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Calculators / Quarter-Wave Antenna
Quarter-Wave Antenna
Calculator
Calculate the exact physical length of a quarter-wave (λ/4) monopole antenna for any frequency — used in WiFi antennas, RF modules, IoT devices, and PCB designs. Includes ground-plane radial length, velocity factor correction, and conductor diameter shortening.
Monopole Element (λ/4)
Ground Plane / Radials (λ/4)
⚙ Quarter-Wave Engine
Free-space λ = — m
Bare copper/aluminium ≈ 0.95. PCB trace ≈ 0.66–0.85
Affects length via thick-element correction
Material correction applied to VF
PCB / Chassis
Infinite ground
4 Radials
Standard GP
8 Radials
+0.5 dB gain
32+ Radials
Near-perfect
Advanced Parameters
Radials as fraction of λ (standard = 0.25 = λ/4)
°
Drooped radials (−45°) raise Zin toward 50 Ω
Free-standing: bare element in air
m
Height above real ground affects Zin and efficiency
Calculated Results
Antenna Length (L = λ/4)
—mm
Free-space λ—
Radial Length—
Length (inches)—
Length (feet)—
Feedpoint Impedance (Zin)—
Gain (dBi)—
Bandwidth (approx.)—
Thick-element correction—
Effective VF (k × mat)—
Number of radials—
Enter values to calculate.
📖 Theory
A quarter-wave monopole antenna is exactly one-quarter of the operating wavelength. It requires a ground plane (or radials) to act as the “missing” quarter-wave, together forming the equivalent of a half-wave dipole.
Formula
L = (k × c) / (4 × f)
Shorthand: L(mm) = 71,500 × k / f(MHz)
Ground Plane Effect
Over a perfect ground: Zin ≈ 36.5 Ω, Gain = 5.19 dBi.
With 4 radials: Zin ≈ 40–50 Ω (near 50 Ω coax).
Drooped radials (−45°) raise Zin toward 50 Ω exactly.
IoT / PCB Rule-of-Thumb
433 MHz → 163 mm
868 MHz → 82 mm
915 MHz → 78 mm
2.4 GHz → 31 mm
5.8 GHz → 13 mm
📡 Radiation Pattern Viewer
Live Simulation
|
◉ Pattern scales with radial count
Plane
Frequency
433 MHz
Radials
4
E-Plane Pattern
3D Elevation View
ℹ
Design Insights
Select a frequency and ground plane configuration to see design insights.
Common Applications
WiFi Antennas
2.4 GHz (31 mm) and 5 GHz (13 mm) PCB quarter-wave whips on routers, access points, and WiFi modules.
RF Modules & IoT
433/868/915 MHz wire antennas on LoRa, Sigfox, Z-Wave, and custom RF transceiver modules.
IoT Devices
Bluetooth, Zigbee (2.4 GHz), NB-IoT, LTE-M antennas for smart home sensors and industrial IoT.
Amateur Radio VHF/UHF
2 m (144 MHz) and 70 cm (433 MHz) ground-plane antennas — the most popular portable VHF antenna.
Use this result with related RF tools
Use the calculated quarter-wave length as a starting dimension. The ground plane, conductor diameter, nearby enclosure, feed arrangement, and installed environment can shift the final resonant frequency.
Get "10 RF Design Principles Every Engineer Should Know" Free
Learn practical principles for better RF circuits, PCB layouts, simulations, measurements, and troubleshooting.