Model linear array beamwidth using practical scan parameters. Compare numerical pattern and approximate formulas instantly. Download reports, inspect lobes, and validate directional performance easily.
This calculator estimates phased array main-lobe beamwidth for a uniform linear array. It combines approximate closed-form equations with numerical array-factor sampling, so you can compare fast design estimates against sampled angular behavior. It also reports wavelength, aperture length, steering phase shift, first-null beamwidth, and a grating-lobe spacing check.
The model assumes isotropic elements, uniform excitation, and narrowband operation. That makes it useful for first-pass design, classroom work, beam steering studies, and engineering tradeoff reviews before adding element-pattern and coupling effects.
| Elements | Frequency (Hz) | Spacing (m) | Scan angle (deg) | Wavelength (m) | Numerical HPBW (deg) | Approximate HPBW (deg) | Numerical FNBW (deg) |
|---|---|---|---|---|---|---|---|
| 8 | 6,000,000,000 | 0.025000 | 0.00 | 0.04996541 | 12.793603 | 12.682235 | 28.934556 |
| 16 | 10,000,000,000 | 0.015000 | 20.00 | 0.02997925 | 6.763807 | 6.748077 | 15.296290 |
| 32 | 5,000,000,000 | 0.030000 | 30.00 | 0.05995849 | 3.662810 | 3.661046 | 8.278635 |
These rows are generated with the same model used by the calculator.
For a uniform linear array, the steering relation is based on the array factor. With wavelength λ = v / f, the wavenumber is k = 2π / λ. The steering phase between adjacent elements is β = -k d sin(θ₀), where d is spacing and θ₀ is the scan angle.
The sampled array factor magnitude is:
|AF(θ)| = |sin(Nψ/2) / (N sin(ψ/2))|
where:
ψ = k d [sin(θ) - sin(θ₀)]
The calculator finds half-power points numerically from the sampled main lobe. It also reports these common approximations for a uniform array:
HPBW ≈ rad2deg[0.886 λ / (N d cos(θ₀))]
FNBW ≈ rad2deg[2 λ / (N d cos(θ₀))]
These approximations are most reliable near the main lobe and for narrowband, uniformly excited arrays without element-pattern effects.
Beamwidth is the angular spread of the main lobe. This page reports half-power beamwidth and first-null beamwidth for a uniform linear array using steering angle, spacing, frequency, and numerical array-factor sampling.
Scanning away from broadside reduces projected aperture. As effective aperture becomes smaller, the main lobe broadens. Large scan angles can also push the pattern toward distortion and increase the chance of grating-lobe issues.
This tool uses a scan-dependent limit: λ divided by 1 plus the absolute sine of scan angle. Half-wavelength spacing remains a common conservative choice for many practical steering cases.
Approximate formulas are fast for early design checks. Numerical beamwidth comes from the sampled array factor and better reflects the selected angular grid, scan location, and the actual main-lobe crossings detected by the solver.
No. The current implementation uses an ideal uniform linear array factor only. Real element patterns, tapering, coupling, losses, and bandwidth effects can change final beamwidth and sidelobe behavior.
It is the phase step applied between adjacent elements to steer the beam. The calculator derives that shift from scan angle, spacing, wavelength, and the steering relation for a linear phased array.
Yes. Changing propagation speed changes wavelength. That directly changes steering phase, beamwidth estimates, null locations, and the spacing limit used for the grating-lobe guidance shown in the result section.
If the angular sweep misses a half-power crossing, or the beam lies too close to the sweep boundary, both -3 dB points may not be found. Expanding the sampled range or using a finer step usually helps.
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.