RC Time Constant Calculator | τ = RC Charging & Discharging
Calculate the RC time constant (τ=RC) and charging/discharging times to 63.2%, 86.5%, 95%, 98.2%, and 99.3% of supply voltage.
How to Use
- Enter the resistance value (R) and select the unit (Ω, kΩ, or MΩ).
- Enter the capacitance value (C) and select the unit (pF, nF, or µF).
- Click 'Calculate' to compute the time constant τ = R × C.
- The table shows the time to reach each charge percentage (1τ through 5τ).
- After 5 time constants (5τ), the capacitor is considered fully charged (99.3%).
- These values also apply to discharging: at 1τ, the capacitor retains 36.8% of its charge.
About RC Circuits
The RC Time Constant
The time constant τ (tau) = R × C is the fundamental parameter of an RC (resistor-capacitor) circuit. It defines the rate of charging and discharging. In one time constant, a charging capacitor reaches 63.2% of the supply voltage. In five time constants, it reaches 99.3%, which is considered 'fully charged' for practical purposes. The unit of τ is seconds when R is in ohms and C is in farads.
Exponential Charging Curve
The capacitor voltage during charging follows: V(t) = Vs × (1 − e^(−t/τ)), where Vs is the supply voltage. During discharging: V(t) = V₀ × e^(−t/τ), where V₀ is the initial voltage. The exponential nature means the capacitor charges quickly at first and then increasingly slowly. This non-linear behavior is important for timing circuits, filters, and integrators.
RC Filters and Signal Processing
The RC time constant determines the cutoff frequency of an RC low-pass or high-pass filter: f_c = 1/(2π × R × C). A low-pass filter passes frequencies below f_c and attenuates those above. A high-pass filter does the reverse. RC filters are used extensively in audio processing, power supply smoothing, anti-aliasing before ADC conversion, and signal conditioning.
RC Timing Circuits
RC circuits are used in timer ICs like the 555 timer, where the charge/discharge time determines the output frequency or pulse width. Typical applications include delay circuits, debounce circuits for mechanical switches, oscillators, and PWM generators. The 555 timer in astable mode: frequency = 1.44 / ((R1+2×R2) × C), where R1, R2 and C form the RC network.
Key Features
- Calculates τ = R × C with flexible unit selection
- Shows charging/discharging times for 1τ through 5τ (63.2% to 99.3%)
- Results in seconds, milliseconds, microseconds, or nanoseconds
- Useful for filter cutoff frequency estimation
Common Applications
- 555 timer circuit design (monostable and astable modes)
- RC filter cutoff frequency calculation
- Capacitor charge/discharge timing in power circuits
- Switch debounce delay circuit design
- ADC anti-aliasing filter design