RLC Impedance Calculator

Impedance is the total opposition of a series RLC circuit to AC current.

How the Math Works

The RLC Impedance Calculator uses the fundamental formula Z = √(R² + (X_L − X_C)²) to determine the total impedance of a series RLC circuit. This equation combines the resistance (R) with the net reactance, which is the difference between inductive reactance (X_L = 2πfL) and capacitive reactance (X_C = 1/(2πfC)). The square root of the sum of squares gives the total impedance magnitude, representing how much the circuit opposes alternating current flow. The calculation accounts for both energy dissipation in the resistor and energy storage in the inductor and capacitor.

Practical Applications

To use this calculator practically, enter your circuit's resistance value in ohms, inductance in henries, capacitance in farads, and frequency in hertz. The calculator automatically computes X_L and X_C, then determines the total impedance. Engineers use this to design filters, tuning circuits, and power systems. For example, when designing a radio receiver, you'd calculate the impedance at the desired frequency to ensure maximum power transfer and proper signal selection. The result helps you select appropriate component values and predict circuit behavior before building.

Day-to-Day Use

This calculation impacts many devices you encounter daily. Your smartphone's radio circuits use RLC principles to tune into Wi-Fi and cellular signals. The speakers in your devices rely on impedance matching to deliver clear sound. Power systems in your home use these calculations to minimize energy loss during transmission. Even the touchscreen in your phone employs impedance measurements to detect your fingers. Understanding impedance helps manufacturers create more efficient, reliable electronics that charge faster and last longer on a single battery charge.

Worked example

R = 100, X_L = 80, X_C = 40 → Z ≈ 107.7 Ω at 21.8°.

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