RC Time Constant Calculator
Calculate RC time constant, charge/discharge time, and low-pass cutoff frequency for filters and timing circuits.
RC Circuit Formulas
Time Constant: τ = R × C (seconds)
Charging Voltage: V(t) = V₀ × (1 - e^(-t/τ))
Discharging Voltage: V(t) = V₀ × e^(-t/τ)
Cutoff Frequency (Low-Pass): fc = 1 / (2πRC)
Phase Shift @ fc: -45°
RC Filter Applications
| Application | Typical fc | R / C Values |
|---|---|---|
| Power Supply Ripple Filter | 10–100 Hz | 100 Ω / 100 µF |
| Audio Coupling (DC blocking) | ~10 Hz | 1 kΩ / 10 µF |
| High-Frequency Noise Suppression | 10–100 kHz | 1 kΩ / 10 nF |
| Button Debouncing | ~50 Hz | 10 kΩ / 1 µF |
Frequently Asked Questions
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Time constant (τ = RC) is the time for a capacitor to charge to 63.2% or discharge to 36.8% of its initial value through a resistor. Measured in seconds: τ (tau) = R(Ω) × C(F). Example: 10 kΩ × 100 µF = 1 second. Larger τ = slower charging.
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Theoretically infinite (exponential approach). Practically: 5τ = 99.3% charged, 3τ = 95% charged, 2τ = 86% charged. Design rule: assume capacitor fully charged after 5 time constants. Example: τ = 1 ms → capacitor ~fully charged after 5 ms.
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Time to reach voltage V: t = -τ × ln(1 - V/Vmax) for charging, or t = -τ × ln(V/Vmax) for discharging. For 90% charge: t ≈ 2.3τ. For 50% charge: t = 0.69τ. Exponential curve, not linear.
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Cutoff frequency (fc) is where output power drops to 70.7% (-3dB) of input. Formula: fc = 1 / (2πRC). Lower fc = slower frequency response, more filtering. Used in low-pass, high-pass, and band-pass filters.
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In a low-pass RC filter, signal above fc is attenuated (filtered out). Below fc, signal passes. Roll-off rate = -20dB/decade (first-order). Larger RC = lower fc = more filtering. Example: 1 kΩ and 0.1 µF → fc ≈ 1.6 kHz.
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At cutoff frequency fc, phase shift = -45° (for low-pass). Below fc, shift approaches 0°; above fc, approaches -90°. Phase lag means output lags input. Important in stability analysis and feedback circuits.
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Yes! RC filtering removes switch bounce. Time constant τ = RC should be ~10–50 ms to debounce mechanical switches (typical bounce: 5–20 ms). Higher τ introduces lag; lower τ may not filter completely. Add Schmitt trigger logic for clean edge detection.
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Initial charging current I0 = V / R (ohms law). As capacitor charges, current decreases exponentially: i(t) = (V/R) × e^(-t/τ). Peak current at t=0, zero at t=∞. Larger R = smaller peak current (protects capacitor and circuit).
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Balance desired time constant against practical constraints. R: 100 Ω–10 MΩ (low = more current, fast; high = leakage risk, slow). C: 1 nF–1000 µF (low = fast response, less filtering; high = slow response, more filtering). Use standard values (E12/E24 series).
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Bandwidth (BW, Hz) ≈ 0.16 / τ (approximately). Shorter τ = wider bandwidth = faster response. Longer τ = narrower bandwidth = slower response, more filtering. Trade-off between speed and noise rejection.
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Yes. Audio coupling capacitors and load resistances create RC high-pass filters. Too large τ = bass roll-off (DC blocked but audio preserved). Too small τ = DC not fully blocked. Typical audio coupling: fc ~10 Hz (very low).
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Discharge formula: V(t) = V0 × e^(-t/τ). Voltage falls rapidly at first, then slows asymptotically. Never reaches zero (theoretically infinite discharge time). After 5τ, voltage ~0.7% of initial. Leakage resistance limits practical discharge time.