Enter the diameter of the antenna and the wavelength of the radio wave into the calculator to determine the far-field distance.
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Far-Field Formula
The calculator uses the Fraunhofer far-field distance, with wavelength derived from frequency when needed.
R = 2D² / λ λ = c / f R_reactive = 0.62 · √(D³ / λ)
- R — far-field (Fraunhofer) distance, meters
- D — largest aperture or antenna dimension, meters
- λ — wavelength, meters
- c — wave propagation speed (≈ 2.998 × 10⁸ m/s for EM in air; 343 m/s for sound in air at 20 °C)
- f — frequency, Hz
- R_reactive — outer boundary of the reactive near field
The 2D²/λ rule applies when D ≥ λ. For electrically small antennas (D < λ), a fixed boundary near λ/2π is often used instead. The formula assumes a single radiating aperture in free space and ignores ground reflections, multipath, and atmospheric effects.
Reference Values
Typical wavelengths for common frequencies (EM in air):
| Frequency | Wavelength | Common use |
|---|---|---|
| 100 MHz | 3.00 m | FM radio |
| 915 MHz | 328 mm | ISM, RFID |
| 2.4 GHz | 125 mm | Wi-Fi, Bluetooth |
| 5.8 GHz | 51.7 mm | Wi-Fi, ISM |
| 28 GHz | 10.7 mm | 5G mmWave |
| 77 GHz | 3.90 mm | Automotive radar |
Field regions around a radiating aperture:
| Region | Range from aperture | Behavior |
|---|---|---|
| Reactive near field | 0 to 0.62·√(D³/λ) | Stored energy dominates; pattern not formed |
| Radiating near field (Fresnel) | 0.62·√(D³/λ) to 2D²/λ | Pattern shape varies with distance |
| Far field (Fraunhofer) | ≥ 2D²/λ | Pattern stable; 1/r amplitude falloff |
Worked Example
A 0.6 m parabolic dish operating at 2.4 GHz:
- λ = 3 × 10⁸ / 2.4 × 10⁹ = 0.125 m
- R = 2 × (0.6)² / 0.125 = 5.76 m
- Reactive boundary = 0.62 · √(0.6³ / 0.125) ≈ 0.81 m
Any gain or pattern measurement should be taken at 5.76 m or beyond. Closer than 0.81 m, the field is reactive and antenna analyzers will read incorrectly.
FAQ
Why 2D²/λ? It is the distance at which the maximum phase error across the aperture drops to π/8 radians (22.5°), the standard threshold for treating a wavefront as planar.
D is the diameter or the radius? D is the largest physical dimension of the radiating aperture. For a circular dish, that is the diameter. For a rectangular array, it is the longest edge or the diagonal.
Does this apply to acoustic transducers? Yes. Switch the wave type to sound and the same 2D²/λ rule applies, using the speed of sound in your medium.
What if my test range is shorter than 2D²/λ? You are measuring in the Fresnel region. Use near-field-to-far-field transformation, a compact antenna test range (CATR), or correct for the known phase taper.
