Why 2.4 GHz Has Only Three Channels

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Why 2.4 GHz Has Only Three Channels

The chapter states plainly that the 2.4 GHz band has “effectively three usable channels” — 1, 6, and 11 — and that an access point parked on 3, 8, or 9 gains no new channel, only more noise. Each channel is 20 MHz wide while the numbering sits on a 5 MHz grid with 25 MHz between those three centres. This audit takes that count off faith and derives it from the geometry: why does 2.4 GHz have only three?

Companion to the chapter Lab: Wi-Fi Spectrum Analysis — every number here comes from that chapter.

Ada: The chapter says 2.4 GHz has “effectively three usable channels” - 1, 6, and 11 - with 25 MHz centre spacing. That count falls straight out of the geometry, so let me derive it rather than memorise it.

• A 2.4 GHz Wi-Fi channel n is centred at 2412 + 5 x (n - 1) MHz: channel 1 is 2412, channel 6 is 2412 + 25 = 2437, and channel 11 is 2412 + 50 = 2462 MHz - the 25 MHz spacing the chapter quotes.
• Each channel is 20 MHz wide, so two channels avoid overlap only when their centres are at least 20 MHz apart. Channels 1 and 6 clear that at 2437 - 2412 = 25 MHz (a 5 MHz guard), but 1 and 3 are only 2422 - 2412 = 10 MHz apart - under 20, so they overlap and cannot decode each other.
• Fitting 25-MHz-spaced non-overlapping slots across the centres from channel 1 (2412) to channel 11 (2462) gives 50 / 25 = 2 gaps, or 2 + 1 = 3 channels. Even the EU reach to channel 13 (2472) is only 60 / 25 = 2.4 - still three fully clean channels.

So “use 1, 6, 11” is not a convention to accept on faith - it is the arithmetic of 20 MHz channels on a 5 MHz grid. An AP parked on 3, 8, or 9 buys no new channel; it just straddles two of the three real ones and raises everyone’s noise floor.

Every number above is taken from the chapter’s own material and re-derived step by step.