How to Calculate Antenna Length
Antenna length depends on the wavelength of the operating frequency. The full wavelength is λ(m) = 300 / f(MHz). The most common quarter-wave antenna = λ/4 = 75/f(MHz) × velocity factor (≈ 0.95 for thin wire). For example, a quarter-wave antenna is about 16.4 cm at 433 MHz and about 3.0 cm at 2.4 GHz.
Antenna length is the physical length an antenna must have — matched to the wavelength of its operating frequency — to work efficiently. A wrong-length antenna radiates and receives weakly; range and efficiency drop sharply. Antenna length is calculated from the wavelength with simple formulas.
What is wavelength?
The distance an electromagnetic wave travels in one full cycle is its wavelength (λ). Since the speed of light c ≈ 3×108 m/s:
λ (m) = 300 / f (MHz)
For example, λ = 3 m at 100 MHz and 0.3 m at 1 GHz.
Quarter-wave and half-wave antennas
Antennas are usually a fraction of the wavelength. The two most common:
| Antenna type | Length formula |
|---|---|
| Quarter-wave (monopole / whip) | λ/4 = 75/f(MHz) × VF |
| Half-wave (dipole) | λ/2 = 150/f(MHz) × VF |
Here VF = velocity factor.
Velocity factor
A signal travels slightly slower in a conductor than in free space, so a real antenna is made a little shorter than the theoretical length. For thin-wire antennas the velocity factor is ≈ 0.95, so in practice a quarter-wave ≈ 71.25/f(MHz) m.
How to calculate it, step by step
- Write the operating frequency in MHz (e.g. 433 MHz).
- Choose the antenna type (quarter-wave is most common).
- Find the wavelength: λ = 300/f.
- Apply the fraction: λ/4 for quarter, λ/2 for half.
- Multiply by the velocity factor (≈ 0.95).
Worked examples
- 433 MHz quarter-wave: 75/433 × 0.95 ≈ 0.164 m ≈ 16.4 cm
- 2.4 GHz (2400 MHz) quarter-wave: 75/2400 × 0.95 ≈ 0.0297 m ≈ 3.0 cm
Quarter-wave length for common frequencies
| Frequency | Quarter-wave (VF = 0.95) |
|---|---|
| 433 MHz | ≈ 16.4 cm |
| 868 MHz | ≈ 8.2 cm |
| 915 MHz | ≈ 7.8 cm |
| 2.4 GHz | ≈ 3.0 cm |
Practical notes
- Monopole (quarter-wave) antennas need a ground plane; performance drops without one.
- PCB-embedded antennas (meander/chip) differ; follow the manufacturer's layout guide.
- The final length shifts slightly with the environment and enclosure; tune with an antenna analyzer for critical applications.
Use the calculator
To find the length instantly from the frequency and antenna type, use our Antenna Length Calculator.