RC Time Constant Calculator

Compute time constant, cutoff frequency, settling time, and visualize the exponential charging curve. Perfect for filter design, timing circuits, and education.

Ω
Ohms — supports decimals & scientific (e.g., 1e3)
F
Farads — 1 µF = 1e-6, 1 nF = 1e-9
Steady-state voltage for charging
Time to reach this voltage from 0V (charging)
1kΩ + 1000µF (τ=1s)
10kΩ + 100nF (τ=1ms, fc=159Hz)
47kΩ + 0.1µF (τ=4.7ms)
100kΩ + 10µF (τ=1s, timing)
50Ω + 10µF (τ=500µs)

Understanding the RC Time Constant

The RC time constant (τ = R × C) defines the exponential response of a resistor-capacitor circuit. After one time constant, the capacitor voltage reaches approximately 63.2% of its final value (charging) or decays to 36.8% (discharging).

VC(t) = Vsrc · (1 − e−t/τ)     (charging)
fc = 1 / (2πRC)   (cutoff frequency for RC filter)

Engineers use the 5τ rule: after 5 time constants, the voltage reaches >99.3% of final value — considered fully charged for most practical purposes.

? Practical Applications

  • Low-pass / High-pass filters: fc defines -3dB point in audio crossovers and anti-aliasing filters.
  • Pulse shaping & debouncing: RC networks clean switch bounces and create precise delays.
  • Power supply decoupling: Time constant determines transient response.
  • 555 timer circuits: Classic RC timing configuration.

? Reference Table

R (Ω)C (F)τ (s)fc (Hz)5τ settlingUse case
1k1000µF (1e-3)1.00159.25 sLED fading, relay timer
10k100nF (1e-7)0.0011591.55 msAudio treble cut
47k0.1µF (1e-7)0.004733.923.5 msGuitar tone control
100k10µF (1e-5)1.01.595 s555 astable blinker
Case study: Microcontroller debounce — RC filter with 10kΩ + 100nF (τ=1ms). Switch bounce (~5ms) is longer than 5τ, ensuring stable logic level before reading.

❓Expert FAQs

At t = τ, e⁻¹ ≈ 0.368, so charging reaches 1−0.368 = 0.632 (63.2%). This unique point is where the initial slope intersects final voltage.

Yes, the same τ applies. For discharge, V(t)=V₀·e⁻ᵗ⁄τ. You can compute time to target using t = -τ·ln(V_target/V₀).

High‑precision floating point math with 300+ sample points per curve, providing accurate visual feedback for engineering estimation.
References: Horowitz & Hill "The Art of Electronics", IEEE Std 1241, MIT 6.002.