Impedance Calculator

Introduction

Impedance is the total opposition a circuit offers to the flow of alternating current (AC). It combines two things: resistance and reactance. Resistance slows down current in a simple, steady way. Reactance comes from components like capacitors and inductors, which store and release energy as the current changes direction. Together, they form impedance, measured in ohms (Ω).

This Impedance Calculator helps you quickly find the impedance of a circuit based on its resistance, inductance, capacitance, and frequency. Instead of working through complex formulas by hand, you can plug in your values and get accurate results in seconds. Whether you are a student learning about AC circuits or an engineer designing a filter or amplifier, this tool saves time and reduces errors. Simply enter your known values, and the calculator does the rest.

How to Use Our Impedance Calculator

Enter the resistance, inductance, capacitance, and frequency of your AC circuit to calculate the total impedance in ohms.

Resistance (R): Enter the resistance of your circuit in ohms (Ω). This is the part of impedance that does not change with frequency. You can measure it with a multimeter or find it on a component datasheet. If you need to determine the resistance from voltage and current measurements, our Ohm's Law Calculator can help.

Inductance (L): Enter the inductance of your circuit in henrys (H). Inductors resist changes in current and add positive reactance to your circuit. If your circuit has no inductor, enter 0.

Capacitance (C): Enter the capacitance of your circuit in farads (F). Capacitors resist changes in voltage and add negative reactance to your circuit. If your circuit has no capacitor, enter 0. For more detailed capacitor calculations, you can use our Capacitor Calculator.

Frequency (f): Enter the frequency of the AC signal in hertz (Hz). This is how many times the signal cycles per second. The frequency affects how much the inductor and capacitor contribute to the total impedance. If you need to convert frequency to wavelength, our Wavelength Calculator is a useful companion tool.

Once you fill in all the fields, the calculator will give you the total impedance magnitude in ohms, the phase angle in degrees, and the inductive and capacitive reactance values. These results help you understand how your circuit behaves at the given frequency.

Understanding Impedance in Electrical Engineering

Impedance is the total opposition a circuit offers to the flow of alternating current (AC). It is measured in ohms (Ω) and combines two things: resistance, which blocks current equally at all frequencies, and reactance, which changes depending on the signal frequency. Reactance comes from inductors and capacitors. Inductors resist changes in current, creating inductive reactance that grows as frequency rises. Capacitors resist changes in voltage, creating capacitive reactance that shrinks as frequency rises. Impedance is written as a complex number (Z = R + jX) that captures both the magnitude and phase relationship between voltage and current.

PCB Trace Impedance

When electrical signals travel along a copper trace on a printed circuit board (PCB), the trace behaves like a tiny transmission line. It has a characteristic impedance determined by the trace's physical dimensions and the materials around it. The key factors are trace width, dielectric height (the distance between the trace and the ground plane), copper thickness, and the dielectric constant (εr) of the board material. Common target impedances are 50 Ω for single-ended signals and 100 Ω for differential pairs. For determining the appropriate copper conductor size in your designs, our Wire Size Calculator can assist with wire gauge selection.

There are several trace geometries used in PCB design. A microstrip sits on the outer surface of the board with a ground plane below it. A stripline is buried between two ground planes inside the board. Coplanar waveguides (CPW) have ground copper on the same layer as the signal trace, separated by small gaps. Each geometry has its own formula for calculating impedance. Differential versions of these geometries use two traces running side by side, and the spacing between them affects the differential impedance through electromagnetic coupling.

RLC Circuit Impedance

An RLC circuit contains resistors (R), inductors (L), and capacitors (C) connected in series or parallel. In a series RLC circuit, the impedance is the sum of the resistance and the net reactance: Z = R + j(X_L − X_C). In a parallel RLC circuit, the reciprocals of each component's impedance are added together, which makes the math more involved but the concept the same. If you are working with parallel resistor networks as part of a larger circuit, our Parallel Resistor Calculator can simplify that step.

Every RLC circuit that contains both an inductor and a capacitor has a resonant frequency (f₀ = 1 / 2π√LC). At this frequency, inductive and capacitive reactances cancel each other out. In a series circuit, impedance drops to its minimum (just R) at resonance. In a parallel circuit, impedance reaches its maximum at resonance. The quality factor (Q) describes how sharp the resonance peak is. A high Q means a narrow bandwidth and low energy loss, while a low Q means a wide bandwidth and higher loss.

Why Impedance Matters

Impedance matching is critical in electronics. When a signal source, transmission line, and load all share the same impedance, maximum power transfers and reflections are minimized. Mismatched impedance on a high-speed PCB causes signal reflections, ringing, and data errors. In filter and amplifier design, controlling impedance at specific frequencies determines which signals pass through and which are blocked. Understanding how voltage distributes across impedance elements is essential — our Voltage Divider Calculator can help with that analysis. Additionally, when running long conductors, impedance-related losses manifest as voltage drop, which you can estimate using our Voltage Drop Calculator.

Whether you are designing a circuit board for a computer, tuning an antenna, or building an audio crossover, getting the impedance right is one of the most important steps in the process. For power-related calculations in your electrical systems, the Power Calculator and Amp Calculator are also helpful resources. And if you are working with sound systems and need to calculate speaker enclosure impedance effects, our Subwoofer Box Calculator and dB Calculator can complement your impedance analysis.

Frequently Asked Questions

What is impedance?

Impedance is the total opposition a circuit gives to alternating current (AC). It combines resistance and reactance into one value measured in ohms (Ω). Resistance stays the same at all frequencies, while reactance changes with frequency due to inductors and capacitors.

What is the difference between impedance and resistance?

Resistance only opposes current flow in a steady, fixed way. Impedance includes resistance plus reactance, which changes with frequency. In a DC circuit, impedance equals resistance. In an AC circuit, impedance also accounts for the effects of inductors and capacitors.

What units does this calculator use for PCB trace dimensions?

All PCB trace dimensions like trace width, dielectric height, copper thickness, and spacing are entered in millimeters (mm). The dielectric constant (εr) has no unit since it is a ratio.

What is a typical target impedance for PCB traces?

The most common target is 50 Ω for single-ended signals and 100 Ω for differential pairs. These values are standard in most high-speed digital and RF designs. Your specific design requirements may call for different values.

What is the difference between microstrip and stripline?

A microstrip trace sits on the outer surface of a PCB with one ground plane below it. A stripline trace is buried inside the board between two ground planes. Stripline offers better shielding from interference, while microstrip is easier to manufacture and access.

What is a coplanar waveguide (CPW)?

A coplanar waveguide is a trace model where the signal trace and ground copper sit on the same layer of the PCB. Small gaps separate the signal trace from the ground on each side. It can also have a ground plane below it for added shielding.

What is the dielectric constant (εr)?

The dielectric constant is a number that describes how well the board material stores electric energy compared to empty space. Common PCB material FR-4 has an εr of about 4.2 to 4.5. A higher εr lowers the impedance and slows down signal speed.

Can I use this calculator to find trace width for a target impedance?

Yes. Switch to the "Calculate Trace Width" mode under Calculation Direction. Enter your target impedance and other parameters like dielectric height, copper thickness, and εr. The calculator will solve for the trace width you need.

What is the difference between series and parallel RLC circuits?

In a series RLC circuit, the resistor, inductor, and capacitor are connected end to end. The impedance is the sum of each part. In a parallel RLC circuit, all three components share the same voltage across them, and their effects combine differently. Series circuits have minimum impedance at resonance, while parallel circuits have maximum impedance at resonance.

What is resonant frequency?

Resonant frequency is the frequency where inductive reactance and capacitive reactance are equal and cancel each other out. It is calculated as f₀ = 1 / (2π√(LC)). At this frequency, a series RLC circuit has its lowest impedance and a parallel RLC circuit has its highest impedance.

What is the quality factor (Q)?

The quality factor measures how sharp the resonance peak is. A high Q means the circuit responds strongly to a narrow range of frequencies. A low Q means it responds to a wider range. In a series RLC circuit, Q = (1/R)√(L/C). In a parallel RLC circuit, Q = R√(C/L).

What does the phase angle mean in impedance?

The phase angle tells you how much the voltage leads or lags behind the current. A positive phase angle means the circuit is inductive (voltage leads current). A negative phase angle means the circuit is capacitive (current leads voltage). At 0°, the circuit is purely resistive.

What does the j in complex impedance mean?

The letter j represents the imaginary unit in electrical engineering. In the expression Z = R + jX, R is the real part (resistance) and X is the imaginary part (reactance). This notation lets engineers work with both magnitude and phase at the same time.

What is differential impedance?

Differential impedance is the impedance seen by a signal traveling on a pair of traces that carry equal and opposite signals. It depends on each trace's single-ended impedance and the electromagnetic coupling between the two traces. Closer spacing lowers the differential impedance.

What is propagation delay?

Propagation delay is how long it takes a signal to travel a certain distance along a trace. It is measured in picoseconds per millimeter (ps/mm). A higher dielectric constant means a slower signal and a longer propagation delay.

How accurate are the PCB impedance results?

The calculator uses well-known closed-form models like Hammerstad-Jensen for microstrip and Cohn for stripline. These give good estimates for most designs, usually within 5% of a full electromagnetic simulation. For production boards, always verify with your PCB manufacturer's impedance modeling tools.

Why does trace width affect impedance?

A wider trace has more capacitance to the ground plane and less inductance per unit length. This lowers the characteristic impedance. A narrower trace has less capacitance and more inductance, which raises the impedance.

Can I calculate impedance for RL or RC circuits only?

Yes. In the RLC Circuit Impedance tab, you can select "RL Only" or "RC Only" modes. The calculator will hide the unused component and compute the impedance for just the two components you choose.

What is bandwidth in an RLC circuit?

Bandwidth is the range of frequencies around the resonant frequency where the circuit responds strongly. It equals the resonant frequency divided by the quality factor (BW = f₀ / Q). A higher Q gives a narrower bandwidth.

What happens if I enter zero for a component value?

Entering zero for resistance, inductance, or capacitance removes that component from the calculation. For example, zero resistance in a series RLC circuit means only the reactance determines the impedance. Zero capacitance removes the capacitive effect entirely.