Same week, three conversations: a vendor swears his radio "pushes 400 mW", the SFP datasheet talks about a 28 dB optical budget, and a client wants to know why the WiFi reads −72 dBm "when the router is brand new". Milliwatts, dB, dBm — they sound like three languages, but it's one language with three accents. And the whole grammar fits on a napkin: one logarithm, a few magic numbers, and a reference. Let's take it apart, no drama required.
A dB is not a unit: it's a comparison
First, the uncomfortable part: a decibel measures nothing on its own. It's a way of saying "how many times more" (or less) between two quantities:
dB = 10 · log10(P2 / P1)
That's it. Everything else — dBm, dBi, dB SPL — is a variant of this one formula where somebody nailed down the reference P1. If someone tells you "the signal is 40 dB" without saying relative to what, they're telling you "my house is at 40" without saying 40 what.
So why drag a logarithm into something as simple as dividing? Because in RF and optics the ratios are monstrous. A 10 km link at 5.8 GHz loses a factor of almost six trillion along the way (a 6 followed by 12 zeros). Nobody does arithmetic with numbers like that. The logarithm squashes them down to human scale: that atrocious loss becomes 127.7 dB, a number you can jot on a napkin. Think of the logarithm as a zero counter: 10 dB for every zero in the ratio.
And the logarithm brings the gift that justifies the whole invention: multiplying ratios equals adding their dB. A chain of amplifiers, cables and air — every stage multiplying or dividing the power — collapses into grade-school addition: +14 here, −127.7 there, +14 on the way back in. That's why link budgets are added: not a convention for the lazy, but the mathematical property that makes the decibel useful.
The magic numbers: 3, 10 and their combinations
To work in dB you don't need to compute logarithms. You need to memorize two equivalences and combine them:
- +10 dB = ×10 exactly. Straight from the definition: log10(10) = 1. From there, +20 dB = ×100 and +30 dB = ×1000.
- +3 dB ≈ ×2. The real value is ×1.995 — a quarter of a percent short of doubling, and nothing in the field measures that finely. Its mirror image: −3 dB ≈ ÷2 (×0.501).
With those two pieces you build anything, LEGO-style: +6 dB = 3+3 = ×4 (really 3.98). +13 dB = 10+3 = ×20. −23 dB = ÷200. And +1 dB? That's ×1.26 — a quarter more — but honestly, the 3 and the 10 cover 95% of your life. The dB converter supplies the decimals when the napkin runs out.
dBm: the dB that actually is a quantity
Enter the star of the family. A dBm is a dB whose reference got fixed by decree: P1 = 1 mW. Pin the reference and the comparison becomes absolute: 0 dBm isn't "zero power", it's exactly 1 mW. From there, the ladder runs in steps of 10:
- +30 dBm = 1 W (1 mW × 1000).
- 0 dBm = 1 mW — the reference, the zeroth rung.
- −30 dBm = 1 µW, −60 dBm = 1 nW, −90 dBm = 1 pW.
Look at the span: from −90 to +30 dBm is a factor of one trillion, and the scale covers it in 120 equal little steps. Your entire working day lives on that ladder: a WiFi radio transmits around +23 dBm (200 mW), a fiber receiver is comfortable at −8 dBm (0.16 mW), and a well-designed WiFi cell delivers about −65 dBm at the edge — which is 316 picowatts, and your phone holds a video call on it. Modern radio is, quite literally, the art of listening to picowatts.
Because the reference is fixed, the unit algebra stays clean: dBm + dB = dBm (you apply a gain or loss to a level), and dBm − dBm = dB (the difference between two levels is a ratio). When you need real decimals, the dBm/mW converter handles both directions.
Calculator head: dBm to mW in one afternoon
The mental conversion trick is to break the number into tens and threes, starting from the nearest multiple of 10:
$ dbm 23 23 dBm = 20 dBm + 3 dB = 100 mW × 2 = 200 mW (exact: 199.5) $ dbm 27 27 dBm = 30 dBm − 3 dB = 1000 mW ÷ 2 = 500 mW (exact: 501.2)
That's the whole method: anchor on 0, 10, 20 or 30 dBm and adjust by ±3. One afternoon of practice and you'll translate datasheets faster than the vendor's page loads:
| dBm | Decomposition | Mental | Exact |
|---|---|---|---|
| 0 | reference | 1 mW | 1 mW |
| 3 | 0 + 3 | 2 mW | 1.995 mW |
| 10 | 10 | 10 mW | 10 mW |
| 14 | 20 − 3 − 3 | 25 mW | 25.1 mW |
| 17 | 20 − 3 | 50 mW | 50.1 mW |
| 20 | 10 + 10 | 100 mW | 100 mW |
| 23 | 20 + 3 | 200 mW | 199.5 mW |
| 26 | 20 + 3 + 3 | 400 mW | 398.1 mW |
| 27 | 30 − 3 | 500 mW | 501.2 mW |
| 30 | ×1000 | 1 W | 1 W |
Notice the 26? That's the vendor's radio from the opening: "pushes 400 mW" translates to 26 dBm, and now you can compare it against anything without reaching for your phone. To go from dBm to dBW, subtract 30 and you're done: +23 dBm = −7 dBW (which is why almost nobody uses dBW indoors — the negatives get confusing).
The dB family: same movie, different opening scene
Once you see the pattern — generic dB + fixed reference = absolute unit — you recognize the whole clan:
- dBi: antenna gain relative to an isotropic antenna, the ideal sphere that radiates equally in all directions. It doesn't physically exist; it's the measuring stick.
- dBd: the same, but relative to a half-wave dipole, which has gain of its own. The conversion is fixed: dBi = dBd + 2.15. Watch the catalogs: the same antenna "performs better" in dBi, and some marketing department knows it.
- dBµV: voltage level relative to 1 µV, common in cable TV and broadcast. Party trick: 0 dBm into 50 Ω equals 107 dBµV (224 mV).
- dB SPL: sound pressure relative to 20 µPa, the threshold of human hearing. That's why microphone calibrators scream at 94 dB SPL — it's exactly 1 pascal. If you install audio too, the speaker SPL calculator runs on this very scale.
Same formula, same mental trick, different yardstick. You learned one unit and got five for free.
10·log or 20·log: the fine print of the square
You may have noticed dBµV and dB SPL use 20·log instead of 10·log. It's not a different definition — it's the same one. Power grows with the square of voltage (P = V²/R) and of sound pressure, and the logarithm pulls the square out front as a ×2: 10·log10(V²) = 20·log10(V). That keeps the dB consistent across worlds: doubling the voltage is +6.02 dB, exactly the same as quadrupling the power (+6 dB = ×4, really 3.98). One language, no translation. The working rule: power quantities (watts) take 10·log; field quantities (volts, amps, pascals) take 20·log. The dB converter has both modes, so the square doesn't bite you.
The example that ties it all together: 10 km at 5.8 GHz
Let's borrow the exact link from the point-to-point links guide — the guides around here greet each other — and look at it purely through decibel glasses. A 23 dBm radio, 14 dBi antennas on both ends, 10 km of air at 5.8 GHz (a wavelength of about 5.2 cm, by the way — the frequency and wavelength converter will confirm it):
- You leave the radio at +23 dBm. You can read that without a calculator now: 20 + 3 → 100 mW × 2 = 200 mW.
- The transmit antenna adds its gain: 23 + 14 = +37 dBm EIRP. In linear terms, about 5 W equivalent concentrated in the beam — you just multiplied by 25 without multiplying: you only added 14.
- The path charges its toll: free space at 5.8 GHz over 10 km takes 127.7 dB. In ratios: one part in almost six trillion arrives. In dB: 37 − 127.7 = −90.7 dBm. A subtraction.
- The receive antenna pulls you back up: −90.7 + 14 = Prx = −76.7 dBm. There's the entire magic in one line: +23 + 14 − 127.7 + 14 = −76.7. Four additions modeling twelve-digit multiplications.
- Translate the result: −76.7 dBm is about 21 pW. Yes, picowatts: you left with 200 mW and arrive with the power of a dying firefly — and it works, because the receiver claims −85 dBm sensitivity. Margin: −76.7 − (−85) = 8.3 dB. Too thin to sleep well; how to fatten it up is exactly what the point-to-point links guide covers.
If the install had 10 meters of coax between radio and antenna, it would enter the same sum as one more negative term — the coax loss calculator tells you how many dB for your cable and frequency. That's the elegance of the system: air, cable, connectors, antennas and amplifiers all speak the same language, and they all join the same sum.
Now the drama is back where it belongs: in the soap operas. Drill the ladder with the dBm/mW converter until 23 → 200 comes out without thinking, sanity-check your ratios in the dB converter, and next time a datasheet talks to you in milliwatts, translate it yourself before the page finishes loading.