RC Time Constant Calculator

Calculation of the time constant τ (Tau) of RC circuits

Calculation

Time Constant τ (Tau)

Calculate the time constant of an RC circuit or its capacitor or resistor. Two values must be known to calculate the third.

Result
Time constant τ:
Capacitor C:
Resistor R:

Good to know

What is the time constant?

The time constant τ (Tau) of an RC circuit is the product of R × C. Its unit is the second. It determines how quickly a capacitor charges or discharges.

Basic formulas
\[\tau = R \times C\]
\[R = \frac{\tau}{C}\]
\[C = \frac{\tau}{R}\]
Practical charging times
  • 1τ: 63.2% charged/discharged
  • 3τ: 95.0% charged/discharged
  • 5τ: 99.3% charged/discharged

RC Time Constant - Theory and Application

The time constant of an RC circuit (low pass) is the product of R × C. Its unit is the second. The symbol is the Greek letter τ (tau). The time constant is needed to calculate the charge state of the capacitor at a certain time during charging or discharging.

Meaning of the time constant

Charging behavior

After one time constant τ, the capacitor voltage has reached 63.2% of the input voltage.

\[U_C(1\tau) = 0.632 \times U_0\]
Discharging behavior

After one time constant τ, the capacitor voltage has dropped to 36.8% of the initial voltage.

\[U_C(1\tau) = 0.368 \times U_0\]

Time constant table

Time Charge (%) Discharge (%) Remaining (%) Practical meaning
0.5τ 39.3 39.3 60.7 First noticeable change
1τ 63.2 63.2 36.8 One time constant
2τ 86.5 86.5 13.5 Mostly charged/discharged
3τ 95.0 95.0 5.0 Practically complete
5τ 99.3 99.3 0.7 Fully charged/discharged

Calculation formulas

Time constant:
\[\tau = R \times C\]

Basic formula for the time constant of an RC circuit. Result in seconds.

Resistor:
\[R = \frac{\tau}{C}\]

Calculation of the resistance with known time constant and capacitance.

Capacitor:
\[C = \frac{\tau}{R}\]

Calculation of the capacitance with known time constant and resistance.

Practical Applications

Timing circuits:
• Delay relays
• Flashers
• Debouncing circuits
• Timers
Filters:
• Low-pass filters
• Signal smoothing
• Interference suppression
• Anti-aliasing
Energy storage:
• Buffer capacitors
• Voltage smoothing
• Backup supply
• Soft start

Calculation examples

Example 1: Timer circuit

Desired delay: 5 seconds
Capacitor: 100µF

\[R = \frac{\tau}{C} = \frac{5s}{100\mu F} = 50k\Omega\]

A 50kΩ resistor produces a time constant of 5 seconds.

Example 2: Low-pass filter

Resistor: 1kΩ
Cutoff frequency: 1.6 kHz (τ = 100µs)

\[C = \frac{\tau}{R} = \frac{100\mu s}{1k\Omega} = 100nF\]

A 100nF capacitor produces the desired cutoff frequency.

Important notes
  • The time constant is independent of the applied voltage
  • After 3τ, the RC circuit is practically fully charged/discharged (95%)
  • After 5τ, the RC circuit is considered fully charged/discharged (99.3%)
  • The cutoff frequency of an RC low pass: f₀ = 1/(2π × τ)
  • Temperature changes can slightly affect R and C
  • For very small or large values, watch out for parasitics
Relation to cutoff frequency
RC low pass cutoff frequency
\[f_0 = \frac{1}{2\pi \times \tau} = \frac{1}{2\pi \times R \times C}\]

At the cutoff frequency f₀, the output voltage has dropped by 3dB (-3dB), i.e. to 70.7% of the input voltage.


Capacitor functions

Series connection with capacitors  •  Series connection with 2 capacitors  •  Reactance Xc of a capacitor  •  Time constant of an R/C circuit  •  Capacitor charging voltage  •  Capacitor discharge voltage  •  R/C for the charging voltage  •  Series circuit R/C  •  Parallel circuit R/C  •  Low pass-filter R/C  •  High pass-filter R/C  •  Integrator R/C  •  Differentiator R/C  •  Cutoff-frequency R,C  •  R and C for a given impedance  •