Microstrip Width Calculator (Impedance to Width)
Use this tool to estimate PCB trace width for a target microstrip impedance using Hammerstad/Wheeler-style closed-form equations.
What this microstrip width calculator does
A microstrip is a PCB trace on an outer layer referenced to a nearby ground plane. At RF and fast digital edge rates, that trace behaves like a transmission line and needs controlled impedance. This calculator finds the required trace width for your chosen impedance, board stackup height, and dielectric constant.
In plain language: if you want 50 Ω, 75 Ω, or another impedance, this tool estimates how wide your trace should be so your board is closer to spec on the first pass.
Inputs explained
1) Target impedance (Z0)
Common values are 50 Ω for RF/single-ended lines and 75 Ω for some video/coax systems. Choose based on your interface standard and system requirements.
2) Relative dielectric constant (εr)
This is the substrate permittivity. FR-4 is often roughly 4.0 to 4.7 depending on resin, glass weave, and frequency. For better accuracy, use your PCB fabricator’s stackup data at your operating frequency.
3) Substrate height (h)
Distance between the signal trace and its reference plane. Larger height generally means wider traces for the same impedance.
4) Copper thickness (t)
Thicker copper slightly reduces impedance for a fixed geometric width (because effective electrical width increases). Including copper thickness makes results more realistic.
Equations used (overview)
The calculator uses standard closed-form microstrip approximations:
εeff = (εr+1)/2 + (εr-1)/2 · [1/√(1+12/u) + (u<1 ? 0.04(1-u)^2 : 0)]
If u ≤ 1:
Z0 = (60/√εeff) · ln(8/u + 0.25u)
If u > 1:
Z0 = (120π)/(√εeff · (u + 1.393 + 0.667 ln(u + 1.444)))
To find width from impedance, the script performs a numeric solve (binary search) until it converges.
Practical design tips
- Always verify with your PCB manufacturer’s impedance calculator before release.
- Keep a solid, uninterrupted reference plane under controlled-impedance traces.
- Avoid stubs, abrupt neck-downs, and unnecessary vias on RF paths.
- For high-frequency work, include solder mask effects and copper roughness in final checks.
- Use field solver tools for very tight tolerance, mmWave, or unusual geometries.
Example quick check
A common setup is FR-4 with εr ≈ 4.2, h = 1.6 mm, and 35 µm copper. For 50 Ω, you typically get a few millimeters of width (often around 3 mm on this coarse stackup). Your exact value depends on actual laminate and process tolerances.
Limitations
This is a strong first-order calculator, not a replacement for stackup-specific simulation. Real boards include dispersion, resin-content variation, etch profile, solder mask, and fabrication tolerance. Use this tool for design estimation, then confirm with your fab notes and SI/RF verification workflow.