The Time Constant (τ) represents the speed at which a circuit responds to a change in voltage. It defines the time required to charge a capacitor (or energize an inductor) to 63.2% of its maximum capacity.

This tool supports both RC (Resistor-Capacitor) and RL (Resistor-Inductor) circuits. It generates a Precision Charge Curve to visualize the transient response over time.

Circuit Parameters

Resistor (R)

Capacitor (C)

Inductor (L)

Time Constant (τ)

Instantaneous Voltage

At Time (t)

Charge %: — %

Dynamic Charge Curve

Live Graph

Full Charge (5τ)

—

Cutoff Freq (fc)

—

Circuit Diagram

Physics & Formulas

RC Formula

τ = R × C

Time (s) = Resistance (Ω) × Capacitance (F). Measures charging speed.

RL Formula

τ = L / R

Time (s) = Inductance (H) / Resistance (Ω). Measures energizing speed.

5-Tau Rule

t_full ≈ 5 × τ

A capacitor is considered “fully charged” (99.3%) after 5 time constants.

Cutoff Frequency

f_c = 1 / (2πτ)

The frequency at which the filter attenuates signal power by half (-3dB).

Common Questions

What is 1 Time Constant?

One time constant (1τ) is the time it takes for a capacitor to charge to 63.2% of the supply voltage, or for an inductor to reach 63.2% of its maximum current.

How long does it take to discharge?

The discharge curve is the inverse of the charge curve. After 1τ, the voltage drops to 36.8% of the initial value. After 5τ, it is effectively discharged (0.7%).

How to Use

Calculate circuit timing in 3 steps.

Select Circuit Type

Toggle between RC (Capacitor) and RL (Inductor) using the buttons at the top.

Enter Values

Input the Resistance and Capacitance/Inductance. Use the dropdowns to select units (e.g., µF, kΩ).

Analyze Transient Response

The tool calculates τ instantly. Use the “At Time (t)” input to find the exact charge percentage at any specific moment.