Microstrip Trace Impedance Calculator

Calculate characteristic impedance Z₀ of a microstrip trace on FR4 or any substrate. Uses the Hammerstad-Jensen formula with effective permittivity correction.

Calculator Electronics Updated Apr 23, 2026
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How to Use
  1. Enter trace width W, substrate height H (prepreg or core), trace thickness T (1oz = 35µm).
  2. Enter substrate dielectric constant εr (FR4 ≈ 4.3, Rogers 4350B ≈ 3.48, PTFE ≈ 2.1).
  3. Result: characteristic impedance Z₀ and effective εr.
  4. Target 50Ω for single-ended RF; 100Ω differential is 2× single-ended with close coupling.
Input
mm
mm
mm (1oz = 0.035)
Presets
Cross Section
Z₀
—Ω
εeff
—
W/H ratio
—
Prop. Delay
—ps/mm

Show Work

Enter dimensions.

Formulas (Hammerstad-Jensen)

Effective εr
εe = (εr+1)/2 + (εr−1)/2 · (1+12h/w)−½
Partial-fill compensation.
Z₀ (w/h < 1)
60/√εe · ln(8h/w + w/4h)
Narrow trace formula.
Z₀ (w/h ≥ 1)
120π / (√εe · [w/h + 1.393 + 0.667·ln(w/h + 1.444)])
Wide trace formula.
Propagation Delay
tpd = √εe / c
About 6.2 ps/mm on FR4.
50Ω Rule
w ≈ 1.8 × h (1oz FR4)
Quick bench estimate.
Validity
0.05 < w/h < 20
Hammerstad accuracy ±2%.

History of Microstrip

Microstrip transmission lines emerged in the 1950s at ITT Labs as a compact alternative to waveguide for microwave electronics. The first practical formulas for characteristic impedance were developed by Harold Wheeler (Hewlett-Packard) in 1964, refined by Erik Hammerstad at SINTEF Norway in 1975, and extended by Hammerstad and Øystein Jensen in 1980 into the widely-used H-J formula this calculator implements.

The H-J formulas achieve ±2% accuracy across the practical trace-geometry range (0.05 < w/h < 20) by empirically fitting to numerical-field-solver data. They account for the fact that the field doesn't completely fill the substrate — it fringes into air above the trace — requiring the "effective dielectric constant" correction εe.

Modern field solvers (Ansys HFSS, CST Microwave Studio, Polar Si9000) give sub-1% accuracy but require substantial compute time and software cost. The H-J closed-form formulas remain the go-to for first-pass design and educational use, and still power the built-in impedance calculators in every major ECAD tool (Altium, KiCad, Mentor Graphics).

About This Calculator

Enter microstrip geometry: trace width W, substrate height H, trace copper thickness T, and dielectric constant εr. The tool computes Z₀ using the Hammerstad-Jensen formula and effective εr for the propagation-delay correction.

Common targets: 50Ω for SMA connectors and most RF, 75Ω for video coax, 90Ω for USB 2.0 differential, 100Ω for DDR memory and Ethernet. For tight tolerance (±5%), use a field solver and validate with TDR on a prototype board. Everything runs client-side.

Frequently Asked Questions

What is microstrip?

An outer-layer PCB trace with a ground plane directly below. Common for RF and high-speed signals where the return path is well-defined.

Why match impedance?

Mismatched transmission lines reflect energy back to the driver, causing ringing, overshoot, and EMI. Match source/load to Z₀ for clean signals.

FR4 limitations?

FR4 εr drifts with frequency (~4.5 at 100 MHz, ~4.0 at 10 GHz) and has significant loss above a few GHz. Use Rogers/PTFE above 5 GHz.

Common Use Cases

50Ω RF Trace

1.6mm FR4 (εr=4.3), 1oz Cu: ~2.95mm wide for 50Ω.

USB 2.0 Diff Pair

90Ω differential: ~0.5mm traces, 0.125mm gap on typical FR4.

DDR3/4 Memory

40-50Ω single-ended, 80-100Ω diff — depends on board stackup.

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