What it does
Most antennas are sized from the wavelength, λ = c / f. This calculator turns a frequency into the lengths you cut or etch for four common antennas, shows each formula, and draws the result:
- Half-wave dipole: two equal wires fed in the centre, the reference antenna of radio.
- Quarter-wave monopole: a whip or ground-plane antenna, half a dipole above a conducting surface.
- Rectangular microstrip patch: a copper rectangle on a circuit board, used in Wi-Fi, GPS and 5G devices. It uses the transmission-line model to give the width, effective permittivity, fringing extension and length, then the edge resistance and the inset depth for a 50 Ω (or other) feed.
- Yagi-Uda beam: a driven element with a reflector and directors, laid out from common rules of thumb as a starting point.
All the arithmetic happens in your browser.
How to use it
- Choose the antenna with the buttons at the top.
- Type the frequency and choose kHz, MHz or GHz. Choose metric or imperial lengths.
- Dipole and monopole: the shortening factor allows for the end effect: a real resonant wire is a little shorter than the free-space half wavelength. About 0.95 to 0.98 for thin wire is the usual starting point; thick tubes need less.
- Patch: type the board’s relative permittivity εr and thickness h, and the impedance of the feed line you want to match (50 Ω is usual). Use the εr your laminate’s maker gives at your frequency.
- Yagi: pick the number of directors. Every ratio (element lengths and spacings in wavelengths) can be changed.
Worked example
The page opens with a dipole for 145 MHz (the 2 m amateur band). The wavelength is 2.0675 m, so the free-space half wavelength is 1.0338 m. With a shortening factor of 0.95 the dipole is 98.21 cm long, each side 49.1 cm.
Switch to Patch: the frequency changes to 2.45 GHz. On a 1.6 mm board with εr = 4.4, the patch is 3.723 cm wide and 2.881 cm long, εeff = 4.081 and ΔL = 0.7386 mm. The edge resistance is 321.4 Ω, so a 50 Ω line is fed through notches 1.069 cm deep. The ground plane should be at least 4.683 × 3.841 cm.
Formulas
- Wavelength: λ = c / f, with c = 299,792,458 m/s.
- Dipole: L = k·λ/2. Monopole: L = k·λ/4.
- Patch width: W = c/(2f) · √(2/(εr + 1)).
- Effective permittivity: εeff = (εr + 1)/2 + (εr − 1)/2 · (1 + 12h/W)^(−1/2).
- Fringing: ΔL = 0.412h (εeff + 0.3)(W/h + 0.264) / ((εeff − 0.258)(W/h + 0.8)).
- Patch length: L = c / (2f√εeff) − 2ΔL.
- Edge resistance: Rin = 1 / (2(G1 + G12)), with the slot conductance G1 and mutual conductance G12 found by numerical integration; inset depth y0 = (L/π)·acos(√(Z0/Rin)).
FAQ
How accurate is the patch? The transmission-line model is usually within a few percent for thin boards (h well below λ/10). The εr of FR-4 varies from batch to batch, so expect to trim or tune. A full-wave simulator gives the final answer.
Are the Yagi numbers a design? No. They are the commonly quoted rule-of-thumb proportions, good for a first build or for understanding the layout. Gain and front-to-back ratio depend strongly on the exact lengths and spacings; optimise them in a modelling program.
Why is the dipole feed about 73 Ω, not 50 Ω? That is the radiation resistance of a thin, resonant half-wave dipole in free space. Near the ground or with bent (inverted-V) legs it drops, often close to 50 Ω.
Was it checked? The patch formulas reproduce Balanis’s worked examples (10 GHz on εr 2.2: W 1.186 cm, L 0.906 cm, Rin about 228 Ω, inset about 0.31 cm) and match an independent scipy calculation of the integrals.
For study and planning, not a substitute for professional judgement. Check local rules for transmitting antennas.
Where the numbers come from
- Dipole and monopole: standard antenna theory (resonant half-wave dipole, image theory), for example Balanis, Antenna Theory: Analysis and Design, chapter 4.
- Microstrip patch: transmission-line model with Hammerstad's fringing extension, radiating-slot and mutual conductances and inset feed, as described in Balanis, Antenna Theory, chapter 14; checked against Balanis's worked examples and an independent scipy implementation.
- Yagi-Uda element lengths and spacings: widely quoted rules of thumb (in wavelengths), stated as approximate starting values, not taken from any one design table.
- Speed of light: exact SI value. Example values are made up by fibub.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.