// reference · rf mathematics · cwna ch.3
802.11 RF Math Reference
No logarithms required. The Rule of 3 and 10 gives you close-enough answers for every CWNA exam question and most field calculations. Source: IEEE 802.11-2020, CWNA-109 study guide, FCC Part 15.
// interactive converter - enter either value
// rule of 3 and 10 - the only rf math you need
Rule of 3
+3 dB × 2 (double the mW)
-3 dB ÷ 2 (half the mW)
Example: 20 dBm = 100 mW
20 + 3 = 23 dBm = 200 mW ✓
20 - 3 = 17 dBm = 50 mW ✓
20 + 3 = 23 dBm = 200 mW ✓
20 - 3 = 17 dBm = 50 mW ✓
Rule of 10
+10 dB × 10 (ten times the mW)
-10 dB ÷ 10 (one tenth the mW)
Example: 0 dBm = 1 mW
0 + 10 = 10 dBm = 10 mW ✓
10 + 10 = 20 dBm = 100 mW ✓
0 + 10 = 10 dBm = 10 mW ✓
10 + 10 = 20 dBm = 100 mW ✓
// dBm ↔ mW reference table - memorise the anchors
| dBm | mW | Typical use | Derived by |
|---|---|---|---|
| -30 | 0.001 | Noise floor territory | 0 dBm - 10 - 10 - 10 |
| -20 | 0.01 | Deeply attenuated signal | 0 dBm - 10 - 10 |
| -10 | 0.1 | Weak received signal | 0 dBm - 10 |
| 0 | 1 | Anchor - memorise this | Definition: 0 dBm = 1 mW |
| 1 | 1.25 | — | 0 + 1 (approx) |
| 3 | 2 | Common low power | 0 dBm + 3 |
| 6 | 4 | — | 0 dBm + 3 + 3 |
| 7 | 5 | Bluetooth class 2 | 0 + 10 - 3 |
| 10 | 10 | Anchor - memorise this | 0 dBm + 10 |
| 13 | 20 | Common low AP setting | 10 + 3 |
| 14 | 25 | FCC limit some bands | 10 + 3 + (approx) |
| 15 | 32 | — | 10 + 3 + (approx) |
| 16 | 40 | — | 10 + 3 + 3 |
| 17 | 50 | — | 10 + 10 - 3 |
| 20 | 100 | Typical AP TX power | 0 + 10 + 10 |
| 23 | 200 | — | 20 + 3 |
| 24 | 250 | FCC EIRP limit 5 GHz indoor | 20 + 3 + (approx) |
| 27 | 500 | — | 20 + 10 - 3 |
| 30 | 1000 (1W) | Anchor - memorise this | 0 + 10 + 10 + 10 |
| 36 | 4000 | Outdoor bridge common | 30 + 3 + 3 |
// eirp - equivalent isotropically radiated power
EIRP (dBm) = TX Power (dBm) + Antenna Gain (dBi) - Cable Loss (dB)
TX Power (IR)
Power at the intentional radiator - from transmitter output to the antenna connector. Regulated by FCC as IR power. Measured in mW or dBm.
Antenna Gain (dBi)
Passive gain - antenna focuses energy, does not amplify. dBi = gain relative to isotropic radiator. Typical omni = 2-5 dBi. High-gain yagi = 15+ dBi.
Cable Loss (dB)
Every cable has ~0.2-0.8 dB/ft loss. Every connector has ~0.5 dB insertion loss. Add all losses and subtract from EIRP.
EIRP
Total power at antenna output. Highest RF energy leaving the system. Regulated by FCC - 36 dBm (4W) for most 2.4 GHz, 30 dBm (1W) for many 5 GHz indoor.
Worked example: AP TX power = 20 dBm, cable loss = 2 dB, antenna gain = 6 dBi
EIRP = 20 - 2 + 6 = 24 dBm (250 mW)
Convert: 20 dBm = 100 mW. -2 dB ≈ ÷1.5 ≈ 63 mW. +6 dB = ×4 = 252 mW ≈ 250 mW. Close enough for the exam.
EIRP = 20 - 2 + 6 = 24 dBm (250 mW)
Convert: 20 dBm = 100 mW. -2 dB ≈ ÷1.5 ≈ 63 mW. +6 dB = ×4 = 252 mW ≈ 250 mW. Close enough for the exam.
Link Budget
Rx Signal = TX Power + Tx Antenna - Cable Loss - FSPL - Rx Antenna Loss
Start at the transmitter, add gains, subtract losses all the way to the receiver. If the result is above the receiver sensitivity, the link works. Typical fade margin target: 20-25 dB above sensitivity.
TX: 20 dBm, FSPL: -69 dB, Rx antenna: +3 dBi → Rx = 20 - 69 + 3 = -46 dBm (excellent)
SNR (Signal-to-Noise Ratio)
SNR (dB) = RSSI (dBm) - Noise Floor (dBm)
SNR is the gap between the signal and the background noise. The larger the gap, the higher the MCS index you can use. 25 dB SNR = good for 64-QAM. 33+ dB = needed for 1024-QAM.
RSSI: -65 dBm, Noise: -90 dBm → SNR = 25 dB ✓ (64-QAM capable)
Fade Margin
Fade Margin = Rx Signal - Rx Sensitivity
How much signal you have above the minimum needed. A 20 dB fade margin means the signal can drop 20 dB before the link fails. Used primarily for outdoor point-to-point link design.
Rx: -55 dBm, Sensitivity: -82 dBm → Fade margin = 27 dB (solid)
// dBi vs dBd - two antenna gain references
dBi - decibels isotropic
Gain relative to a theoretical isotropic radiator (radiates equally in all directions). Most antennas and regulatory documents use dBi. A typical rubber duck (half-wave dipole) = 2.14 dBi.
dBd - decibels dipole
Gain relative to a half-wave dipole antenna. Conversion: dBi = dBd + 2.14. So a 3 dBd antenna = 5.14 dBi. Some vendors spec in dBd - always convert before comparing.
// cwna exam field notes
01 No calculator on the CWNA exam. All RF math questions use the Rule of 3/10 - never exact logarithms. Build the conversion table (0→1mW, 10→10mW, 20→100mW, 30→1000mW) and derive everything from there.
02 The exam asks about EIRP limits, not IR limits. Know FCC EIRP: 2.4 GHz = max 36 dBm (4W). 5 GHz indoor U-NII-1/2 = max 30 dBm (1W). 5 GHz U-NII-3 = 30 dBm point-to-multipoint.
03 dBd confuses many candidates. Memorise: a dipole antenna itself has 2.14 dBi gain. 3 dBd = 5.14 dBi. If an antenna spec says dBd, add 2.14 to get dBi before doing EIRP math.
04 -6 dB halves the usable signal distance. +6 dB doubles it. This appears in coverage questions: "AP loses 6 dB of power - what happens to coverage?" Answer: coverage radius is approximately halved.
See RSSI and SNR in your own PCAP
WiFi Analyser reads radiotap.dbm_antsignal for every frame - shows average RSSI, MCS correlation, and noise floor per client.