?
The cutoff frequency indicates where the filter begins to attenuate the signal by -3 dB (half power). For a low-pass filter, frequencies below fc pass through, while frequencies above fc are attenuated.
Sources
- RC Circuit transient analysis and exponential charging equations.
- First-order filter transfer functions (fc = 1 / (2πRC)).
Results are for engineering assistance. Verify important calculations and check official datasheets. See the Engineering Disclaimer.