Impedance Calculator

Q: What trace model should I use for a standard 2-layer PCB?

Use the Microstrip Single-Ended model. On a 2-layer board, your signal trace sits on the top or bottom layer with a ground plane on the other side. This is the most common setup for simple PCBs.

Q: What dielectric constant should I use for FR-4?

A value of 4.3 is a good starting point for standard FR-4 material. FR-4 circuit board is listed at 4.3 to 4.5 at 10 GHz. 10 FR-4 is a weave of fiberglass in resin, so the mix of glass and resin can vary across a board. 10 Check your laminate datasheet for the exact number at your operating frequency.

Q: How does trace width affect impedance?

A wider trace has lower impedance , and a narrower trace has higher impedance . 11 This is because a wider trace has more capacitance to the ground plane and less inductance per unit length. The impedance vs. trace width chart in the calculator shows this relationship clearly.

Q: What is the difference between series and parallel RLC circuits?

In a series RLC circuit, the components are connected end to end. At resonance, impedance drops to its minimum (just R). 4 In a parallel RLC circuit, the components are connected side by side. At resonance, impedance rises to its maximum. 6 They behave oppositely at the resonant frequency. 6

Impedance Calculator

Introduction

Impedance is how much a circuit resists the flow of alternating current (AC).² It combines resistance, which blocks current equally at all speeds, with reactance, which changes based on the signal frequency.⁵ Getting impedance right is a key part of electrical engineering. It affects everything from PCB trace design to filter circuits. Our Impedance Calculator helps you solve for impedance quickly in two common situations: PCB trace impedance and RLC circuit impedance.

In PCB trace mode, you can pick from 7 trace models, including microstrip, stripline, coplanar waveguide, and differential pairs. Enter your trace width, dielectric height, copper thickness, and dielectric constant, and the tool gives you the characteristic impedance, effective dielectric constant, propagation delay, and per-unit-length capacitance and inductance. You can also flip the calculation to find the trace width needed for a target impedance, a common task when designing controlled-impedance boards.

In RLC circuit mode, you can choose series or parallel configurations, or simple RL, RC, and LC combinations. Enter your resistance, inductance, capacitance, and frequency, and the calculator returns the total impedance magnitude, complex impedance, phase angle, inductive and capacitive reactance, resonant frequency, quality factor, and bandwidth. Both modes include interactive charts so you can see how impedance changes as you sweep trace width or frequency.

How to Use Our Impedance Calculator

This calculator has two modes: PCB Trace Impedance and RLC Circuit Impedance. Enter your circuit or trace details, and the tool will compute impedance values, phase angles, and other key electrical properties.

PCB Trace Impedance Mode

Calculation Direction: Choose whether you want to calculate the impedance from a known trace width, or find the trace width needed to hit a target impedance.

Trace Model: Pick the type of PCB trace you are working with. Options include microstrip, stripline, coplanar waveguide, and differential pairs. Use the filter buttons to narrow down your choices by category. A cross-section diagram will appear to show you the layout of your selected model.

Trace Width (W): Enter the width of the copper trace in millimeters. If you chose "Calculate Trace Width" mode, enter your target impedance instead.

Dielectric Height (H): Enter the distance in millimeters between the trace and the ground plane (or between ground planes for stripline models). For the coplanar waveguide model, enter the thickness of the substrate.

Copper Thickness (T): Enter the thickness of the copper trace in millimeters. Copper foil is specified by weight in ounces per square foot, and 1 oz foil is 35 µm thick.¹⁸ That is 0.035 mm, a common value. The differential pair models treat the traces as having no thickness, so they do not use this field.

Dielectric Constant (εr): Enter the relative permittivity of your PCB substrate material. For example, FR-4 circuit board is listed at 4.3 to 4.5 at 10 GHz.¹⁰

Trace Spacing (S): For differential pair models, enter the edge-to-edge gap between the two traces in millimeters. For the broadside-coupled stripline model, where one trace sits directly above the other, enter the vertical distance between the two traces, and enter the distance between the two ground planes as the Ground Plane Spacing (H). This model covers trace widths from 0.909 to 2.985 times H and spacings between the traces from 0.075 to 0.130 times H, which suits tightly coupled pairs such as couplers.

Gap to Coplanar Ground (G): For coplanar waveguide models, enter the distance in millimeters between the signal trace and the adjacent ground pour on the same layer.

Height to Trace (H1) and Height Above Trace (H2): The asymmetric stripline model uses these two heights instead of H. Enter the distance from the trace to each of the two ground planes in millimeters, as shown in the diagram.

RLC Circuit Impedance Mode

Circuit Configuration: Select how your components are connected. Choose from Series RLC, Parallel RLC, RL Only, RC Only, or LC Only. A circuit diagram will update to show your selected layout.

Resistance (R): Enter the resistance value and select the unit (Ω, kΩ, MΩ, or mΩ).

Inductance (L): Enter the inductance value and select the unit (H, mH, μH, or nH).

Capacitance (C): Enter the capacitance value and select the unit (F, mF, μF, nF, or pF).

Frequency (f): Enter the signal frequency at which you want to calculate impedance, and select the unit (Hz, kHz, MHz, or GHz).

After entering your values, click Calculate to see results including total impedance magnitude, complex impedance, phase angle, reactance, resonant frequency, quality factor, and bandwidth. An interactive chart will also display how impedance and phase change across a range of frequencies.

What Is Impedance?

Impedance is a measure of how much a circuit resists the flow of alternating current (AC).² It is similar to resistance, but it also accounts for the effects of capacitors and inductors, which store and release energy as the current changes direction.² Impedance is measured in ohms (Ω) and is written as a complex number with a real part (resistance) and an imaginary part (reactance).⁵ The real part represents energy lost as heat, while the imaginary part represents energy that is stored and returned to the circuit.³

PCB Trace Impedance

When electrical signals travel along a copper trace on a printed circuit board (PCB), the trace acts like a tiny transmission line.⁹ The shape of the trace, the thickness of the copper, the height of the dielectric material (the insulating layer between the trace and the ground plane), and the dielectric constant of that material all affect how signals move through it.¹⁵ This is called the characteristic impedance of the trace, and it is usually written as Z₀.

Getting the right trace impedance matters a lot in high-speed digital and radio-frequency (RF) design.¹⁵ If the impedance is not matched between a source, the trace, and the load, signals can bounce back and forth along the trace.¹⁵ These reflections cause ringing, signal distortion, and data errors. A common target is 50 Ω for single-ended traces.¹⁵ Differential pairs often target 100 Ω, though other values are used depending on the design standard. For high-speed serial links, cables and connectors are typically chosen with a differential impedance of 100 Ω.¹⁹

Common PCB Trace Models

Microstrip – A trace on the outer layer of a board with a ground plane below it.⁹ This is the most common type.¹³
Stripline – A trace sandwiched between two ground planes inside the board.¹² It offers better shielding from noise.
Coplanar Waveguide (CPW) – A trace with ground copper on either side of it on the same layer, sometimes with a ground plane below.
Differential Pair – Two traces that carry opposite signals.¹⁴ The spacing between them controls the differential impedance. The microstrip pair is calculated with the Hammerstad and Jensen formulas for coupled microstrip lines.¹⁶ The stripline pair is calculated with Cohn's formulas for edgewise coupled stripline.¹⁷ The broadside-coupled stripline pair, with one trace above the other between two ground planes, is calculated with Cohn's formulas for broadside-coupled stripline.¹⁷

RLC Circuit Impedance

An RLC circuit contains up to three types of components: a resistor (R), an inductor (L), and a capacitor (C). Each one affects impedance differently. A resistor provides a fixed opposition to current.⁵ An inductor's reactance increases with frequency, meaning it blocks high-frequency signals more.¹ A capacitor's reactance decreases with frequency, meaning it blocks low-frequency signals more.¹

When these components are connected in series, you add their impedances together.⁵ The total reactance is the difference between the inductive reactance (X_L = 2πfL) and the capacitive reactance (X_C = 1/(2πfC)).⁵ When they are connected in parallel, the math uses reciprocals, the same way parallel resistors combine.⁸

Resonance and Quality Factor

At a specific frequency called the resonant frequency (f₀ = 1 / (2π√(LC))), the inductive and capacitive reactances cancel each other out.⁵ In a series circuit, this makes the impedance drop to its lowest point (equal to R alone).⁴ In a parallel circuit, the impedance rises to its highest point at resonance.⁶ The quality factor (Q) tells you how sharp the resonance peak is.⁴ A high Q means a narrow, sharp peak, which is useful for filters and tuning circuits.⁴ The bandwidth is the range of frequencies around resonance where the circuit responds strongly, and it equals f₀ divided by Q.⁵

Phase Angle

The phase angle describes whether the current leads or lags behind the voltage.² When the circuit is mostly inductive, current lags voltage and the phase angle is positive.² When it is mostly capacitive, current leads voltage and the phase angle is negative.² At resonance, the phase angle is zero, meaning voltage and current are perfectly in sync.⁴ Understanding phase relationships is also important when working with voltage divider circuits, where impedance ratios determine output voltage levels at a given frequency.

Formulas used

Microstrip Effective Dielectric Constant ¹¹

\varepsilon_{eff} = \frac{\varepsilon_r + 1}{2} + \frac{\varepsilon_r - 1}{2} \cdot \frac{1}{\sqrt{1 + 12H/W}}

Microstrip Z₀ (W/H ≤ 1)

Z_0 = \frac{60}{\sqrt{\varepsilon_{eff}}} \ln\!\left(\frac{8H}{W} + \frac{W}{4H}\right)

Microstrip Z₀ (W/H > 1)

Z_0 = \frac{120\pi}{\sqrt{\varepsilon_{eff}}\left(\frac{W}{H} + 1.393 + 0.667\ln\!\left(\frac{W}{H}+1.444\right)\right)}

Stripline Z₀ ¹²

Z_0 = \frac{30\pi}{\sqrt{\varepsilon_r}} \cdot \frac{1 - T/b}{W_{eff}/b + C_f}

CPW Z₀ ¹³

Z_0 = \frac{30\pi}{\sqrt{\varepsilon_{eff}}} \cdot \frac{K(k')}{K(k)}, \quad k = \frac{W}{W + 2G}

Differential Impedance ¹⁴

Z_{diff} = 2\,Z_{odd}

Series RLC Impedance ⁵

Z = R + j\!\left(\omega L - \frac{1}{\omega C}\right), \quad |Z| = \sqrt{R^2 + \left(\omega L - \frac{1}{\omega C}\right)^2}

Resonant Frequency ⁴

f_0 = \frac{1}{2\pi\sqrt{LC}}

Frequently asked questions

What is the difference between impedance and resistance?

Resistance works the same way in direct current (DC) and alternating current (AC) circuits.⁷ It stays the same no matter the frequency.⁵ Impedance applies to alternating current (AC) and includes both resistance and reactance.² Reactance comes from inductors and capacitors and changes with frequency.¹ Impedance is written as a complex number in ohms (Ω), with resistance as the real part and reactance as the imaginary part.⁵

What trace model should I use for a standard 2-layer PCB?

Use the Microstrip Single-Ended model. On a 2-layer board, your signal trace sits on the top or bottom layer with a ground plane on the other side. This is the most common setup for simple PCBs.

What dielectric constant should I use for FR-4?

A value of 4.3 is a good starting point for standard FR-4 material. FR-4 circuit board is listed at 4.3 to 4.5 at 10 GHz.¹⁰ FR-4 is a weave of fiberglass in resin, so the mix of glass and resin can vary across a board.¹⁰ Check your laminate datasheet for the exact number at your operating frequency.

How do I convert copper weight to thickness in mm?

Copper foil weight sets its thickness: ½ oz foil is 18 µm and 1 oz foil is 35 µm, and foils run up to 2 oz at 70 µm.¹⁸ In millimeters that is 0.018 mm for 0.5 oz, 0.035 mm for 1 oz and 0.070 mm for 2 oz. Enter the thickness in millimeters in the Copper Thickness (T) field.

Why does my PCB trace impedance matter for high-speed signals?

When a signal travels along a trace, it behaves like a wave.⁹ If the trace impedance does not match the source and load impedance, part of the signal bounces back.¹⁵ These reflections cause ringing, overshoot, and data errors. Matching impedance keeps signals clean and reliable.¹⁵

What is the difference between single-ended and differential impedance?

Single-ended impedance (Z₀) is the impedance of one trace measured against a ground plane.⁹ Differential impedance (Zdiff) is the impedance between two traces in a differential pair.¹⁴ Differential impedance is twice the odd-mode impedance of each trace.¹⁴ A common single-ended target is 50 Ω.¹⁵ Differential pairs often target 100 Ω. High-speed serial links typically use cables and connectors with a differential impedance of 100 Ω.¹⁹

How does trace width affect impedance?

A wider trace has lower impedance, and a narrower trace has higher impedance.¹¹ This is because a wider trace has more capacitance to the ground plane and less inductance per unit length. The impedance vs. trace width chart in the calculator shows this relationship clearly.

What is the difference between series and parallel RLC circuits?

In a series RLC circuit, the components are connected end to end. At resonance, impedance drops to its minimum (just R).⁴ In a parallel RLC circuit, the components are connected side by side. At resonance, impedance rises to its maximum.⁶ They behave oppositely at the resonant frequency.⁶

What is resonant frequency and why does it matter?

Resonant frequency is the frequency where the inductive reactance and capacitive reactance are equal and cancel each other out.⁵ The formula is f₀ = 1 / (2π√(LC)).⁵ At this frequency, energy swaps back and forth between the inductor and capacitor with no net reactance.² It is important for designing filters, oscillators, and tuning circuits.

What does the quality factor (Q) tell me?

The quality factor measures how sharp the resonance peak is.⁴ A high Q means the circuit responds strongly to a narrow band of frequencies, which is good for precise filters.⁴ A low Q means a wider response.⁵ In a series RLC circuit, Q = (1/R)√(L/C).⁵ In a parallel RLC circuit, Q = R√(C/L).⁶

What does a positive or negative phase angle mean?

A positive phase angle means the circuit is mostly inductive and current lags behind voltage.² A negative phase angle means the circuit is mostly capacitive and current leads voltage.² A phase angle of zero means the circuit is at resonance or purely resistive.⁴

What is effective dielectric constant (εeff)?

For microstrip traces, the electric field travels partly through the substrate and partly through the air above the trace.¹¹ The effective dielectric constant is a weighted average of these two regions.⁹ It is always between 1 (air) and εr (substrate).¹¹ Stripline traces are fully enclosed in substrate, so εeff equals εr.¹²

What is propagation delay and why is it shown in the results?

Propagation delay is the time it takes for a signal to travel a unit distance along the trace, shown in picoseconds per millimeter (ps/mm). It depends on the effective dielectric constant.¹¹ Higher εeff means slower signal speed and longer delay.⁹ This is critical for timing in high-speed digital designs.

What is the difference between microstrip and stripline?

A microstrip trace sits on an outer layer of the PCB with one ground plane below it.⁹ Part of its field is in air.¹¹ A stripline trace is buried between two ground planes inside the board.¹² Stripline has better shielding from noise and crosstalk but is harder to access for probing and debugging.

What is a coplanar waveguide (CPW)?

A coplanar waveguide has ground copper on the same layer as the signal trace, with gaps on each side.¹³ It may or may not have a ground plane below. This calculator models coplanar waveguide without a ground plane below the substrate. CPW gives you more control over impedance by adjusting the gap width.¹³ It is commonly used in RF circuits and chip packaging.

How do I find the trace width I need for 50 ohms?

Switch the Calculation Direction to Calculate Trace Width. Enter 50 in the Target Impedance field, then fill in your dielectric height, copper thickness, and dielectric constant. Click Calculate, and the tool will solve for the trace width needed to achieve 50 Ω.

What are capacitance and inductance per unit length in the results?

These values show how much capacitance (pF/cm) and inductance (nH/cm) the trace has for every centimeter of length. They are useful for building lumped-element circuit models of transmission lines and for estimating signal integrity behavior over a given trace length.

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