PCB Trace Impedance Calculator
Work out the characteristic impedance of a PCB trace. Microstrip, stripline and edge-coupled differential pairs, each with two independent formulas side by side, the width needed for a target impedance, and the propagation delay.
How to Use
- Pick the structure: Microstrip for an outer-layer trace over a plane, Stripline for an inner-layer trace between two planes, or Differential pair for an edge-coupled pair (then choose microstrip or stripline for the pair).
- Enter the trace width W, the dielectric height H (or the plane-to-plane spacing B for stripline), the copper thickness T and the dielectric constant εr. Every length has its own unit: mm, mil, µm or inches.
- For a pair, also enter the gap S between the two traces.
- Optionally type a target impedance, such as 50 Ω or 90 Ω, to get the width that hits it.
- Read the first readout, compare it with the second formula, and check Show Work for each step and any range warning.
Worked Example
A 50 Ω microstrip. A 3 mm trace of 35 µm copper over 1.6 mm FR-4 (εr = 4.3). W/H = 1.875. Wheeler’s formula, with the copper widening the trace by ΔW′ = 0.043 mm, gives Z₀ = 50.6 Ω. The same line in air would be 90.68 Ω, so εeff = (90.68 ÷ 50.6)² = 3.212 and the delay is √3.212 ÷ c = 5.978 ps/mm. Solving the other way, 50.0 Ω needs a 3.06 mm trace.
An inner-layer trace. 0.2 mm wide, centred between planes 0.5 mm apart, 18 µm copper, εr = 4.0: IPC-2141 gives Z₀ = 60/√4 × ln(1.9 × 0.5 ÷ (0.8 × 0.2 + 0.018)) = 50.24 Ω. Cohn’s exact answer for the same trace with no thickness is 56.42 Ω, which shows how much 18 µm of copper matters in a 0.5 mm gap.
The common mistake: using a single-trace rule for a tight pair. Two 0.5 mm traces 0.125 mm apart on 0.25 mm of εr 4.3 are often quoted as a 90 Ω USB pair. The IPC-2141 pair formula gives 63.19 Ω and the Kirschning–Jansen coupled-line formulas give 77.74 Ω (Zo = 38.87 Ω): neither is 90 Ω. At that gap the traces need to be about 0.372 mm wide for 90 Ω.
Show Work
Formulas
Background
Seymour Cohn worked out the exact impedance of a thin strip centred between two ground planes in 1954 (IRE Transactions MTT-2), using elliptic integrals, and extended it to two coupled strips in 1955. Those results are still the reference that every stripline formula is checked against, and Rogers Corporation’s coupler design note uses them unchanged.
A microstrip has no exact closed form because the field runs partly in the board and partly in air. Harold Wheeler’s 1977 approximation, given in Brian Wadell’s Transmission Line Design Handbook (1991), is quoted at 2 % for any width and dielectric. Erik Hammerstad and Øystein Jensen published their accurate microstrip models in 1980, and Manfred Kirschning and Rolf Jansen built their coupled-line formulas on them in 1984. The IPC published its own simpler equations in IPC-2141 (1996) and IPC-2141A (2004); they are easy to use by hand but, as Analog Devices’ tutorial MT-094 warns, approximate.
In 1999 Andrew Burkhardt, Christopher Gregg and Alan Staniforth of Polar Instruments compared formulas with a boundary-element field solver and with over 1,500 test tracks made by three UK board makers and measured by TDR. The field solver matched the measurements with a mean difference under 0.5 % and a standard deviation under 2 %, which is why fabricators quote field-solver numbers for controlled-impedance orders.
About This Calculator
This calculator replaces separate microstrip, stripline and differential-pair pages. Each structure shows two independent results: Wheeler against IPC-2141 for microstrip, IPC-2141 (with copper) against Cohn’s exact zero-thickness answer for stripline, and Kirschning–Jansen or Cohn coupled-line theory against the IPC-2141 pair formula for differential pairs. When the two disagree by more than the source documents allow, it says so. It also solves for the width that gives a target impedance.
Sources: Analog Devices MT-094 (IPC-2141 equations, accuracy and delay rules), Texas Instruments LVDS Owner’s Manual figure 5-1 (IPC-2141 differential equations), Polar Instruments’ “Calculation of PCB Track Impedance” (Wheeler and Cohn equations, test table), Rogers design note 3.2.1 (coupled stripline, example table) and Kirschning & Jansen 1984 (coupled microstrip). All of them are closed-form approximations: a field solver, and a TDR coupon on the real board, are more accurate. Everything runs in your browser.
Related calculators: PCB Trace Width Calculator, PCB Stackup Impedance, and Differential Termination.
Frequently Asked Questions
What trace width gives 50 Ω on a 1.6 mm FR-4 board?
On 1.6 mm FR-4 with εr = 4.3 and 35 µm (1 oz) copper, the Wheeler formula gives 50 Ω at a width of 3.06 mm. A 3 mm trace is 50.6 Ω. The rough rule that a 50 Ω microstrip is about twice as wide as the dielectric is thick comes from the same physics.
Why do different impedance calculators give different answers?
They use different formulas. Analog Devices tutorial MT-094 works a 20 mil trace on 10 mil FR-4 (εr 4.0, 1.4 mil copper): the IPC-2141 formula gives 46.18 Ω, while the more accurate Wheeler formula gives 48.85 Ω. MT-094 says the IPC microstrip equation is most accurate between 50 and 100 Ω and the IPC stripline equation is typically within about 6 %.
What are odd-mode, even-mode and differential impedance?
Odd mode is the impedance of one trace when its partner carries the opposite signal; even mode is when both carry the same signal. Differential impedance is twice the odd mode and common-mode impedance is half the even mode. A 0.37 mm pair with a 0.2 mm gap on 0.2 mm FR-4 has Zo = 44.92 Ω and Ze = 57.59 Ω, so Zdiff = 89.83 Ω.
Does copper thickness change the impedance?
Yes, thicker copper lowers it, and more so on thin dielectrics. A 0.2 mm stripline in 1 mm of εr 4.3 is 71.6 Ω by IPC-2141 with no copper thickness and 65.87 Ω with 35 µm copper. On a 3 mm microstrip over 1.6 mm the same copper only moves Wheeler from 51.03 Ω to 50.60 Ω.
How fast does a signal travel along a PCB trace?
The delay is √εeff divided by the speed of light. The 3 mm microstrip on εr 4.3 has εeff = 3.212, so it delays 5.978 ps per mm. A stripline sits wholly in the dielectric, so εr 4.3 gives 6.917 ps/mm; MT-094 rounds this to 85√εr ps/in, about 170 ps/in for εr 4.0.
How do I use the PCB Trace Impedance Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
A 50 Ω RF feed on a two-layer board
Over 1.6 mm FR-4 (εr 4.3, 35 µm copper) the trace for 50 Ω is 3.06 mm wide; a 3 mm trace comes out at 50.6 Ω.
A 90 Ω USB-style pair
Two 0.37 mm traces 0.2 mm apart on 0.2 mm of εr 4.3 give 89.83 Ω differential by the Kirschning–Jansen coupled-line formulas.
A 50 Ω inner-layer trace
A 0.2 mm trace centred between planes 0.5 mm apart, εr 4.0 and 18 µm copper, is 50.24 Ω by IPC-2141.
A 75 Ω video line
MT-094’s 8.3 mil trace on 10 mil FR-4 is 75.05 Ω by IPC-2141 and 75.85 Ω by Wheeler.
Checking a stripline coupler
Rogers’ RT/duroid 5880 example (0.025 in lines, 0.005 in gap, 0.062 in between planes) gives Ze = 96.11 Ω, Zo = 48.86 Ω, √(Ze·Zo) = 68.53 Ω and 9.74 dB coupling, the same as Rogers’ table.
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