// reference · rf mathematics · cwna ch.3
802.11 RF Math Reference
No logarithms required. The Rule of 3 and 10 handles every CWNA exam question and most field calculations. Sources: IEEE 802.11-2020, CWNA-109 study guide, FCC 47 CFR 15.407, Wi-Fi Alliance.
// interactive converter - enter either value
// every whole-number dB value decomposes
Most training material claims values like 12 dBi "need a calculator" because they contain no clean 10. That is wrong.
10 and 3 share no common factor, so 10a + 3b reaches any integer for some choice of a and b.
The trick is allowing negative steps, which nobody teaches.
12 dB = four threes = ×16 · 7 dB = +10 −3 = ×5 · 14 dB = +10 +10 −3 −3 = ×25 · 1 dB = +10 −3 −3 −3 = ×1.25
The converter above finds the shortest recipe for whatever you type, including negatives.
12 dB = four threes = ×16 · 7 dB = +10 −3 = ×5 · 14 dB = +10 +10 −3 −3 = ×25 · 1 dB = +10 −3 −3 −3 = ×1.25
The converter above finds the shortest recipe for whatever you type, including negatives.
// 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 ✓
Not exact: 3 dB is really 3.0103 dB, so each step drifts 0.23%.
20 + 3 = 23 dBm = 200 mW ✓
20 - 3 = 17 dBm = 50 mW ✓
Not exact: 3 dB is really 3.0103 dB, so each step drifts 0.23%.
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 ✓
Exact. Ten is a true factor of 10, so tens cost you no accuracy.
0 + 10 = 10 dBm = 10 mW ✓
10 + 10 = 20 dBm = 100 mW ✓
Exact. Ten is a true factor of 10, so tens cost you no accuracy.
// how far the shortcut drifts
1 three
+0.23%
3 dB → ×2 vs ×1.995
2 threes
+0.46%
6 dB → ×4 vs ×3.98
4 threes
+0.93%
12 dB → ×16 vs ×15.85
any tens
0.00%
exact by definition
Under 3% error, use the shortcut. Proving compliance to a regulator, use 10^(dB/10). Prefer tens over threes where you have a choice — same answer, no drift.
// dBm ↔ mW reference table - memorise the anchors
| dBm | mW | Typical use | Derived by |
|---|---|---|---|
| -100 | 0.0000000001 | Noise floor, quiet 20 MHz channel | 0 dBm - 10 ×10 |
| -90 | 0.000000001 | Typical Wi-Fi noise floor | 0 dBm - 10 ×9 |
| -70 | 0.0000001 | Minimum for stable VoIP | 0 dBm - 10 ×7 |
| -50 | 0.00001 | Strong client signal | 0 dBm - 10 ×5 |
| -30 | 0.001 | Very strong - metres from the AP | 0 dBm - 10 - 10 - 10 |
| -10 | 0.1 | Overloading a receiver front end | 0 dBm - 10 |
| 0 | 1 | Anchor - memorise this | Definition: 0 dBm = 1 mW |
| 1 | 1.26 | — | 0 + 10 - 3 - 3 - 3 |
| 3 | 2 | Common low power | 0 + 3 |
| 4 | 2.5 | Bluetooth Class 2 max | 0 + 10 - 3 - 3 |
| 6 | 4 | — | 0 + 3 + 3 |
| 7 | 5 | — | 0 + 10 - 3 |
| 10 | 10 | Anchor - memorise this | 0 + 10 |
| 13 | 20 | Common low AP setting | 10 + 3 |
| 14 | 25 | 6 GHz VLP EIRP limit, indoor | 10 + 10 - 3 - 3 |
| 17 | 50 | — | 10 + 10 - 3 |
| 20 | 100 | Typical AP TX power | 0 + 10 + 10 |
| 23 | 200 | — | 20 + 3 |
| 24 | 250 | 6 GHz GVP EIRP limit (FCC, Jan 2026) | 20 + 10 - 3 - 3 |
| 27 | 500 | — | 20 + 10 - 3 |
| 30 | 1000 (1W) | Anchor · 5 GHz U-NII-1/2 EIRP limit | 0 + 10 + 10 + 10 |
| 36 | 4000 (4W) | 2.4 GHz and U-NII-3 EIRP limit | 30 + 3 + 3 |
// eirp - equivalent isotropically radiated power
EIRP (dBm) = TX Power (dBm) - Cable Loss (dB) + Antenna Gain (dBi)
TX Power
Conducted power at the transmitter output, before the cable. Measured in mW or dBm.
Intentional Radiator (IR)
Transmitter plus all cable, connectors and attenuators, up to but not including the antenna. This is the point the FCC calls the IR.
Antenna Gain (dBi)
Passive gain - the antenna focuses energy, it does not amplify. Relative to an isotropic radiator. Typical omni 2-5 dBi, high-gain yagi 15+ dBi.
EIRP
IR power plus antenna gain. The highest RF energy leaving the system in the antenna main lobe. This is what the FCC regulates, not conducted power.
Worked example A: TX = 20 dBm, cable loss = 2 dB, antenna gain = 6 dBi
EIRP = 20 - 2 + 6 = 24 dBm
In mW: 20 dBm = 100 mW. Net change is +4 dB, which is +10 -3 -3, so ×10 ÷2 ÷2 = ×2.5 → 250 mW. Exact: 251.2 mW.
EIRP = 20 - 2 + 6 = 24 dBm
In mW: 20 dBm = 100 mW. Net change is +4 dB, which is +10 -3 -3, so ×10 ÷2 ÷2 = ×2.5 → 250 mW. Exact: 251.2 mW.
Worked example B: TX = 20 mW, cable loss = 6 dB, antenna gain = 12 dBi
20 mW = 13 dBm. EIRP = 13 - 6 + 12 = 19 dBm
In mW: net change is +6 dB, two doublings. 20 → 40 → 80 mW. Exact: 79.6 mW. Only the net matters — a 3 dB cable with 9 dBi gain gives an identical EIRP.
20 mW = 13 dBm. EIRP = 13 - 6 + 12 = 19 dBm
In mW: net change is +6 dB, two doublings. 20 → 40 → 80 mW. Exact: 79.6 mW. Only the net matters — a 3 dB cable with 9 dBi gain gives an identical EIRP.
// 6 ghz power classes - eirp is not the only ceiling
| Class | Max EIRP | PSD limit | Coordination | Where |
|---|---|---|---|---|
| LPI | 30 dBm | 5 dBm/MHz | None | Indoor only |
| SP | 36 dBm | 23 dBm/MHz | AFC required | Indoor and outdoor |
| VLP | 14 dBm indoor / 10 outdoor | -1 dBm/MHz | None | Anywhere, short range |
| GVP | 24 dBm | 11 dBm/MHz | Geofence database | Indoor and outdoor |
// psd calculator - which limit actually binds?
Actual ceiling
Link Budget
Rx Signal = TX Power - Cable Loss + Tx Antenna Gain - FSPL + Rx Antenna Gain
Start at the transmitter, subtract every loss and add every gain all the way to the receiver. If the result is above 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)
The gap between signal and background noise. The larger the gap, the higher the MCS index you can sustain. 25 dB is good for 64-QAM. 256-QAM wants about 27-30 dB. 1024-QAM needs 33+ dB.
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 vs ERP - three references, one mistake
dBi - decibels isotropic
Gain relative to a theoretical isotropic radiator. Most antennas and all FCC documents use dBi. A half-wave dipole is 2.14 dBi.
dBd - decibels dipole
Gain relative to a half-wave dipole. Conversion: dBi = dBd + 2.14. A 3 dBd antenna is 5.14 dBi. Some vendors spec in dBd - convert before comparing.
ERP is not EIRP
ERP references a dipole, EIRP references an isotropic radiator. EIRP = ERP + 2.14 dB. FCC Part 15 regulates EIRP. Training material that uses the two words interchangeably is wrong by 2.14 dB.
// cwna exam field notes
01 No calculator on the CWNA exam. Build the anchor table (0→1 mW, 10→10 mW, 20→100 mW, 30→1000 mW) and derive everything from there using tens and threes, positive or negative.
02 The exam asks about EIRP limits, not conducted limits. FCC EIRP ceilings: 2.4 GHz = 36 dBm (4 W). 5 GHz U-NII-1, 2A and 2C = 30 dBm (1 W). 5 GHz U-NII-3 = 36 dBm (4 W). U-NII-1 fixed point-to-point may use up to 23 dBi antenna gain with no reduction in conducted power.
03 dBd trips people up. A dipole itself is 2.14 dBi. 3 dBd = 5.14 dBi. If a spec sheet says dBd, add 2.14 before doing any EIRP math.
04 -6 dB roughly halves usable range, +6 dB roughly doubles it, because free space path loss goes as 20·log(distance). A 6 dB change is one doubling of distance in free space, less indoors where the exponent is higher.
05 Watch the units. Gain and loss are dB. Absolute power is dBm. Antenna gain is dBi. "A loss of -3 dBm" is meaningless - it is -3 dB. Exam distractors are built on exactly this confusion.
06 At 6 GHz, check PSD before EIRP. An LPI AP at 5 dBm/MHz on 80 MHz is capped at 24 dBm, not the 30 dBm EIRP ceiling. The PSD limit binds first at every width below 320 MHz.