Antenna Gain to Beamwidth Calculator
Enter antenna gain in dBi to estimate its beamwidth.
Result
How it is calculated
The gain in dBi is first turned into a plain ratio: G = 10(gain/10). For a beam that is the same width in both planes, the width in degrees is estimated as θ = √(K / G). The tool shows two versions: one with K = 41253 (the number of square degrees on a full sphere, for an ideal pattern) and one with K = 52525 (the Kraus constant, often used for real parabolic dishes). The linear gain is shown too. These are rules of thumb for a symmetric pencil beam; the true half-power width depends on the antenna's shape and efficiency. At gains around 0 dBi the formula gives angles above 180°, which are not meaningful for a single beam.
Worked example
An antenna is rated at 20 dBi. The linear gain is 1020/10 = 100. With the first constant, √(41253 / 100) = √412.53 ≈ 20.31, so the beamwidth is 20.31°. With the Kraus constant, √(52525 / 100) ≈ 22.92°. So the antenna's main beam is roughly 20 to 23 degrees wide, and you would aim it with that much tolerance.
Common mistakes
- Entering gain as a plain ratio. The field is dBi, so a gain of 100 times must be entered as 20.
- Treating the two results as separate antennas. They are two estimates for the same gain, using different constants, so expect a difference of roughly 10%.
- Applying it to a sector or omnidirectional antenna. The formula assumes one narrow beam of equal width in both planes, so it misleads for fan-shaped patterns.
- Mixing up dBi and dBd. The tool expects dBi, which is 2.15 dB higher than dBd; entering dBd makes the beam look wider than it is.
- Reading the result as the exact width quoted on a data sheet. It is a rough estimate from gain alone.
About this calculator
For a symmetric, pencil-beam antenna, the half-power (−3 dB) beamwidth can be estimated from gain alone using a standard empirical approximation, roughly θ ≈ √(41253 / G_linear) degrees, where the gain in dBi is first converted to a linear ratio. A second figure uses the constant 52525 (θ ≈ √(52525 / G_linear)), a variant often quoted for parabolic dishes. Higher gain concentrates energy into a narrower beam, so this relationship trades off coverage angle against signal strength in one direction — it's an approximation because true beamwidth also depends on the antenna's exact aperture shape and efficiency.
RF and wireless network engineers use this trade-off when choosing between a high-gain, narrow-beam antenna and a lower-gain, wide-coverage one for a given site, satellite and point-to-point link technicians use estimated beamwidth to judge how precisely a dish needs to be aimed, and WiFi and cellular site planners use it to predict a sector antenna's coverage footprint.
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