RC Time Constant Calculator

Find tau, charging and discharging times, and the −3 dB cutoff frequency for any resistor-capacitor pair.

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How to use the RC Time Constant Calculator

  1. Enter the resistance.
  2. Choose the resistance unit.
  3. Enter the capacitance.
  4. Choose the capacitance unit.
  5. Enter the charge to.
  6. Press Calculate. The result updates automatically as you type, and you can switch the result unit at any time.

About the RC Time Constant Calculator

When a capacitor charges through a resistor, the voltage rises quickly at first and then slows as it approaches the supply voltage. The time constant τ (tau) sets the pace: after one τ the capacitor reaches about 63.2% of full charge, and after five τ it is above 99%, which engineers treat as fully charged.

RC timing is everywhere: switch debouncing, power-on reset delays, 555 timers, soft-start circuits and simple low-pass or high-pass filters. The same product R × C fixes a filter's cutoff frequency, where the output is down 3 dB (about 70.7% of the input amplitude). Real capacitors have tolerances of ±10–20%, so measure or trim if the timing must be precise.

Formula

τ = R × C
Charging: V(t) = Vs × (1 − e−t/τ)  →  t = −τ × ln(1 − p)
Discharging: V(t) = V₀ × e−t/τ
fc = 1 ÷ (2π × R × C)

R is in ohms, C in farads and τ in seconds; p is the target fraction (90% = 0.9). Example: 10 kΩ × 100 µF = 1 s, and reaching 90% takes 2.303 s.

Example calculation

Using the default values:

  • Resistance = 10
  • Resistance unit = kΩ
  • Capacitance = 100
  • Capacitance unit = µF
  • Charge to = 90%

the calculator returns:

  • Time constant (τ): 1 s
  • Time to reach chosen %: 2.3026 s
  • Cutoff frequency (−3 dB): 0.1592 Hz

Frequently asked questions

What does one time constant mean?

After one τ a charging capacitor reaches 63.2% of the supply voltage, and a discharging one falls to 36.8% of its starting voltage.

How long does a capacitor take to fully charge?

Mathematically it never reaches 100%, but after 5τ it is at 99.3%, which is considered fully charged for practical purposes.

Is ohms times farads really seconds?

Yes. An ohm is a volt per amp and a farad is a coulomb per volt, so Ω × F = coulombs per amp = seconds.

Last updated: · Category: Electrical calculators

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