RC and RL Time Constant Calculator (Charge and Discharge)

What is a time constant?

When an RC or RL circuit is switched, voltage and current do not jump to their final values. They approach them along an exponential curve, and the time constant τ (tau) sets how fast.

• For an RC circuit τ = R × C
• For an RL circuit τ = L / R

With resistance in ohms, capacitance in farads and inductance in henries, τ comes out in seconds.

Charge and discharge curves

An empty capacitor charged through a resistor rises as v = V × (1 − e^(−t/τ)). A charged capacitor discharging through a resistor falls as v = V × e^(−t/τ). In an inductor the current follows the same curves.

After one time constant the charge reaches 63.2 percent. It takes about 3τ to reach 95 percent and 4.6τ to reach 99 percent. In practice the transient is treated as over after 5τ, when 99.3 percent is complete.

Example

For a 10 kΩ resistor and a 100 µF capacitor, τ = 10,000 × 0.0001 = 1 s. Charging from a 12 V source, the capacitor reaches 12 × 0.632 = 7.59 V after one second. Reaching 8 V takes −1 × ln(1 − 8/12) = 1.10 s.

Cutoff frequency

A low pass or high pass filter built from the same parts has its cutoff at f = 1 / (2π × τ). The tool reports it too.

Limits

The calculation is for a circuit with one resistor and one capacitor or inductor. With several resistors, enter the equivalent resistance seen from the capacitor or inductor terminals. Capacitor leakage, inductor winding resistance and saturation are not modelled. Circuits with both an inductor and a capacitor are second order and outside the scope of this tool.