Explore far field limits for any aperture. Choose wavelength or frequency, set units, and calculate. Designed for engineers, students, and lab testing workflows today.
The Fraunhofer distance estimates where the far-field region begins for an aperture or antenna:
R = 2 D² / λ
This is a practical boundary used in antenna testing, radar, and optics when the source is effectively planar in the observation region.
| # | Aperture D (m) | Wavelength λ (m) | Fraunhofer distance R (m) | Typical context |
|---|---|---|---|---|
| 1 | 0.50 | 0.030 | 16.67 | Small antenna test range |
| 2 | 1.20 | 0.010 | 288.00 | Microwave far-field setup |
| 3 | 0.08 | 0.00000055 | 23272.73 | Optical aperture benchmark |
The Fraunhofer distance is a practical boundary where wavefront curvature becomes small enough that field patterns behave like plane waves. It is widely used in antenna ranges, radar measurements, and optical setups to justify far-field assumptions. Using a consistent boundary helps compare gain, beamwidth, and sidelobe data between labs and test sites.
The calculator uses R = 2D²/λ, showing that far-field distance rises with the square of aperture size and drops with wavelength. Doubling the aperture multiplies R by four. Doubling frequency halves wavelength and roughly doubles R. This quadratic behavior is why large dishes and arrays need long ranges.
For a 0.5 m aperture at 10 GHz, free-space wavelength is about 0.03 m and the far-field boundary is roughly 16.7 m. A 1.2 m aperture at 30 GHz has λ ≈ 0.01 m, pushing R to about 288 m. In optics, λ ≈ 550 nm with an 80 mm aperture gives tens of kilometers, illustrating why optical “far field” is often achieved with lenses rather than distance.
Range length is only one constraint. You also need clear aperture, low reflections, stable mounts, and alignment control. For outdoor ranges, the computed R helps set minimum separation, while additional margin may be added to reduce phase error. For compact ranges, reflectors and collimators are used to synthesize a far-field region in a shorter footprint.
If you enter frequency, the calculator computes wavelength using λ = v/f. In free space, v is 299,792,458 m/s. In materials and waveguides, effective phase velocity can differ. Entering the correct wave speed improves accuracy when estimating where patterns stabilize in the medium or guided structure.
Use the largest physical dimension of the radiating or transmitting aperture. For a circular dish, D is the diameter. For a rectangular horn, use the larger side. For phased arrays, use the maximum array extent. Choosing a smaller dimension can underpredict range length and increase measurement uncertainty.
The output includes unit conversions so you can plan in meters, feet, or kilometers quickly. Engineers often add margin above the computed boundary for tighter phase criteria, low sidelobe work, or high-dynamic-range measurements. If you see unexpected pattern ripples, insufficient distance or multipath reflections are common culprits.
Always verify units: mixing millimeters and meters can shift results by a factor of 1,000. Confirm whether your wavelength is in free space or within a medium. When using frequency, ensure the unit is correct (MHz vs GHz). Finally, remember the formula is an engineering guideline; geometry and test objectives may demand stricter limits.
It is an estimated boundary where an aperture’s radiation pattern can be treated as far field, meaning the wavefront is approximately planar and angular field distribution becomes distance-invariant.
Use the largest physical dimension of the aperture or antenna. For dishes it is diameter; for rectangular apertures use the longer side; for arrays use the maximum overall span.
Yes. Select frequency mode and enter frequency and wave speed. The calculator computes wavelength as λ = v/f and then calculates the far-field distance.
Because the relationship is quadratic: R = 2D²/λ. Doubling the aperture increases the required distance by four, which quickly affects large antennas and optical apertures.
No. It is a widely used engineering guideline. Real measurements can require extra margin based on phase-error limits, reflections, alignment tolerances, and the dynamic range of the test.
Use the phase velocity for your environment. Free space is 299,792,458 m/s. In materials or guided systems, effective velocity may be lower and should be used for better estimates.
Consider compact-range techniques, near-field scanning with transformation, or a larger facility. If you must test shorter, expect larger phase errors and more sensitivity to multipath and alignment.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.