About the Microstrip Impedance Calculator
This microstrip impedance calculator gives the characteristic impedance (Z0) of a trace on the outer layer of a printed circuit board, running over a solid ground plane. Enter the trace width, the dielectric thickness to the plane, the copper thickness and the board’s relative permittivity (Er, about 4.2–4.6 for FR-4), and it returns Z0 along with the effective dielectric constant, the propagation delay per inch and per millimetre, and the signal velocity as a fraction of light speed. A second mode solves for the trace width that gives a target impedance such as 50 Ω or 90 Ω differential-pair halves.
It is for anyone routing RF feeds, antenna lines, high-speed digital buses like USB, HDMI or DDR, or fast clock edges, where an impedance mismatch causes reflections, ringing and EMI. Use it for a quick first pass before confirming the stack-up with your board fabricator, who will adjust widths for their exact material.
The main result uses the Hammerstad and Bahl–Trivedi closed-form equations with a correction for copper thickness, generally within 1–2% of field-solver results for typical geometries. The older IPC-2141 formula is shown for comparison; it is only reasonable for width-to-height ratios between about 0.1 and 2. Solder mask lowers Z0 by a few ohms and is not included.
With the default inputs, the characteristic impedance z0 is 47.01 Ω. Change any value above to recalculate instantly.
How to use the microstrip impedance calculator
- 1Choose whether to find the impedance or the width for a target impedance.
- 2Pick mil or mm, then enter the dielectric height to the ground plane and the copper thickness.
- 3Enter the trace width (or the target impedance, e.g. 50 Ω).
- 4Set Er for your laminate — about 4.3 for FR-4 at 1 GHz.
- 5Read Z0, effective permittivity and delay, and confirm final widths with your PCB fabricator.
Formula and method
Microstrip fields run partly through the board and partly through the air above it, so the line behaves as if it were in a uniform medium with an effective permittivity εeff between 1 and εr. The Hammerstad equations give εeff and Z0 from the width-to-height ratio; the 0.04(1 − W/H)² term applies only to narrow lines. Copper thickness makes the trace act slightly wider: the effective width is We = W + (T/π)(1 + ln(2H/T)) (or ln(4πW/T) for very narrow traces), and thickness also slightly reduces εeff, following Bahl and Trivedi.
Propagation delay is √εeff / c, which is about 84.7 ps per inch multiplied by √εeff. The IPC-2141 estimate 87/√(εr + 1.41) × ln(5.98H/(0.8W + T)) is a simpler legacy formula. Width synthesis repeatedly halves the search interval until the computed Z0 matches the target.
- Z0
- Characteristic impedance (Ω)
- W, We
- Trace width and thickness-corrected effective width
- H
- Dielectric thickness between trace and reference plane
- T
- Copper thickness
- εr, εeff
- Relative and effective permittivity
- c
- Speed of light, 299,792,458 m/s
Worked examples
10 mil trace on 5 mil FR-4 prepreg, 1 oz copper
W/H = 2, so the wide-line formula applies. The 1.4 mil copper widens the trace to an effective 11.32 mil, εeff is 3.13 and Z0 ≈ 47 Ω — slightly low, so narrow the trace to about 9 mil for 50 Ω. Signals travel at about 56.5% of light speed, 150 ps per inch. IPC-2141 underestimates this line at 42 Ω.
Width for 50 Ω on 1.6 mm FR-4 (two-layer board)
On a standard 1.6 mm two-layer board the ground plane is far away, so a 50 Ω line has to be wide: about 2.98 mm with 1 oz copper and Er = 4.5. That is why RF boards use 4-layer stack-ups with thin prepreg under the top layer.
Narrow 4 mil trace on 6 mil dielectric
With W/H = 0.67 the narrow-line formula applies. Half-ounce copper adds about 0.86 mil of effective width; εeff ≈ 2.87 and Z0 ≈ 82 Ω. Narrow traces over thick dielectric give high impedance — widen to about 5 mil for a 75 Ω line.
Frequently asked questions
What trace width gives 50 ohms?+
It depends mainly on the dielectric height: on FR-4 a 50 Ω microstrip is roughly 1.8–2 times as wide as the dielectric is thick. Over 5 mil prepreg that is about 8–9 mil; on a 1.6 mm two-layer board it is close to 3 mm.
What is the difference between microstrip and stripline?+
Microstrip is an outer-layer trace over one ground plane with air above; stripline is buried between two planes. Stripline is fully inside the dielectric, so it has higher εeff, slower propagation and lower impedance for the same width, but better shielding.
What dielectric constant should I use for FR-4?+
FR-4 is typically 4.2–4.6 at 1 GHz and varies with resin content and frequency. Prepreg and core can differ. Ask your fabricator for the Er of the exact materials in your stack-up when impedance tolerance matters.
Does copper thickness affect impedance?+
Yes, slightly. Thicker copper increases the effective width and edge capacitance, lowering Z0 by roughly 1–3 Ω going from 0.5 oz to 2 oz on typical geometries. The calculator includes this correction.
Does solder mask change microstrip impedance?+
Solder mask over the trace adds dielectric above it and typically lowers Z0 by 1–3 Ω. Fabricators account for it in their field-solver models, so treat closed-form results as a starting point.
How accurate is the IPC-2141 formula?+
It is a simple fit that can be off by 5% or more and is only intended for W/H between about 0.1 and 2 and Er between 1 and 15. The Hammerstad equations used for the main result are considerably more accurate.