Transmission Line Impedance Calculator (Microstrip)

Find the characteristic impedance and effective dielectric constant of a PCB microstrip trace from its width, substrate height, and relative permittivity.

🟩 Transmission Line Impedance Calculator (Microstrip)
Trace width (W)3 mm
mm
0.110
Substrate height (h)1.6 mm
mm
0.13
Dielectric constant (εr)4.5
εr
2.010.0
Characteristic impedance (Z0)
—
Effective dielectric constant (εeff)
—
W/h ratio
—
Formula branch used
—
Step-by-step working

🟩 What is Microstrip Transmission Line Impedance?

Microstrip characteristic impedance (Z0) is the impedance a signal sees traveling along a copper trace routed on the outer layer of a printed circuit board, with a continuous ground plane running underneath it. Unlike a coaxial cable, whose field is fully enclosed between two concentric conductors, a microstrip trace has its electromagnetic field split between the PCB substrate below it and the open air above it, which is why the Hammerstad-Jensen formulas used here need an intermediate quantity, the effective dielectric constant, rather than using the substrate's raw permittivity directly.

PCB designers calculate microstrip impedance every time a trace carries a signal fast or sensitive enough to behave as a transmission line rather than a simple wire, high-speed digital buses, RF front-end traces feeding an antenna or mixer, and any single-ended signal with a controlled-impedance requirement from the schematic or a connector datasheet. A hardware engineer routing a 50 ohm RF path from a transceiver IC to an antenna connector uses this exact calculation to pick a trace width for the board's known substrate height and dielectric constant. A PCB fabricator's impedance control team runs the same formulas (or a closer field solver) in reverse, adjusting trace width on the gerbers to hit the impedance target the customer specified.

A common misconception is that trace width alone determines impedance. In reality, Z0 depends on the ratio W/h, so the same trace width gives a different impedance on a thicker or thinner substrate, and the substrate's dielectric constant shifts the result further. Two boards with an identical top-layer trace width but different core thickness will not have the same characteristic impedance.

This calculator takes your trace width, substrate height, and dielectric constant, automatically selects the correct Hammerstad-Jensen formula branch for your W/h ratio, and returns the characteristic impedance, the effective dielectric constant, and a chart showing how Z0 changes across a wide range of W/h ratios, so you can see how much you would need to widen or narrow the trace to hit a different target impedance.

📐 Formula

W/h ≥ 1:   Z0 = (120π/√εeff) / (W/h + 1.393 + 0.667×ln(W/h+1.444))
εeff = (εr+1)/2 + (εr−1)/2 × (1+12h/W)−0.5   for W/h ≥ 1
W/h under 1:   Z0 = (60/√εeff) × ln(8h/W + W/(4h))
εeff = (εr+1)/2 + (εr−1)/2 × [(1+12h/W)−0.5 + 0.04(1−W/h)²]   for W/h under 1
W = trace width (mm), h = substrate height (mm), εr = substrate relative permittivity
Example: W = 3 mm, h = 1.6 mm, εr = 4.5 (FR4) → W/h = 1.875 → εeff ≈ 3.39, Z0 ≈ 50.31 Ω.

📖 How to Use This Calculator

Steps

1
Enter the trace width. Type the microstrip trace width W in millimeters.
2
Enter the substrate height. Type the substrate height h between the trace and the ground plane, in millimeters.
3
Enter the dielectric constant. Type the relative permittivity (dielectric constant) of the substrate material.
4
Read the characteristic impedance and related results. See the characteristic impedance Z0, effective dielectric constant, W/h ratio, active formula branch, and a Z0-versus-ratio chart.

💡 Example Calculations

Example 1 — Standard 50 Ω FR4 Trace

W = 3 mm, h = 1.6 mm, εr = 4.5 (FR4)

1
W/h = 3/1.6 = 1.875, so the W/h ≥ 1 branch applies
2
εeff = (4.5+1)/2 + (4.5−1)/2 × (1+12/1.875)−0.5 = 3.39
3
Z0 = (120π/√3.39) / (1.875 + 1.393 + 0.667×ln(1.875+1.444)) = 50.31 Ω
Z0 = 50.31 Ω, εeff = 3.39, branch = W/h ≥ 1
Try this example →

Example 2 — Narrow High-Impedance Trace

W = 0.9 mm, h = 1.6 mm, εr = 4.5 (FR4)

1
W/h = 0.9/1.6 = 0.563, so the W/h under 1 branch applies
2
εeff = (4.5+1)/2 + (4.5−1)/2 × [(1+12/0.563)−0.5 + 0.04(1−0.563)²] = 3.13
3
Z0 = (60/√3.13) × ln(8/0.563 + 0.563/4) = 90.32 Ω, much higher than the wide-trace example
Z0 = 90.32 Ω, εeff = 3.13, branch = W/h under 1
Try this example →

Example 3 — High-Frequency Laminate

W = 1.2 mm, h = 0.51 mm, εr = 3.38 (Rogers RO4003-like)

1
W/h = 1.2/0.51 = 2.353, so the W/h ≥ 1 branch applies
2
εeff = (3.38+1)/2 + (3.38−1)/2 × (1+12/2.353)−0.5 = 2.67
3
Z0 = (120π/√2.67) / (2.353 + 1.393 + 0.667×ln(2.353+1.444)) = 49.75 Ω, close to 50 Ω on a much thinner board
Z0 = 49.75 Ω, εeff = 2.67, branch = W/h ≥ 1
Try this example →

❓ Frequently Asked Questions

What is microstrip characteristic impedance?+
Microstrip characteristic impedance Z0 is the impedance a signal sees traveling down a copper trace on a PCB with a ground plane below it, set by the trace width W, the substrate height h between trace and ground plane, and the substrate's relative permittivity er. It is calculated here using the Hammerstad-Jensen approximation, choosing between two formulas depending on whether W/h is greater than or less than 1.
How do you calculate microstrip impedance from trace width and substrate height?+
For a wide trace (W/h >= 1), Z0 = (120*pi/sqrt(eeff)) / (W/h + 1.393 + 0.667*ln(W/h+1.444)), where eeff is the effective dielectric constant. For a narrow trace (W/h under 1), Z0 = (60/sqrt(eeff)) * ln(8h/W + W/(4h)). Both use a slightly different formula for eeff itself.
What is effective dielectric constant and why is it different from er?+
A microstrip trace has field lines partly in the PCB substrate (permittivity er) and partly in the air above the trace (permittivity 1), so the signal experiences an intermediate value called the effective dielectric constant eeff, always between 1 and er. A wider trace pulls more of the field into the substrate, pushing eeff closer to er.
Why does this calculator use two different formulas?+
The Hammerstad-Jensen approximation is only accurate across its full geometric range when split into two regimes: a wide-trace formula for W/h >= 1 and a narrow-trace formula for W/h under 1, each derived and curve-fit separately against more exact field solutions. This calculator automatically picks the correct formula based on your entered W/h ratio.
What is a typical dielectric constant for PCB substrate materials?+
Standard FR4 has er around 4.2 to 4.5 (this calculator defaults to 4.5). Rogers RO4003 and similar high-frequency laminates run lower, around 3.38, chosen for lower loss and tighter impedance control. Polyimide flex substrates typically run around 3.4 to 3.5.
How wide should a trace be for 50 ohm impedance on standard FR4?+
On a standard 1.6 mm thick FR4 board with er around 4.5, a trace width of roughly 3 mm lands close to 50 ohms for an outer-layer microstrip. Thinner substrates need a proportionally narrower trace to hit the same target impedance, since Z0 depends on the W/h ratio, not W alone.
Does trace thickness (copper weight) affect the impedance calculated here?+
No, not directly. This calculator uses the standard Hammerstad-Jensen formulas, which assume a negligibly thin conductor. Real copper thickness (measured in ounces per square foot) has a small secondary effect on impedance that becomes more significant for very thin substrates or very precise RF designs, and is not modeled here.
What happens if my trace width equals the substrate height (W/h = 1)?+
At exactly W/h = 1, this calculator uses the wide-trace branch (W/h >= 1), since the Hammerstad-Jensen wide-trace formula is defined and continuous at that boundary point. Both branches produce results that agree closely near W/h = 1 by design.
How accurate is the Hammerstad-Jensen approximation?+
The Hammerstad-Jensen formulas are widely cited as accurate to within about 1 percent of a full electromagnetic field solver for typical microstrip geometries and dielectric constants. For tight-tolerance controlled-impedance PCB manufacturing, fabricators typically run a full field solver against your actual stackup and copper weight for final sign-off.
Can this calculator be used for stripline instead of microstrip?+
No. Stripline (a trace fully embedded between two ground planes) uses a different set of formulas since the field is symmetric above and below the trace, rather than split between substrate and air as in microstrip. This calculator is scoped specifically to single-layer microstrip on top of a substrate with one ground plane below.
Tags: Microstrip Impedance Calculator Characteristic Impedance Calculator Pcb Trace Impedance Calculator Hammerstad Jensen Calculator Controlled Impedance Trace Calculator Calculator Formula Free Online

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What is microstrip characteristic impedance?

Microstrip characteristic impedance Z0 is the impedance a signal sees traveling down a copper trace on a PCB with a ground plane below it, set by the trace width W, the substrate height h between trace and ground plane, and the substrate's relative permittivity er. It is calculated here using the Hammerstad-Jensen approximation, choosing between two formulas depending on whether W/h is greater than or less than 1.

How do you calculate microstrip impedance from trace width and substrate height?

For a wide trace (W/h >= 1), Z0 = (120*pi/sqrt(eeff)) / (W/h + 1.393 + 0.667*ln(W/h+1.444)), where eeff is the effective dielectric constant. For a narrow trace (W/h under 1), Z0 = (60/sqrt(eeff)) * ln(8h/W + W/(4h)). Both use a slightly different formula for eeff itself.

What is effective dielectric constant and why is it different from er?

A microstrip trace has field lines partly in the PCB substrate (permittivity er) and partly in the air above the trace (permittivity 1), so the signal experiences an intermediate value called the effective dielectric constant eeff, always between 1 and er. A wider trace pulls more of the field into the substrate, pushing eeff closer to er.

Why does this calculator use two different formulas?

The Hammerstad-Jensen approximation is only accurate across its full geometric range when split into two regimes: a wide-trace formula for W/h >= 1 and a narrow-trace formula for W/h under 1, each derived and curve-fit separately against more exact field solutions. This calculator automatically picks the correct formula based on your entered W/h ratio.

What is a typical dielectric constant for PCB substrate materials?

Standard FR4 has er around 4.2 to 4.5 (this calculator defaults to 4.5). Rogers RO4003 and similar high-frequency laminates run lower, around 3.38, chosen for lower loss and tighter impedance control. Polyimide flex substrates typically run around 3.4 to 3.5.

How wide should a trace be for 50 ohm impedance on standard FR4?

On a standard 1.6 mm thick FR4 board with er around 4.5, a trace width of roughly 3 mm lands close to 50 ohms for an outer-layer microstrip. Thinner substrates need a proportionally narrower trace to hit the same target impedance, since Z0 depends on the W/h ratio, not W alone.

Does trace thickness (copper weight) affect the impedance calculated here?

No, not directly. This calculator uses the standard Hammerstad-Jensen formulas, which assume a negligibly thin conductor. Real copper thickness (measured in ounces per square foot) has a small secondary effect on impedance that becomes more significant for very thin substrates or very precise RF designs, and is not modeled here.

What happens if my trace width equals the substrate height (W/h = 1)?

At exactly W/h = 1, this calculator uses the wide-trace branch (W/h >= 1), since the Hammerstad-Jensen wide-trace formula is defined and continuous at that boundary point. Both branches produce results that agree closely near W/h = 1 by design.

How accurate is the Hammerstad-Jensen approximation?

The Hammerstad-Jensen formulas are widely cited as accurate to within about 1 percent of a full electromagnetic field solver for typical microstrip geometries and dielectric constants. For tight-tolerance controlled-impedance PCB manufacturing, fabricators typically run a full field solver against your actual stackup and copper weight for final sign-off.

Can this calculator be used for stripline instead of microstrip?

No. Stripline (a trace fully embedded between two ground planes) uses a different set of formulas since the field is symmetric above and below the trace, rather than split between substrate and air as in microstrip. This calculator is scoped specifically to single-layer microstrip on top of a substrate with one ground plane below.

📌 Quick Tips

💡FR4, the most common PCB substrate, has a relative permittivity of about 4.2 to 4.5. High-frequency substrates like Rogers RO4003 use a lower, more tightly controlled er (around 3.38) specifically to reduce loss and improve impedance consistency at RF and microwave frequencies.
💡A 50 ohm trace is the near-universal target for RF and high-speed digital single-ended signals. For a standard 1.6 mm FR4 board (er around 4.5), a trace width close to 3 mm typically lands near 50 ohms, though the exact width depends on your specific board stackup.
💡Widening the trace (increasing W relative to h) lowers Z0. A narrower trace, or a thicker substrate (larger h for the same W), raises Z0. This is the opposite relationship from a coaxial cable, where a larger outer/inner diameter ratio raises Z0.
💡The Hammerstad-Jensen formulas used here are a widely cited closed-form approximation, accurate to roughly 1 percent for typical PCB geometries, but a full 2D field solver is still recommended for tight-tolerance RF designs where the last few ohms matter.
💡This calculator assumes a trace on the top layer of a two-layer or multi-layer board with a solid reference plane directly below at distance h, with no adjacent copper pours close enough to load the field. Coplanar ground pours next to the trace change the effective impedance and are not modeled here.