Antenna Length Calculator
Calculate dipole, monopole, and 5/8 wave antenna lengths for any frequency.
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Common Antenna Frequencies
| Application | Frequency | Wavelength (λ) | Dipole | Monopole |
|---|---|---|---|---|
| CB Radio | 27 MHz | 11.10 m | 5.55 m | 2.78 m |
| FM Radio | 100 MHz | 3.00 m | 1.50 m | 74.9 cm |
| VHF Amateur | 145 MHz | 2.07 m | 1.03 m | 51.7 cm |
| ISM 433 | 433 MHz | 69.2 cm | 34.6 cm | 17.3 cm |
| LoRa (EU) | 868 MHz | 34.5 cm | 17.3 cm | 8.6 cm |
| LoRa (US) | 915 MHz | 32.8 cm | 16.4 cm | 8.2 cm |
| WiFi 2.4 GHz | 2.4 GHz | 12.5 cm | 6.2 cm | 3.1 cm |
| Bluetooth | 2.4 GHz | 12.5 cm | 6.2 cm | 3.1 cm |
| Zigbee | 2.4 GHz | 12.5 cm | 6.2 cm | 3.1 cm |
| WiFi 5 GHz | 5 GHz | 6.0 cm | 3.0 cm | 1.5 cm |
Antenna Length and RF Design
Antenna length is directly related to the operating frequency through the wavelength. The wavelength λ = c/f, where c is the speed of light (299,792,458 m/s) and f is the frequency in hertz. A half-wave dipole antenna is λ/2 long, and a quarter-wave monopole is λ/4 long.
The half-wave dipole is the most fundamental antenna type. It has a feed-point impedance of approximately 73 ohms, making it a good match for 75-ohm coaxial cable. Each arm of the dipole is λ/4 long, and the radiation pattern is omnidirectional in the plane perpendicular to the antenna.
A quarter-wave monopole antenna is half the length of a dipole and requires a ground plane to work. The ground plane acts as a mirror, creating a virtual image of the antenna. Its feed-point impedance is approximately 36 ohms. This is the most common antenna type for handheld radios, WiFi routers, and IoT devices.
The 5/8 wave antenna provides about 3-4 dB gain over a quarter-wave monopole by concentrating radiation at lower angles toward the horizon. It requires a matching network (usually a coil at the base) because its natural impedance is not 50 ohms. It is widely used in VHF/UHF mobile and base station applications.
Antenna Length Formula
λ = c / f Dipole = λ/2 Monopole = λ/4Key Points
- λ = c/f — wavelength is inversely proportional to frequency
- Dipole (λ/2) — ~73Ω impedance, omnidirectional pattern
- Monopole (λ/4) — ~36Ω impedance, requires ground plane
- 5/8 wave — ~3 dB gain over λ/4, needs matching network
- Real antennas are ~5% shorter due to end effects (velocity factor)
Applications
- WiFi and Bluetooth antenna design
- LoRa and IoT node antenna sizing
- Amateur radio antenna construction
- RF system design and link budgets
Antenna length formulas
Half-wave dipole: L = λ/2 = c/(2f) × 0.95 (×0.95 velocity factor)
Quarter-wave monopole: L = λ/4 = c/(4f) × 0.95
Full-wave loop: L = λ = c/f × 0.98
c = 299,792,458 m/s (speed of light)
Practical dipole shortening factor: 0.93–0.97 (end effect)Ham radio band reference
| Band | Frequency | Half-dipole | Quarter monopole | Notes |
|---|---|---|---|---|
| 80m | 3.7 MHz | 38.6 m | 19.3 m | Nighttime DX |
| 40m | 7.1 MHz | 20.1 m | 10.1 m | Most popular HF |
| 20m | 14.2 MHz | 10.1 m | 5.0 m | DX workhorse |
| 17m | 18.1 MHz | 7.9 m | 3.9 m | WARC band |
| 15m | 21.2 MHz | 6.7 m | 3.4 m | Solar cycle dep. |
| 10m | 28.5 MHz | 5.0 m | 2.5 m | Best for DX at peak |
| 2m | 145 MHz | 0.98 m | 0.49 m | Local VHF FM |
| 70cm | 433 MHz | 33 cm | 16.5 cm | LoRa, ISM band |
| WiFi | 2450 MHz | 5.8 cm | 2.9 cm | 2.4GHz PCB antenna |
| 5GHz | 5800 MHz | 2.5 cm | 1.2 cm | WiFi 5GHz |
Practical examples
Quarter-wave: L = (299,792,458 / 433,000,000) / 4 × 0.95 = 16.4 cm
Use 1.6mm copper wire, bend 5mm at bottom for feed. SWR < 1.5.
Quarter-wave: L = (0.122m) / 4 × 0.64 = 19.5mm (0.64 = PCB velocity factor)
Use 50Ω microstrip (1.6mm FR4: width ≈ 3mm). Keep ground clearance > 3mm.
Design tip: Real antennas are shorter than the theoretical λ/2 due to end effects. Use 0.95× multiplier for wire antennas in free space. PCB antennas: velocity factor ≈ 0.60–0.70 (depends on substrate εᵣ). Feed impedance: dipole ≈ 73Ω, monopole over ground ≈ 36Ω.
Quarter-wave whip lengths for ISM bands
This is the table everyone building a LoRa or ESP32 radio wants on screen. Theoretical length is λ/4 with λ = c/f and c = 3×10⁸ m/s. Cut the wire about 5% shorter than that — real wire resonates short because of end effects and the finite wire diameter, a velocity factor around 0.95.
| Band | λ/4 theoretical | Practical (cut to) |
|---|---|---|
| 433.92 MHz | 173 mm | ~164 mm |
| 868 MHz | 86 mm | ~82 mm |
| 915 MHz | 82 mm | ~78 mm |
| 2.4 GHz | 31 mm | ~30 mm |
Practical aside: for an 868 MHz LoRa module, cut about 82 mm of stiff wire and solder it as a quarter-wave whip straight against the board ground. It costs nothing, beats a mistuned chip antenna, and is the fastest way to get a node talking.
Velocity factor: why the textbook length is always too long
A wire antenna resonates a few percent shorter than the textbook λ/4 or λ/2. The fields fringe past the physical ends, and a fatter wire shifts resonance further down — so the thicker the conductor relative to its length, the more you trim. The 0.95 factor in the table covers a typical thin whip; for fat elements or close-coupled metal you tune by trimming a millimetre at a time while watching SWR. Cut long, then shorten — you can't add copper back.
The ground plane is not optional
A quarter-wave monopole only works because it sees its own reflection. The ground plane (or a counterpoise — a few radial wires) mirrors the missing half of the antenna, so the radio "sees" a full half-wave dipole. Take the ground plane away and efficiency collapses, the feed impedance wanders, and the resonant frequency shifts on you. On a small PCB the copper pour is your ground plane, and if it's too small the antenna detunes the moment you put the board in a case or pick it up. Wikipedia's monopole antenna article covers the image-theory in depth.
Monopole vs dipole vs whip vs PCB vs helical
| Type | Size | Needs ground plane? | Where it shows up |
|---|---|---|---|
| Monopole (λ/4) | λ/4 | Yes — mirrors the missing half | Whip on a board ground |
| Half-wave dipole | λ/2 | No — self-balanced | Tuned reference, ~73 Ω feed |
| Whip | λ/4 flexible | Yes | Handhelds, modules |
| PCB trace | Shrunk by substrate εᵣ | Yes (board pour) | BLE, 2.4 GHz, cheap nodes |
| Helical | Much shorter than λ/4 | Usually | Size-constrained designs |
The dipole is the honest reference — self-resonant, no ground plane, predictable ~73 Ω. Everything else is a trade: the monopole halves the height by borrowing the ground, the PCB trace shrinks further by living in FR4 dielectric, and the helical coils the element up when there's simply no room. Whatever you pick still has to be matched to the radio, and that's an L or pi network you can size with the LC resonance calculator. At 2.4 GHz and up, conductor loss creeps in too — see how thin the current layer gets in the skin effect calculator.
Did you know? A dipole antenna half-wavelength long at 2.4 GHz (Wi-Fi) is only ~6 cm. GPS satellites broadcast at 1.575 GHz with a signal power of about 20–50 W, yet after travelling 20,200 km the power received by your phone antenna is less than 10⁻¹⁵ W.