What is half-power beamwidth (HPBW)?

HPBW (also called 3 dB beamwidth) is the angular width between the two directions where the radiation intensity drops to half (−3 dB) of its peak value. It defines the main beam's useful coverage area.

What is the relationship between beamwidth and gain?

Higher gain = narrower beamwidth. Approximate: G ≈ 32400 / (θ_E × θ_H) where θ are HPBW in degrees. Doubling gain roughly halves the beamwidth in each plane.

How do you calculate beamwidth of a parabolic dish?

HPBW ≈ 70λ/D degrees, where λ is wavelength and D is dish diameter. For a 1 m dish at 10 GHz (λ=3 cm): HPBW ≈ 70×0.03/1 = 2.1°.

What is first null beamwidth (FNBW)?

FNBW is the angle between the first nulls on either side of the main beam. It is approximately twice the HPBW for most antennas: FNBW ≈ 2 × HPBW.

What is beam solid angle?

Beam solid angle Ω_A is the solid angle through which all the radiated power would pass if the radiation intensity were constant at its peak value. Ω_A = 4π/G_linear steradians.

How does frequency affect beamwidth?

Higher frequency = shorter wavelength = narrower beam for a fixed aperture size. HPBW ∝ λ/D, so doubling frequency halves beamwidth.

What is a pencil beam?

A pencil beam is a highly directional radiation pattern with a narrow, symmetrical main lobe — typically HPBW < 10°. Common in radar, satellite, and point-to-point links.

How do sidelobes affect beamwidth?

Sidelobes don't change HPBW (which is measured at −3 dB of peak), but high sidelobes reduce antenna efficiency and can cause interference. Aperture tapering reduces sidelobes at the cost of slightly wider HPBW.

What beamwidth do I need for a point-to-point link?

Narrow enough to concentrate energy on the remote antenna (typically 1–10° for long links) but wide enough to tolerate wind-induced sway and alignment error. Add 2–3× the expected pointing error as margin.

Antenna Beamwidth Calculator – HPBW, FNBW, Directivity & Beam Pattern

HPBW = k × λ / D

Half-Power Beamwidth formula (k ≈ 70° for parabolic dish)

🔴 Aperture Diameter (D)

0.1 m10 m

📻 Frequency (f)

0.1 GHz100 GHz

🔵 Beamwidth Factor (k)

degrees

55° (horn)90° (uniform)

Beamwidth Factor Guide:
k = 58–65° — Horn antenna
k = 70° — Parabolic dish (typical)
k = 75–80° — Circular aperture (uniform)
k = 85–90° — Rectangular aperture (uniform)

HPBW (-3 dB)

2.50°

Half-Power Beamwidth

FNBW (First Null)

5.00°

First Null Beamwidth ≈ 2×HPBW

Directivity (D)

—

D = 41253 / HPBW²

Wavelength (λ)

0.030 m

λ = c / f

Beam Solid Angle

—

Ω = (π/180)² × HPBW²

Beam Classification

Narrow Beam

High gain antenna

ℹ️

HPBW decreases as diameter (D) increases or frequency (f) increases. A narrower beam means higher directivity and gain. Adjust the beamwidth factor (k) for different aperture distributions.

⚙️ Calculation Steps

Determine the aperture diameter (D) in meters.

Calculate wavelength: λ = c / f = 3×10⁸ / f

Apply HPBW formula: HPBW = k × λ / D (result in degrees)

Calculate FNBW ≈ 2 × HPBW (first null beamwidth)

Calculate directivity: D = 41253 / (HPBW_az × HPBW_el) for pencil beam

Calculate beam solid angle: Ω = (π/180)² × HPBW² (steradians)

📊 Live Calculation

Step 1 — Diameter

D = 1.2000 m

Step 2 — Wavelength

λ = c / f = 3×10⁸ / 10×10⁹ = 0.0300 m

Step 3 — HPBW

HPBW = 70 × 0.0300 / 1.2000 = 1.75°

Step 4 — FNBW & Directivity

FNBW = 2 × 1.75° = 3.50° | D = 13464

📋 Quick Reference — Typical Beamwidths by Antenna Type

Antenna Type	Typical HPBW	Freq Range	Typical Gain	k Factor	Application
Isotropic	360°	All	0 dBi	—	Reference standard
Half-Wave Dipole	78° (E-plane)	HF–UHF	2.15 dBi	—	General purpose
Yagi-Uda (5-el)	50–60°	100 MHz–1 GHz	10–12 dBi	—	TV, amateur radio
Horn Antenna	15–30°	1–100 GHz	15–25 dBi	58–65	Microwave links
Parabolic Dish (0.6m)	5–15°	1–30 GHz	25–35 dBi	70	Satellite, radar
Parabolic Dish (1.2m)	2–6°	2–30 GHz	30–42 dBi	70	Satellite comms
Parabolic Dish (3m+)	< 2°	4–100 GHz	42–55 dBi	70	Deep space, VSAT
Phased Array	1–5°	1–100 GHz	30–50 dBi	~70	Radar, 5G mMIMO

ℹ️

HPBW and gain are inversely related — a narrower beam concentrates energy more efficiently, resulting in higher gain. A pencil beam antenna with HPBW = 1° has a directivity of approximately 41,253 (≈ 46 dBi).

Antenna Beamwidth Calculator — Complete Guide to HPBW, FNBW & Directivity

This antenna beamwidth calculator computes half-power beamwidth (HPBW), first null beamwidth (FNBW), directivity, beam solid angle, and effective aperture for any antenna gain or aperture dimension, with an interactive polar beam pattern that updates in real time. Whether you are designing a satellite dish, a Wi-Fi sector antenna, or a radar system, understanding beamwidth is essential for predicting coverage, pointing accuracy, and interference.

Key Beamwidth Formulas

Parameter	Formula	Notes
HPBW (from gain)	θ ≈ √(32400 / G_linear) °	Assumes symmetric beam
HPBW (parabolic dish)	θ ≈ 70λ / D °	λ = c/f, D = dish diameter
FNBW	≈ 2 × HPBW	For most antenna types
Directivity (from BW)	D ≈ 32400 / (θ_E × θ_H)	θ in degrees, both planes
Beam solid angle	Ω_A = 4π / G_linear	steradians
Effective aperture	A_e = G λ² / (4π)	m²

Beamwidth by Antenna Type

Antenna Type	Typical HPBW	Gain (dBi)	Application
Isotropic (theoretical)	360° (omni)	0	Reference only
Half-wave dipole	78°	2.15	Omnidirectional base
Patch / microstrip	60–90°	5–9	Wi-Fi, RFID, IoT
Yagi-Uda (5-element)	50–60°	8–10	TV, amateur radio, P2P
Horn antenna	15–60°	10–25	Feeds, radar, test
Parabolic dish (1 m, 10 GHz)	~2°	~38	Satellite, microwave link
Phased array (32 elements)	5–15°	15–20	5G, radar, beamforming

Worked Examples

📡 Example 1 — 1.2 m Parabolic Dish at 12 GHz (Ku-band Satellite)

GivenD = 1.2 m, f = 12 GHz → λ = 0.025 m, efficiency η = 0.55

Step 1HPBW = 70 × 0.025 / 1.2 = 1.46°

Step 2Gain = η × (πD/λ)² = 0.55 × (π×1.2/0.025)² = 12,483 = 40.96 dBi

Step 3Ω_A = 4π / 12483 = 0.001007 sr | FNBW ≈ 2 × 1.46° = 2.92°

ResultHPBW = 1.46° | Gain = 41.0 dBi | Very narrow beam — precise pointing required

📶 Example 2 — Wi-Fi Patch Antenna at 5.8 GHz

GivenGain = 9 dBi → G_linear = 7.94, f = 5.8 GHz → λ = 0.0517 m

Step 1HPBW ≈ √(32400 / 7.94) = √(4081) = 63.9°

Step 2A_e = 7.94 × (0.0517)² / (4π) = 1.69 × 10⁻³ m² ≈ 16.9 cm²

Step 3Ω_A = 4π / 7.94 = 1.584 sr | FNBW ≈ 128°

ResultHPBW ≈ 64° | Wide beam — good for indoor coverage

Practical Applications

Satellite dishes: Narrow HPBW (1–3°) concentrates energy on a geostationary satellite 36,000 km away.
Wi-Fi access points: Sector antennas with 60–120° HPBW cover a building floor from a corner mount.
Radar: Pencil beams (< 5°) provide angular resolution to distinguish nearby targets.
5G beamforming: Phased arrays dynamically steer narrow beams (5–15°) to track mobile users.
Amateur radio: Yagi antennas with 30–60° beamwidth balance gain and pointing ease for DX contacts.

Frequently Asked Questions

Does narrower beamwidth always mean better?

Not always — a narrower beam gives higher gain and longer range but requires more precise pointing and tracking. For mobile or wide-area coverage, a broader beam is better.

How do I measure beamwidth in practice?

Rotate the antenna on a positioner while recording received signal strength. Plot power vs angle. The −3 dB points (where power drops to half) define HPBW.

Related Calculators

Antenna Gain Calculator — gain from aperture, efficiency, and frequency
Antenna Aperture Efficiency — effective vs physical aperture
Attenuation Calculator — dB, FSPL, cable loss
ADC Calculator — resolution and SNR