Microstrip Patch Antenna Calculator computes patch length, width, effective dielectric constant, fringing extension, and minimum ground plane dimensions for a target frequency.
Microstrip Patch Antenna Calculator for Rectangular Patch Design
This tool computes the physical length, width, and recommended ground plane size for a rectangular microstrip patch antenna resonating at a target frequency on a given substrate. RF and antenna engineers use it to size patches for WLAN, IoT, and other microwave-band designs before simulation or fabrication.
How to Use
Enter resonance frequency, substrate dielectric constant, and substrate thickness. The calculator returns patch length and width, effective dielectric constant, fringing extension, and the minimum recommended ground plane and substrate dimensions.
Formula
The design equations follow the transmission-line model in Constantine Balanis’s Antenna Theory: Analysis and Design, the standard reference for rectangular microstrip patch design. Patch width comes first:
$$W = \frac{c}{2f_0}\sqrt{\frac{2}{\varepsilon_r+1}}$$
Effective dielectric constant accounts for fields fringing partly through air, partly through substrate:
$$\varepsilon_{eff} = \frac{\varepsilon_r+1}{2} + \frac{\varepsilon_r-1}{2}\left[1+12\frac{h}{W}\right]^{-1/2}$$
Fringing at the radiating edges electrically lengthens the patch, so the extension $\Delta L$ is subtracted twice from the theoretical length $L_{eff} = c/(2f_0\sqrt{\varepsilon_{eff}})$:
$$\Delta L = 0.412h\,\frac{(\varepsilon_{eff}+0.3)\left(\frac{W}{h}+0.264\right)}{(\varepsilon_{eff}-0.258)\left(\frac{W}{h}+0.8\right)}$$
$$L = L_{eff} – 2\Delta L$$
Minimum ground plane and substrate size follow the commonly cited margin of six substrate heights beyond the patch on each dimension: $W_g = W+6h$, $L_g = L+6h$. The most common input mistake is inverting $h/W$ as $W/h$ inside the effective dielectric constant term — the formula uses $h/W$, and swapping it changes $\varepsilon_{eff}$ enough to shift every downstream dimension.
The $L$ and $W$ equations assume the substrate and ground plane are effectively infinite — that assumption is where the fringing-field model comes from. The $W+6h$/$L+6h$ ground plane size is a separate, practical minimum recommendation, not something derived from the same equations.
Cutting the ground plane down to exactly $W \times L$, with no margin, will measurably shift the actual resonant frequency below what this calculator predicts, because the fringing capacitance the formula relies on no longer has room to form the way the model assumes.
FAQ
Why is the patch shorter than the theoretical length?
Fringing fields at the radiating edges make the patch behave electrically longer than it physically is. The calculator subtracts $2\Delta L$ from the theoretical length so the built patch resonates at the target frequency.
Does a wider patch change the resonant frequency?
Width mainly sets input impedance and radiation efficiency, not resonant frequency, which is controlled by length. Width does feed back into $\varepsilon_{eff}$ and $\Delta L$, so it has a small secondary effect on length.
Can I use a smaller ground plane than recommended?
You can, but the resonant frequency and radiation pattern will drift from the calculated values. The $W+6h$/$L+6h$ margin is a practical minimum for the fringing-field assumptions to hold reasonably well.
Why does a higher dielectric constant shrink the patch?
Higher $\varepsilon_r$ raises $\varepsilon_{eff}$, which shortens the effective wavelength at the same frequency. Both $L$ and $W$ scale down as a result, which is why high-$\varepsilon_r$ substrates are used for compact antennas.
Does this account for substrate loss or bandwidth?
No. It solves the geometry for a target resonant frequency only. Bandwidth, loss tangent, and efficiency depend on substrate material properties and feed design that this calculator doesn’t model.