Microstrip line calculator
A strip over a ground plane is a line with a very non-uniform dielectric: part of the field runs in the substrate, part in the air. So the formulas carry not the material's permittivity but an “effective” one, somewhere between it and unity. The wavelength in the line comes from the same figure: shorter than in free space, longer than in solid dielectric.
| What to compute | |
| Substrate material | |
| Relative permittivity εr | |
| Substrate thickness h | |
| Strip width W (mm) | |
| Frequency (MHz) | |
| Result | |
| Strip width W | |
| Characteristic impedance Z₀ | |
| Effective permittivity εeff | |
| W/h ratio | |
| Wavelength in the line λg | |
| Quarter-wave section | |
📐 The formulas
Effective permittivity:
εeff = (εr + 1)/2 + (εr − 1)/2 × (1 + 12h/W)^(−1/2)
Characteristic impedance (Hammerstad):
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) ) ]
Wavelength in the line:
λg = λ₀ / √εeff
The inverse problem — the width for a given Z₀ — is solved by bisection.
A check point:
FR-4, εr = 4.4, h = 1.6 mm, W = 3.0 mm → εeff = 3.325, Z₀ = 50.8 Ω. So 50 Ω on a standard 1.6 mm board is about 3.08 mm.
- Hammerstad's formulas are accurate for W/h roughly between 0.1 and 20; outside that the calculator warns you
- εr = 4.4 for FR-4 is an average: in reality 4.2…4.8, and it falls with frequency. At gigahertz, design in some adjustment
- Copper thickness (a 1–3 % correction) and dispersion (εeff rising with frequency) are not accounted for
- Losses are not accounted for, neither in the metal nor in the dielectric
🎯 In practice
- Laying out an RF board: what trace width gives 50 Ω.
- Quarter-wave transformers on the board instead of in cable.
- Checking someone else's design: is it really 50 Ω.
- 50 Ω on 1.6 mm FR-4 is about 3 mm. Remember that number, it saves time.
- A thinner substrate gives a narrower trace for the same impedance — and less stray radiation.
- For accurate work at gigahertz, order impedance-controlled boards: the fabricator will pick the width.
- Work out section lengths in λg, not λ₀ — the difference is nearly a factor of two.
© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.
How to cite this calculator
UR3PKI. «Microstrip line calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/lines/microstrip (licence CC BY-NC-SA 4.0).The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.