Microstrip Impedance and Width Calculator (FR-4, Rogers)
On 1.6 mm FR-4 a 50 Ω microstrip is about 3.06 mm wide (w/h 1.91, effective permittivity 3.33). Enter your substrate height and permittivity to get the width, impedance, guided wavelength and a quarter-wave length.
For practitioners
Results
- Strip width W
- 3.059 mm
- W / h
- 1.912
- Effective permittivity εeff
- 3.33
- Guided wavelength λg
- 68.45 mm (2.695 in)
- Quarter-wave length (λg/4)
- 17.11 mm
- Phase per mm
- 5.259° / mm
Quasi-static Hammerstad-Jensen model, zero copper thickness, no dispersion or conductor loss. Accuracy is about 1–2% for t/h below 0.05 and moderate frequencies. Use a field solver for tight tolerances, thick copper or millimeter-wave work.
How to use the calculator
Choose a substrate (or Custom εr), set the substrate height h in the unit you prefer, and then either:
- Find the width for a target impedance. Enter the impedance, for example 50 Ω, and the calculator returns the strip width W, the width-to-height ratio, the effective permittivity and the wavelengths at your frequency.
- Find the impedance for a given width. Enter the width and read the characteristic impedance.
The wavelength section is useful for stubs and quarter-wave transformers. The quarter-wave length is the physical length that gives 90° of phase at the frequency you entered, using the guided wavelength rather than the free-space wavelength.
Typical 50 Ω widths
| Substrate and height | Width for 50 Ω | W / h | Effective εr |
|---|---|---|---|
| FR-4 (εr 4.4), 1.6 mm | 3.06 mm | 1.91 | 3.33 |
| FR-4 (εr 4.4), 0.8 mm | 1.53 mm | 1.91 | 3.33 |
| FR-4 (εr 4.4), 0.2 mm | 0.382 mm | 1.91 | 3.33 |
| RO4003C (nominal εr 3.38), 0.508 mm | 1.18 mm | 2.32 | 2.67 |
| RO4350B (nominal εr 3.48), 0.508 mm | 1.15 mm | 2.27 | 2.73 |
| RO4350B (nominal εr 3.48), 0.254 mm | 0.576 mm | 2.27 | 2.73 |
| RT/duroid 5880 (εr 2.2), 0.787 mm | 2.42 mm | 3.08 | 1.87 |
For the material properties behind these numbers see the RF View glossary pages on Rogers RO4350B and RT/duroid 5880, and for the theory of the line itself microstrip line theory and characteristic impedance.
The width scales with the substrate height, so a thinner dielectric gives a proportionally narrower 50 Ω line. That is why dense boards with thin prepreg layers have very narrow traces.
Impedance versus width on 1.6 mm FR-4
| Width (mm) | Z0 (Ω) | Effective εr |
|---|---|---|
| 0.5 | 112 | 3.00 |
| 1 | 87.5 | 3.09 |
| 2 | 63.6 | 3.22 |
| 3 | 50.8 | 3.32 |
| 4 | 42.5 | 3.41 |
| 6 | 32.1 | 3.53 |
A wider strip lowers the impedance, and the effective permittivity rises slowly as the strip gets wider because more of the field is confined in the dielectric.
The model behind the numbers
The calculator uses the quasi-static formulas of Hammerstad and Jensen (1980, "Accurate models for microstrip computer-aided design"). For a strip of width W on a substrate of height h and relative permittivity εr, with u = W/h, the effective permittivity is:
with a small extra term for narrow strips (u < 1). The characteristic impedance is then:
To go the other way (find the width for a given impedance) the calculator uses Hammerstad's synthesis equations. The guided wavelength is the free-space wavelength divided by the square root of the effective permittivity:
The two impedance expressions join at u = 1 with a known step of about 0.4%, which is inside the accuracy of the model.
Where the model is accurate, and where it is not
The calculator is a good starting point for design, not a substitute for a field solver or for measurement. Keep these limits in mind:
- Copper thickness. The model assumes an infinitely thin strip. For typical 35 µm (1 oz) copper on a 0.2 mm substrate the thickness is not negligible and the real impedance will be a little lower. Include it in a field solver for tight tolerances.
- Frequency. The formulas are quasi-static. As frequency rises, dispersion increases the effective permittivity and the impedance drifts. For millimeter-wave work or very thick substrates use a full-wave solver.
- Material variation. FR-4 permittivity is not a single number: it depends on the glass and resin content, the manufacturer, and frequency, and values from about 4.2 to 4.8 are common. A 5% change in εr moves the 50 Ω width by only a few percent, but it also shifts phase length. For repeatable results use a controlled-impedance stackup and ask the fabricator for the actual value.
- Solder mask and nearby structures. A mask layer, a ground plane that is not far below, coplanar ground pours and neighboring traces all change the impedance. Coplanar waveguide with ground is a different structure and needs a different calculator; see coplanar waveguide and stripline.
- Conductor and dielectric loss. The calculator gives impedance and wavelength, not attenuation. See skin depth and how to minimize RF PCB insertion loss.
Practical tips
When you place a 50 Ω line, keep the width constant along its length, because every width change is a small impedance step that reflects. Use curves or mitered corners rather than sharp right angles for wide traces, and keep the return path continuous under the line. If the line crosses a gap in the ground plane, the impedance and the return current path change at that point and the model above no longer applies.
Check the finished design with a measurement. A time-domain reflectometry (TDR) trace or the return loss of a test coupon shows quickly whether the fabricated impedance matches your target, and the VSWR and return loss calculator converts the result into the numbers used in specifications.
In plain words · for students and beginners
Microstrip lines in plain words
What a microstrip is
A microstrip is a narrow strip of copper on the top of a circuit board, with a solid sheet of copper (the ground plane) on the other side of the board. The signal travels in the electric field between the strip and the ground. So the strip is not just a wire: it is a small transmission line.
What "impedance" means here
Impedance tells you how much voltage the line needs for a given current. You can think of it as the line's "push-back" against the signal. Two things set it: how wide the strip is, and how far it sits above the ground plane. A wider strip is closer, in effect, to the ground, so it carries more current for the same voltage and its impedance goes down. A narrower strip does the opposite. The picture is only a guide: the exact numbers come from the formulas above, and the board material matters as well.
Why 50 ohm
Most RF equipment, cables and connectors are built for 50 ohm, so the lines on the board should be 50 ohm too. The value is a historical compromise between power handling and loss in air-filled coaxial cable that became the standard. What matters for you is that everything in the chain agrees on it.
Why the board is "slower" than air
Part of the field travels inside the board and part in the air above it. The signal therefore feels a mixture of the two, and the effective permittivity is a value between 1 (air) and the board's own value. A bigger effective permittivity means a shorter wavelength on the board, which is why a quarter-wave line on FR-4 is much shorter than in air.
Using the calculator, step by step
- Choose the board material and enter the height of the dielectric between the strip and the ground plane. Take it from the stackup of your board.
- Type 50 for the target impedance and read the strip width.
- Ask your board manufacturer for the real permittivity and tolerance of the material, and check the result with a test coupon.
Mistakes beginners make
- Using the free-space wavelength to size a line. On a board the wavelength is shorter.
- Forgetting that the height is the distance to the ground plane, not the thickness of the whole board.
- Assuming FR-4 has exactly the nominal permittivity. It varies from batch to batch and with frequency.
Remember
- Wider strip means lower impedance. Thicker dielectric means higher impedance.
- On FR-4, a 50 ohm line is roughly twice as wide as the dielectric is thick.
- The calculator is a starting point: confirm with the manufacturer's data and a measurement.
Related pages on RF View
Theory and substrates
- Microstrip line theory
- Characteristic impedance Z0
- Rogers RO4350B substrate
- Rogers RT/duroid 5880 substrate
- Skin depth
- Coplanar waveguide and stripline, the other common line structures
Board design
- RF PCB stackup design
- How to minimize RF PCB insertion loss
- Transmission-line impedance transformer and how to design a quarter-wave transformer
Calculators
- Quarter-wave length calculator and wavelength and frequency calculator, to check the quarter-wave length from the results above
- L-network matching calculator for the parts that connect to the line
- VSWR and return loss calculator to turn a measured result into specification numbers
RF View can plot the S-parameters of a measured or simulated line and compare it with the target.
Frequently asked questions
What width is a 50 ohm microstrip on 1.6 mm FR-4?
About 3.06 mm for a relative permittivity of 4.4, which is a width-to-height ratio of 1.91. Real FR-4 varies between lots and with frequency, so the true value can differ by several percent.
Does copper thickness change the impedance?
Yes, thicker copper makes the line behave as if it were slightly wider, which lowers the impedance by a small amount. This calculator assumes zero thickness, which is accurate to roughly 1–2% when the copper thickness is below 5% of the substrate height.
Which dielectric constant should I use for Rogers materials?
Use the value the manufacturer recommends for microstrip design in the current datasheet, which can differ from the nominal value measured by the standard test method. Choose Custom εr in the calculator to enter it.
Why is the effective permittivity lower than the substrate permittivity?
The field of a microstrip travels partly in the substrate and partly in the air above it, so the wave sees an average of the two. That is why the effective permittivity always lies between 1 and the substrate value.