ElectroHub

RC Time Constant Calculator

A resistor charging a capacitor gives the exponential curve behind every delay, debounce and simple filter. One number — the time constant — describes all of it.

RC Time Constant — τ = R × C

Time constant, 99% charge time (5τ) and the −3 dB cutoff frequency of an RC filter.

Time constant τ
63.2% charged (1τ)
99% charged (5τ)
Cutoff frequency
  1. 1.Given: R = 10 kΩ, C = 1 µF
  2. 2.Formulaτ = R × CSubstituteτ = 10000 Ω × 1e-6 FResultτ = 10 ms
  3. 3.Formulat(99% charged) = 5τSubstitutet = 5 × 10 msResultt = 50 ms
  4. 4.Formulaf꜀ = 1 ÷ (2πτ)Substitutef꜀ = 1 ÷ (2π × 0.01)Resultf꜀ = 15.9155 Hz
Common trap: After one time constant the capacitor is only ~63% charged, not full — "fully charged" in practice means 5τ. And a charged capacitor holds its voltage after power-off: discharge big ones before touching.

The formula

τ = R × C ; f_c = 1 / (2πRC)

τ
time constant, the time to reach 63.2 % of the final value (seconds)
R
series resistance (ohms)
C
capacitance (farads)
f_c
−3 dB cutoff frequency of the same RC as a filter (hertz)

Worked example

R = 10 kΩ charging C = 100 µF.

  1. τ = 10000 × 100 × 10⁻⁶ = 1 s
  2. Practically fully charged after 5τ = 5 s (99.3 %)
  3. As a low-pass filter: f_c = 1 / (2π × 1) = 0.159 Hz

τ = 1 s, 99 % charged in 5 s, cutoff at 0.159 Hz.

Where you'll use it

Timing a 555, debouncing a switch, sizing a decoupling or smoothing capacitor, and setting a filter corner. The same τ governs discharge, so a scope trace falling to 37 % marks one time constant.

The laws behind it

Parts this applies to

Capacitor (ceramic / MLCC)Capacitor (aluminium electrolytic)Capacitor (tantalum)Capacitor (film)SupercapacitorQuartz Crystal / ResonatorMOSFET555 Timer IC

Related calculators

555 Timer CalculatorAstable: t_high = 0.693(R₁+R₂)C, t_low = 0.693 R₂C, f = 1/(t_high+t_low)Capacitive and Inductive Reactance CalculatorX_C = 1 / (2πfC)LC Resonance Calculatorf₀ = 1 / (2π√(LC))Capacitor and Inductor Stored Energy CalculatorE = ½ × C × V² (capacitor)