Parabolic dish gain calculator
A parabolic dish focuses radio energy into a narrow beam, the way a searchlight reflector focuses light. Its gain grows with the square of the diameter-to-wavelength ratio, so doubling the diameter or the frequency adds 6 dB. Enter diameter, frequency and aperture efficiency to get gain in dBi, half-power beamwidth and effective aperture.
How much of the dish area really works. 55% is the standard figure for a prime-focus dish, 65–75% for offset and Cassegrain feeds.
Side view of a prime-focus dish: the feed sits at the focus and the green wedge is the half-power beam leaving the aperture. Its drawn angle follows θ₃dB on a compressed scale, so very narrow and very wide beams both stay readable. The reflector itself is drawn at a fixed size — the corner note gives its real width in wavelengths, D/λ. The bar underneath places the gain on a 0–70 dBi scale.
Applies to a circular aperture measured on the beam axis, and only while the dish is several wavelengths across. Real antennas fall short through feed spillover, blockage, surface tolerance and radome loss, so a measured datasheet figure always wins. Above roughly 10 GHz, rain fading can cost more than the last decibel of gain.
How it works
- 01
Work in wavelengths
λ = c / f. At 12 GHz the wavelength is 2.5 cm, at 1 GHz it is 30 cm. A dish does not care about metres or gigahertz on their own, only about its width in wavelengths, D / λ. A 1.2 m dish is 48 wavelengths wide at 12 GHz and 4 wavelengths wide at 1 GHz.
- 02
Square the ratio for gain
Gain follows the collecting area, so it grows with the square of that ratio, G = η · (π · D / λ)2, and 10 · log10(G) turns it into dBi. Doubling the diameter or the frequency multiplies the gain by four, which is 6 dB.
- 03
Apply the aperture efficiency
No dish uses its whole surface. η covers the illumination taper of the feed, the energy that spills past the rim, the shadow of the feed and its struts, and the surface tolerance of the reflector. 55% is the standard planning figure for a prime-focus dish.
- 04
Read the beamwidth, then check the datasheet
The same ratio sets the beam, θ3dB ≈ 70 · λ / D degrees. Our 1.2 m dish at 12 GHz radiates a 1.5° beam, about three times the width of the full moon. Measured gain from the manufacturer also carries feed, radome and mismatch losses that this formula never sees.
Formulas
- G — power gain over isotropic, linear (dBi = 10 · log10(G))
- η — aperture efficiency, 0 to 1 (0.55 typical)
- D — dish diameter, m
- λ — wavelength, m (λ = c / f)
- A — physical aperture π · D2 / 4, m2 (effective aperture Ae = η · A)
- D — diameter, m
- f — frequency, GHz
- η — aperture efficiency, 0 to 1
- θ3dB — beamwidth between the −3 dB points, degrees
- 70 — common constant, 58 for uniform illumination and up to about 72 for a strongly tapered feed
Worked example
- λ = 299 792 458 / 12×109 = 0.02498 m
- D / λ = 1.2 / 0.02498 = 48.03
- G = 0.55 · (π · 48.03)2 = 12 520
- in dB: 10 · log10(12 520) = 41.0 dBi (38.8 dBd)
- θ3dB ≈ 70 · 0.02498 / 1.2 = 1.46°
- Ae = 0.55 · π · 1.22 / 4 = 0.622 m2
FAQ
- Why does the gain rise 6 dB when the dish diameter doubles?
- Because gain follows area, not width. Twice the diameter is four times the aperture area, and 10 · log10(4) = 6.02 dB. The same holds for frequency: at twice the frequency the wavelength halves, the dish is twice as many wavelengths wide, and the gain rises another 6 dB.
- What does aperture efficiency include, and why 55%?
- It bundles every reason a dish falls short of its geometric area. The feed illuminates the centre more strongly than the rim, some energy spills past the edge, the feed and its struts shadow part of the surface, and surface roughness scatters the rest (Ruze’s equation). A prime-focus dish lands around 0.55 to 0.60, an offset dish 0.65 to 0.75, a Cassegrain 0.65 to 0.70. ITU-R F.699 estimates maximum gain as 20 · log10(D / λ) + 7.7 dBi, about 48 dBi at D/λ = 100, which implies an aperture efficiency near 60%.
- What is the gain of a 60 cm satellite dish?
- A 60 cm dish at 10.5 GHz with 55% efficiency gives about 33.8 dBi, with a beamwidth near 3.3°. That is why a domestic dish can be aimed by hand and still work, while a 3 m dish with its 0.6° beam needs a rigid mount.
- How exact is the 70·λ/D beamwidth rule?
- It is an approximation, good to about ±10% for a normally illuminated dish. The constant depends on how the feed lights the reflector: near 58 for uniform illumination, and up to roughly 72 when the feed strongly tapers the edge to suppress sidelobes. A datasheet beamwidth is measured, so it always beats the formula.
- How accurately must a dish be pointed?
- Mispointing costs roughly 12 · (Δθ / θ3dB)2 dB, so being off by half the beamwidth costs 3 dB and a quarter costs 0.75 dB. With a 1.5° beam you can afford about 0.4° of total error from mount, wind and survey. Above 10 GHz that is a mechanical problem long before it is a radio one.
A narrow beam is only worth its gain if the far end is actually visible. Waveshed draws line-of-sight and RF coverage over real elevation data, free in your browser.
Check the path on the map →Related guides
- Antenna patterns & the sensor panel — the simulator takes gain in dBi and a pattern, so a dish figure goes straight into a coverage run
- Plan radio coverage (RF / ITM) — where antenna gain, path loss and terrain meet in a full RF calculation
Sources & further reading
- ITU-R Recommendation F.699 — Reference radiation patterns for fixed wireless system antennas ↗ — ties maximum gain to D/λ (about 48 dBi at D/λ = 100) and derives D/λ from the measured beamwidths
- Essential Radio Astronomy, ch. 3 — Radio Telescopes (NRAO / University of Virginia) ↗ — aperture efficiency as effective over geometric area, and the gain–aperture relation A_e = G·λ² / 4π
- C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed., ch. 15 (Reflector antennas) ↗ — derivation of aperture gain, illumination taper and the beamwidth constant. Wiley 2016, ISBN 978-1-118-64206-1
- Parabolic antenna — Wikipedia ↗ — gain formula G = e_A·(π·d/λ)², half-power beamwidth θ = k·λ/D with k ≈ 70 for a typical dish, and efficiency by feed type
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