RC Time Constant Calculator
Calculate RC time constant (tau = R x C), charge/discharge time at 63% and 99%, and cutoff frequency for low-pass and high-pass RC filter design.
The RC time constant (τ, tau) describes how quickly a capacitor charges or discharges through a resistor. It is one of the most fundamental concepts in electronics, governing everything from filter design to timer circuits to signal smoothing.
Formula: τ = R × C where:
- τ (tau): the time constant in seconds
- R: resistance in ohms (Ω)
- C: capacitance in farads (F)
Charging voltage over time: V(t) = V_supply × (1 − e^(−t/τ))
Discharging voltage over time: V(t) = V_initial × e^(−t/τ)
What each variable means:
- e: Euler’s number ≈ 2.71828 (base of natural logarithm)
- t: elapsed time in seconds
- V_supply: source voltage applied during charging
- V_initial: voltage across capacitor at start of discharge
Key milestones during charging (% of V_supply reached):
- 1τ: 63.2% charged
- 2τ: 86.5% charged
- 3τ: 95.0% charged
- 4τ: 98.2% charged
- 5τ: 99.3% charged ← considered “fully charged” in practice
Worked example: A circuit uses R = 10,000 Ω (10 kΩ) and C = 100 μF (0.0001 F). τ = 10,000 × 0.0001 = 1 second After 2 seconds (2τ): V = 5V × (1 − e^(−2)) = 5 × 0.865 = 4.32V (86.5% charged) Full charge reached in ≈ 5 seconds.
Common RC circuit applications:
- Low-pass filters: attenuate high-frequency signals, pass low frequencies. Cutoff frequency: f_c = 1 ÷ (2π × R × C)
- High-pass filters: opposite behavior
- 555 timer circuits: RC determines pulse timing
- Debounce circuits: smooth mechanical switch bounce
- Camera flash: capacitor charges slowly, discharges instantly for the flash
Cutoff frequency example: Same circuit above. f_c = 1 ÷ (2π × 10,000 × 0.0001) = 1 ÷ 6.283 = 0.159 Hz — very low cutoff, suitable for DC smoothing only.