Quarter Wavelength Antenna Calculator: Design Guide for Radio Antennas

Basic Antenna Length Formulas

Radio antennas are sized based on the wavelength of the operating frequency. The fundamental relationship is:

Where:

• λ (lambda) = wavelength in meters
• c = speed of light = 299,792,458 m/s ≈ 300,000,000 m/s
• f = frequency in hertz (Hz)

For practical antenna calculations using frequency in MHz:

Or in feet:

Antenna Types by Wavelength Fraction

Quarter-Wave (λ/4) Antenna

The quarter-wave vertical is one of the most common antenna types. It consists of a vertical radiating element over a ground plane.

Characteristics:

• Impedance: Approximately 36 ohms over perfect ground
• Radiation pattern: Omnidirectional in the horizontal plane
• Gain: Approximately 0-2 dBi depending on ground quality
• Requires a ground plane (radials, metal surface, or counterpoise)

Half-Wave (λ/2) Dipole

The half-wave dipole is the fundamental antenna, consisting of two quarter-wave elements fed at the center.

Characteristics:

• Impedance: Approximately 73 ohms (good match to 75-ohm cable)
• Radiation pattern: Figure-8 pattern perpendicular to the wire
• Gain: 2.15 dBi
• No ground plane required

Full-Wave (λ) Loop

A full-wave loop antenna has a perimeter equal to one wavelength.

Characteristics:

• Impedance: Approximately 100-120 ohms (depends on shape)
• Gain: About 1 dB more than a dipole
• Can be configured as horizontal, vertical, or delta loop
• Lower noise pickup than dipoles

5/8 Wave Vertical

A popular mobile and base antenna offering more gain than a quarter-wave.

Characteristics:

• Gain: About 3-4 dB over quarter-wave
• Requires matching network (impedance not 50 ohms)
• Lower radiation angle (better for distance)

Velocity Factor Correction

Real antennas use conductors with finite diameter and materials other than free space, which affects the electrical length. The velocity factor (VF) accounts for this:

Typical Velocity Factors

For a wire antenna in free space, a commonly used velocity factor is 0.95, giving these practical formulas:

Corrected Antenna Formulas (VF = 0.95)

The formula 468/f (feet) for a half-wave dipole is one of the most widely used in amateur radio.

Worked Examples

Example 1: 2-Meter Ham Radio (146 MHz)

Problem: Calculate antenna lengths for the 2-meter amateur band at 146 MHz.

Solution:

Full wavelength: λ = 300/146 = 2.05 m

• Quarter-wave vertical: 2.05/4 × 0.95 = 0.487 m = 48.7 cm (19.2 inches)
• Half-wave dipole: 2.05/2 × 0.95 = 0.975 m = 97.5 cm (38.4 inches total)
• Each dipole element: 48.7 cm (19.2 inches)

Using the simplified formula: 468/146 = 3.21 feet = 38.5 inches total dipole length ✓

Example 2: WiFi 2.4 GHz Antenna

Problem: Design a quarter-wave antenna for 2.4 GHz WiFi.

Solution:

Full wavelength: λ = 300/2400 = 0.125 m = 12.5 cm

Quarter-wave: 12.5/4 × 0.95 = 2.97 cm ≈ 3.0 cm (1.2 inches)

This explains why WiFi antennas are relatively small compared to HF antennas.

Example 3: FM Radio (100 MHz)

Problem: What length is a half-wave FM radio antenna?

Solution:

Full wavelength: λ = 300/100 = 3.0 m

Half-wave: 3.0/2 × 0.95 = 1.425 m ≈ 1.43 m (4.7 feet)

This is why FM car antennas are about 75 cm (quarter-wave) mounted on the car body as a ground plane.

Example 4: 40-Meter Ham Band (7.1 MHz)

Problem: Design a half-wave dipole for 7.1 MHz.

Solution:

Using the 468 formula: L = 468/7.1 = 65.9 feet total

Each leg: 65.9/2 = 33.0 feet (10.1 meters)

Using the metric formula: L = 142.5/7.1 = 20.1 meters total

Example 5: CB Radio (27.185 MHz)

Problem: Calculate antenna lengths for CB channel 19 (27.185 MHz).

Solution:

• Full wavelength: 300/27.185 = 11.04 m
• Half-wave dipole: 468/27.185 = 17.2 feet (5.24 m)
• Quarter-wave vertical: 234/27.185 = 8.6 feet (2.62 m)
• 5/8-wave: 187.5 × 0.95/27.185 = 6.55 m (21.5 feet)

Example 6: 5G mmWave (28 GHz)

Problem: What is the quarter-wave antenna length for 28 GHz 5G?

Solution:

Full wavelength: λ = 300/28,000 = 0.0107 m = 10.7 mm

Quarter-wave: 10.7/4 × 0.95 = 2.54 mm (0.1 inch)

At mmWave frequencies, antennas become tiny and are typically integrated into circuit boards.

Frequency Band Reference Table

Here are wavelengths and common antenna dimensions for major radio bands:

Antenna Design Considerations

Wire Diameter Effects

Thicker antenna elements have lower velocity factors and wider bandwidth:

• Thin wire (#14 AWG): VF ≈ 0.97-0.98
• Medium wire (#10 AWG): VF ≈ 0.96
• Heavy wire (#6 AWG): VF ≈ 0.95
• Aluminum tubing (1 inch): VF ≈ 0.92-0.94

For narrowband applications, start with the standard formulas and trim to resonance. For broadband applications, use slightly larger diameter elements.

Height Above Ground

Antenna height affects radiation pattern and efficiency:

• λ/4 height: Maximum low-angle radiation (good for DX)
• λ/2 height: Good all-around pattern
• λ height: Very low angle radiation
• Below λ/4: Ground losses increase, efficiency decreases

Ground Plane Requirements

Quarter-wave verticals require a ground plane for proper operation:

• Ideal: 4+ radials each λ/4 long, at ground level
• Elevated: 4 radials angled down 45° work well
• Vehicle mount: Car roof acts as ground plane
• No ground plane: Use a half-wave vertical instead

Bandwidth Considerations

Antenna bandwidth depends on the length-to-diameter ratio:

• Thin antennas have narrow bandwidth (high Q)
• Fat antennas have wide bandwidth (low Q)
• Folded dipoles have about 4× the bandwidth of standard dipoles

Typical 2:1 SWR bandwidths:

• Wire dipole (thin): 2-3% of center frequency
• Tubing dipole: 5-8% of center frequency
• Folded dipole: 8-15% of center frequency

Matching and Feed Systems

Antenna Impedances

Baluns and Ununs

Balanced antennas (dipoles) fed with unbalanced lines (coax) need a balun:

• 1:1 current balun: Forces equal currents on both dipole halves
• 4:1 balun: Matches 200-300 ohm antennas to 50-75 ohm cable
• Unun (1:4 or 1:9): Matches low-impedance verticals to 50 ohms

Common Antenna Designs

The Simple Dipole

A horizontal half-wave dipole is the easiest effective antenna to build:

1. Calculate length: L = 468/f (feet) or 142.5/f (meters)
2. Cut wire to length plus a few percent for trimming
3. Feed at center with coax (add 1:1 balun for best results)
4. Support ends with rope or insulators
5. Trim to resonance using SWR meter

The Inverted-V Dipole

An inverted-V uses less space and requires only one high support:

• Feed point at apex, supported by mast
• Elements slope down at 45° angle
• Makes antenna about 5% shorter than horizontal dipole
• More omnidirectional pattern than flat dipole
• Impedance drops to about 50 ohms (good 50-ohm match)

Ground Plane Vertical

A quarter-wave vertical with four radials:

1. Calculate vertical length: L = 234/f (feet)
2. Radials: same length, at 90° from vertical, angled down 45°
3. Feed vertical element center conductor, radials to shield
4. Mounting: elevated on mast or at ground level with buried radials

The J-Pole

A half-wave end-fed vertical with quarter-wave matching stub:

• Total length: 3/4 wavelength
• Radiator: λ/2 upper section
• Matching stub: λ/4 folded section at bottom
• No radials needed
• Popular for VHF/UHF (2m, 70cm)

Tuning and Adjustment

Why Antennas Need Tuning

Calculated lengths are starting points. Real antennas are affected by:

• Proximity to ground, buildings, and other objects
• Wire type and diameter
• Insulation on wire
• Feedline interaction
• Mounting hardware

Tuning Process

1. Cut antenna 2-5% longer than calculated
2. Install antenna in final position
3. Measure SWR at design frequency
4. If SWR minimum is below target frequency, antenna is too long—trim both ends equally
5. If SWR minimum is above target frequency, antenna is too short—add length or start over
6. Repeat until SWR is acceptable (usually <1.5:1)

Tuning Tips

• Trim small amounts (1-2 cm) at a time
• Always trim both sides of a dipole equally
• Use an antenna analyzer for faster, more accurate tuning
• Minimum SWR point indicates resonant frequency

Multi-Band Considerations

Harmonic Operation

A half-wave dipole can work on odd multiples of its fundamental frequency:

• 40m dipole (7 MHz) also works on 15m (21 MHz = 3× frequency)
• 80m dipole (3.5 MHz) also works on 30m (10.1 MHz ≈ 3×) and 17m (18 MHz ≈ 5×)

Impedance and radiation pattern change at harmonics, and a tuner may be needed.

Trap Dipoles

LC traps create multiple resonant lengths in one antenna:

• Traps "block" higher frequencies, making antenna appear shorter
• Common combinations: 40/20m, 80/40m, 20/15/10m
• Trade-off: narrower bandwidth than single-band dipoles

Fan Dipoles

Multiple dipoles connected at a common feed point:

• Each element cut for a different band
• Elements interact, so some adjustment is needed
• Wider bandwidth than trap dipoles

Quick Reference Formulas

All formulas use f in MHz and include typical velocity factor correction (0.95).

Use our antenna calculator to quickly calculate antenna lengths for any frequency and antenna type.

Amateur Radio Band Plan Reference

The following table provides a comprehensive reference for all major amateur (ham) radio bands recognized by the ITU, including frequency allocations, corresponding wavelengths, and typical quarter-wave antenna lengths. These values are essential for antenna planning and are based on standard VF = 0.95 correction.

The HF bands (160 m through 10 m) are best suited for long-distance (DX) communication, while VHF and UHF bands (6 m and above) are primarily used for local and regional contacts, repeater operation, and satellite communication. Antenna size requirements decrease dramatically at higher frequencies, making VHF/UHF antennas much more practical for portable and mobile operation.

Velocity Factor Reference for Transmission Lines

When designing antennas with specific feedline types, or when using coaxial cable as a matching section or phasing line, the velocity factor of the transmission line becomes critical. The following table provides detailed velocity factors for commonly used cables and transmission lines.

Velocity factor directly affects the electrical length of a cable. For example, a quarter-wave matching section at 146 MHz in RG-58 (VF = 0.66) would be: L = (75 / 146) x 0.66 = 0.339 m = 33.9 cm. The same section in LMR-400 (VF = 0.85) would be 43.6 cm. This difference matters when building phasing harnesses, coaxial matching stubs, or quarter-wave transformers.

Common Wireless Standards: Frequencies and Antenna Sizes

Modern wireless technologies operate across a wide range of frequencies. The following table shows popular wireless standards, their operating frequencies, and the resulting quarter-wave antenna dimensions. This reference is invaluable for engineers designing embedded wireless systems, IoT devices, and wireless infrastructure.

Notice the dramatic range in antenna sizes: NFC operates at 13.56 MHz with a theoretical quarter-wave length over 5 meters (so it uses electrically small loop antennas instead), while 5G mmWave antennas at 39 GHz are under 2 mm and can be fabricated directly on chip packages. This illustrates why antenna design is tightly coupled to operating frequency, and why different wireless standards require fundamentally different antenna architectures.

For IoT applications, sub-GHz frequencies like LoRa at 868/915 MHz offer the best balance between antenna size (manageable at about 8 cm) and signal propagation range (several kilometers in open terrain). WiFi and Bluetooth at 2.4 GHz enable very compact antennas (about 3 cm) suitable for smartphones and wearables, but with shorter range.

Summary

Key points for antenna wavelength calculations:

• Basic formula: λ = 300/f(MHz) meters
• Velocity factor (0.95) accounts for real-world conductor effects
• Quarter-wave: 234/f feet—needs ground plane
• Half-wave dipole: 468/f feet—most versatile design
• Calculated lengths are starting points—always tune to final frequency
• Higher frequencies = smaller antennas (inverse relationship)
• Wire diameter affects velocity factor—thicker elements need shorter lengths

Frequently Asked Questions