RC Time Constant Calculator
Calculate the Tau (τ) and cutoff frequency for resistor-capacitor circuits.
Ω
kΩ
MΩ
F
mF
µF
nF
pF
Time Constant (τ):
–
Cutoff Frequency (fc):
–
Time to 95% Charge (3τ):
–
Time to 99% Charge (5τ):
–
What is the RC Time Constant?
The RC time constant, represented by the Greek letter tau (τ), is a fundamental property of an electric circuit composed of a resistor (R) and a capacitor (C). It represents the time required to charge the capacitor, through the resistor, to approximately 63.2% of its final full charge voltage, or to discharge it to approximately 36.8% of its initial voltage.
The Formula
The calculation is straightforward but essential for timing circuits and filters:
τ = R × C
- τ (Tau): Time constant in seconds.
- R (Resistance): Measured in Ohms (Ω).
- C (Capacitance): Measured in Farads (F).
Understanding Cutoff Frequency
In signal processing, an RC circuit often acts as a low-pass or high-pass filter. The cutoff frequency (fc) is the boundary at which the output power has dropped to half of its input power (the -3dB point). It is calculated using the formula:
fc = 1 / (2 π R C)
Practical Example
If you have a 10kΩ (10,000 Ohms) resistor and a 100µF (0.0001 Farads) capacitor:
- Convert units: R = 10,000; C = 0.0001.
- Multiply: 10,000 × 0.0001 = 1 second.
- The time constant τ is 1.0 second.
- The capacitor will be roughly 99% charged after 5τ, which is 5 seconds.