Microstrip Impedance Calculator
Calculate the characteristic impedance of a PCB microstrip trace from trace width, dielectric height, copper thickness and εr (Hammerstad–Wheeler and IPC-2141), plus effective permittivity and delay.
How it works
εeff = (εr + 1)/2 + (εr − 1)/2 × (1 + 12h/w)^−½ [+ 0.04(1 − w/h)² term if w/h < 1] · w/h ≤ 1: Z₀ = 60/√εeff × ln(8h/w + w/4h) · w/h ≥ 1: Z₀ = 120π / [√εeff × (w/h + 1.393 + 0.667 ln(w/h + 1.444))] · thickness: w_eff = w + (t/π)(1 + ln(2h/t)) · IPC-2141: Z₀ = 87/√(εr + 1.41) × ln(5.98h / (0.8w + t))
A microstrip is a trace on an outer PCB layer above a solid ground plane, with dielectric below and air above, so the wave travels partly in each and sees an effective permittivity between 1 and εr. The Hammerstad–Wheeler closed-form equations used here are accurate to about 1% for 0.1 < w/h < 20 (and a little less once copper thickness is added); the simpler IPC-2141 formula is shown for comparison and is only reliable for w/h between about 0.1 and 2. For controlled-impedance boards, confirm the stack-up with your fabricator, since solder mask and the real FR-4 εr at your frequency shift Z₀ by several ohms.
Worked example
A 3 mm trace of 35 µm copper over 1.6 mm FR-4 (εr 4.5): w/h = 1.875, εeff = 3.393, and the thickness widens the trace to an effective 3.061 mm, giving Z₀ = 49.74 Ω — a 50 Ω line. IPC-2141 gives 48.97 Ω, and signals travel at 6.14 ps/mm (velocity factor 0.543).
Sources: Hammerstad, E. & Jensen, O. (1980) — Accurate Models for Microstrip Computer-Aided Design, IEEE MTT-S · Wikipedia — Microstrip (characteristic impedance)
Frequently asked questions
What trace width gives 50 Ω on 1.6 mm FR-4?
About 2.9–3.0 mm for a microstrip with 35 µm copper and εr ≈ 4.5. On a 4-layer board with 0.2 mm to the ground plane it is only about 0.35 mm, which is why RF boards use thin dielectrics.
What is the difference between microstrip and stripline?
A microstrip is on an outer layer with air above; a stripline is buried between two ground planes. Stripline has no radiation and εeff = εr, so the same width gives a lower impedance.
Does solder mask change the impedance?
Yes. A 20–30 µm layer of solder mask (εr ≈ 3.5–4) over the trace typically lowers Z₀ by 1–3 Ω. Fabricators account for it in their impedance models.
Which εr should I use for FR-4?
FR-4 varies with glass weave, resin content and frequency, from about 4.7 at 1 MHz to about 4.2 at a few GHz. Ask your fabricator for the εr of the actual laminate.
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This calculator is for educational purposes. Double-check important results before acting on them.