Wi-Fi power levels span eleven orders of magnitude, from 100 mW at the transmitter to a trillionth of a watt at the edge of coverage. Decibels turn that range into small numbers you can add.
1. DefinitionWhat are dB, dBm and dBi?
- dB (decibel) compares two powers: dB = 10 log10(P2 / P1). It is a ratio, not a unit of power. For amplitude (voltage) the factor is 20 instead of 10, because power goes with amplitude squared.
- dBm is power measured against one milliwatt: dBm = 10 log10(P in mW). So 0 dBm is 1 mW. It is a real power level, written on a log scale.
- dBi is antenna gain measured against an ideal antenna that radiates equally in every direction (an isotropic radiator). An antenna does not make power; it concentrates it, so gain in one direction means less elsewhere. (A half-wave dipole has about 2.15 dBi of gain, so dBd = dBi – 2.15.)
- EIRP (equivalent isotropically radiated power) is the power an ideal isotropic antenna would need to radiate to give the same signal in the strongest direction: transmitter power – cable loss + antenna gain. Regulators limit EIRP.
2. PurposeWhy use a log scale?
- The range is huge. A transmitter at 20 dBm (100 mW) and a weak received signal at -90 dBm (1 pW) differ by a factor of 1011. In dB that is a 110 dB difference, a number you can hold in your head.
- Chains become sums. Gains and losses multiply as plain ratios. In decibels they simply add and subtract, so a link budget is a column of numbers.
- It matches how losses behave. Free-space path loss, walls and cables each remove a fixed fraction of the power, which is a fixed number of dB.
3. MechanismThree ways to feel a decibel
Panel A converts dBm to power. Panel B turns a gain or loss in dB into a multiplier. Panel C adds up a short transmit chain: transmitter, cable and antenna.
Try this. (1) In panel A, set 20 dBm and then 23 dBm: a 3 dB step doubles the power. (2) In panel B, step from 0 to 10 and then 20 dB: each 10 dB is ten times more. (3) In panel C, raise the antenna gain until the dashed line is passed: with the same transmitter, a better antenna can put you over a limit that is written as EIRP.
4. VisualPower levels you will meet
| Level | Power | Meaning |
|---|---|---|
| +30 dBm | 1 W | One full watt |
| +20 dBm | 100 mW | The 2.4 GHz EIRP limit in the UK and the EU |
| 0 dBm | 1 mW | The reference level |
| -30 dBm | 1 µW | A very strong received signal, close to the access point |
| -90 dBm | 1 pW | A very weak received signal |
The scale is anchored at 0 dBm = 1 mW. Each +10 moves up by a factor of ten, so the whole table is one idea repeated.
5. MathematicsThe rules and worked examples
| Gain | Power multiplied by | Loss | Power multiplied by |
|---|---|---|---|
| +1 dB | 1.26 | -1 dB | 0.794 |
| +3 dB | 2 | -3 dB | 0.501 |
| +6 dB | 3.98 | -6 dB | 0.251 |
| +10 dB | 10 | -10 dB | 0.1 |
| +20 dB | 100 | -20 dB | 0.01 |
| +30 dB | 1e+03 | -30 dB | 0.001 |
- From dBm to milliwatts: P = 10(dBm / 10) mW. For 17 dBm that is 101.7 = 50.1 mW.
- Transmit chain: a 15 dBm transmitter, a 2 dB cable and a 5 dBi antenna give 15 – 2 + 5 = 18 dBm EIRP, which is 63 mW.
- Adding two signals: you cannot add dBm values. Convert to milliwatts, add, and convert back. Two 20 dBm signals are 100 + 100 = 200 mW = 23 dBm, not 40 dBm: doubling the power adds 3 dB.
- Received power: take the transmit EIRP and subtract the path loss. From the 2.4 GHz topic, free-space loss at 10 m is 60.2 dB, so 20 dBm – 60.2 dB = -40.2 dBm, about 95 nW. Walls and furniture then subtract more.
6. Real-world behaviourWhere you will see decibels
- Transmit power settings on access points are written in dBm. Doubling the power only buys 3 dB, which is rarely worth the interference it causes to neighbours. Often the weak side of the link is the client, which transmits at much lower power than the access point.
- Regulatory limits are written as EIRP, so a higher-gain antenna means the transmitter must be turned down to stay within the limit.
- Signal strength readings in client tools and captures are negative dBm numbers. Different vendors scale and calibrate their RSSI differently, so compare readings from the same device, not across devices.
- Cable and connector loss is real: a few dB lost between a radio and its antenna is a large share of the power.
Practical validationProve it in a capture and on a spectrum analyser
Reading about a band is one thing; seeing it in your own evidence is the skill. These checks work with any monitor-mode capture:
- Read the transmit power setting of your access point and convert it to milliwatts with 10(dBm / 10).
- In a capture, filter on frames from one access point and look at
radiotap.dbm_antsignal. Convert two readings to milliwatts and compute their ratio in dB to check you get the same difference. - Question to answer: a client reports -70 dBm from an access point radiating 17 dBm EIRP. What path loss does that imply? (Answer: 17 – (-70) = 87 dB.)
Check your understandingQuick quiz
ReferencesSources and further reading
- BIPM: The International System of Units (SI Brochure), including units for logarithmic ratio quantities
- Ofcom: UK Interface Requirement 2030 (IR 2030), current edition
- ETSI EN 300 328 (2.4 GHz harmonised standard)
Decibels are defined by mathematics, not by IEEE. The 20 dBm (100 mW) EIRP figure for 2.4 GHz comes from Ofcom IR 2030 for the UK and from ETSI EN 300 328 for the EU; other regions set different limits, so check the regulator. The 60.2 dB path loss figure is worked in the 2.4 GHz topic.