A Microstrip Inductance Calculator applies the ARRL formula to trace length, width, and height, returning inductance in nH, reactance in ohms, and nH-per-inch density for PCB trace routing.
The Microstrip Inductance Formula
The total inductance of a PCB microstrip trace is given by the closed-form expression
$$L_{ms}=0.00508\,L\left[\ln\left(\frac{2L}{W+H}\right)+0.5+0.2235\frac{W+H}{L}\right]$$
where $L_{ms}$ is the inductance in microhenries ($\mu$H), and $W$, $L$, and $H$ are the trace width, trace length, and height above the ground plane, all in inches. This formula treats the trace as a flat conductor over an infinite ground plane and computes the loop inductance of the magnetic field bounded by the conductor and its return path through the plane.
The logarithmic term dominates for long traces, the constant $0.5$ is a geometry correction, and the $0.2235(W+H)/L$ term accounts for end effects that matter when the trace is short relative to its cross-section.
The code enforces a single hard geometric constraint: the argument of the natural logarithm must exceed $1.0$, which requires $2L/(W+H) > 1$. When this fails, the model breaks down because the trace is not long enough for the quasi-static approximation to hold.
Walking Through a 2-Inch Trace Example
Take a trace with width $W = 0.10$ in, length $L = 2.00$ in, and height $H = 0.06$ in above the ground plane—the defaults the code loads on reset.
First, check the geometry: $2L/(W+H) = 4.00/(0.16) = 25.0$, which is well above $1.0$, so the formula is valid. Compute the bracket term in three pieces:
$$\ln\left(\frac{2 \times 2.00}{0.10 + 0.06}\right) = \ln(25.0) = 3.2189$$
$$0.5$$
$$0.2235 \times \frac{0.10 + 0.06}{2.00} = 0.2235 \times 0.08 = 0.0179$$
Bracket total: $3.2189 + 0.5 + 0.0179 = 3.7368$. Then
$$L_{ms} = 0.00508 \times 2.00 \times 3.7368 = 0.03797\ \mu\text{H} = 37.97\ \text{nH}$$
At $100$ MHz, the inductive reactance is $$X_L = 2\pi f L = 2\pi \times 10^8 \times 37.97 \times 10^{-9} = 23.86\ \Omega$$. The linear density is $37.97\ \text{nH} / 2.00\ \text{in} = 18.99\ \text{nH/in}$, or $7.48\ \text{nH/cm}$ after converting the length to centimeters.
What the Result Tells You About Your Layout
The output is the total loop inductance of the trace-ground pair, not the partial self-inductance of the trace alone. In high-speed or RF design, this number directly sets how much the trace opposes changes in current. A $38$ nH trace at $100$ MHz presents about $24\ \Omega$ of reactance—enough to matter in a $50\ \Omega$ system, where even a few nH of unwanted inductance can shift impedance matching and create reflections.
The code also reports density figures: nH per inch, nH per cm, and nH per square inch. These are useful benchmarks. A typical microstrip on standard $1.6$ mm FR4 with $0.1$ in width produces roughly $15$–$25$ nH per inch of trace length. If your density falls far outside that band, check whether your width is unusually narrow or your height above ground is unusually large.
Why Trace Length Dominates and Width Barely Moves the Needle
Length $L$ appears both as a direct multiplier outside the bracket and inside the logarithm. Doubling the length from $2$ in to $4$ in nearly doubles the inductance because the outer $L$ scales linearly while the logarithm grows slowly. By contrast, doubling the width from $0.1$ in to $0.2$ in only nudges the result downward slightly: the logarithm’s argument shrinks, but the $(W+H)/L$ correction term grows, partially offsetting the change.
Height $H$ behaves similarly to width in the formula, but in practice it is often the most constrained parameter—set by the PCB substrate thickness. The real sensitivity is in the unit conversion. The code accepts mil, mm, cm, and inches, and converts everything to inches before evaluating the formula.
A $100$ mil width is $0.1$ in, but entering $100$ while the unit is set to mm would feed $3.94$ in into the calculation, producing a drastically different and physically nonsensical result for a typical PCB trace.
The frequency input does not affect the inductance itself—the formula is quasi-static and frequency-independent. Frequency only drives the reactance and susceptance cards. At DC ($f = 0$), the reactance is zero and susceptance is undefined, which the code handles by showing zero susceptance when $X_L = 0$.
Frequently Asked Questions
Does dielectric constant affect microstrip inductance?
No. The formula used here computes the external loop inductance, which depends only on geometry—trace width, length, and height above ground. The dielectric constant $\varepsilon_r$ affects capacitance and characteristic impedance, but not the magnetic field geometry that determines inductance.
Why does the calculator reject some width, length, and height combinations?
The logarithm requires $2L/(W+H) > 1$. If your trace is shorter than half the sum of its width and height, the model’s quasi-static assumption fails and the code returns a geometry error rather than a meaningless negative or imaginary inductance.
What units should I use for microstrip inductance calculations?
Any dimension unit is valid as long as you select the matching unit from the dropdown. The code converts mil, mm, cm, and inches to inches internally. For PCB work, mils are common in North America, while mm is standard elsewhere. Just ensure the unit selector matches your input.
How accurate is this formula compared to electromagnetic simulation?
This closed-form expression is accurate to within a few percent for typical PCB geometries where the trace length is much greater than its width and height. For traces near vias, corners, or with non-uniform ground planes, a full 3D electromagnetic solver will give more precise results because this formula assumes an infinite, perfectly conducting ground plane and ignores edge effects.
Can I use this for stripline inductance?
No. This formula is specific to microstrip—a single trace on one side of the board with a ground plane on the opposite side. Stripline, where the trace is sandwiched between two ground planes inside a multilayer board, has a different field distribution and requires a different inductance model.
What is a typical microstrip inductance per inch?
For common PCB geometries—trace widths around $0.1$ in and substrate heights around $0.06$ in ($1.5$ mm)—the inductance density typically falls in the 15–25 nH per inch range. Narrower traces or taller substrates push this higher; wider traces or thinner substrates lower it.
Why is the reactance zero at DC?
Inductive reactance is $X_L = 2\pi f L$. At $f = 0$ (DC), the term $2\pi f L$ evaluates to zero, meaning a pure inductor presents no opposition to steady direct current. The susceptance, being the reciprocal of reactance, is also shown as zero in the code when frequency is at DC.
Model Limits and What This Calculation Omits
This calculator gives the quasi-static external inductance of an ideal microstrip with a perfectly conducting, infinite ground plane and zero-thickness trace.
It does not account for skin effect, which at microwave frequencies redistributes current and slightly reduces inductance; it does not model ground plane discontinuities, vias, or trace bends that add localized inductance; and it does not include the dielectric’s effect on the magnetic field because the formula assumes non-magnetic material. For final high-frequency designs, verify against electromagnetic simulation or measured S-parameters.