dBm, dBW, dBd and dBi
The decibel on its own is a ratio — it tells you how much bigger or smaller one signal is compared to another. But sometimes you need to express an absolute power level, not just a ratio. That is where dBm and dBW come in. And when you want to describe how well an antenna concentrates its radiated energy, dBd and dBi give you a standard way to do that. All four units appear constantly in ham radio technical specifications, and once you understand what each one references, they are straightforward to use.
Why we need absolute decibel units
Suppose a datasheet says a receiver has 20 dB of gain. That is useful — it means the output power is 100 times the input power. But it does not tell you the actual power levels. For that, you need a reference point. If the input is −90 dBm, you know the output is −70 dBm. Without the absolute unit, you can only describe ratios, not levels.
In RF work, two absolute power references are in everyday use:
- dBm — decibels relative to 1 milliwatt. Used for signal levels at any stage in a radio system, receiver sensitivity, and transmitter power for handheld radios.
- dBW — decibels relative to 1 watt. Used for high-power transmitters, microwave link budgets, and satellite power budgets.
dBm — decibels relative to 1 milliwatt
The formula for converting a power in milliwatts to dBm is:
which simplifies to:
P(dBm) = 10 × log10(PmW)
To go the other way — from dBm back to milliwatts:
The reference point, 0 dBm, is exactly 1 milliwatt. Values above 0 dBm represent more than 1 mW; values below 0 dBm represent less.
Key dBm values to memorise
Just as with plain decibels, a handful of reference points get you through most calculations without needing a calculator:
| dBm | Power in milliwatts | Power in watts | Ham radio context |
|---|---|---|---|
| −120 dBm | 0.000 000 001 mW | 1 pW (picowatt) | Noise floor of a sensitive receiver |
| −73 dBm | ~0.000 05 mW | ~50 nW | S9 signal level (traditional reference) |
| −30 dBm | 0.001 mW | 1 μW | Weak signal digital modes |
| 0 dBm | 1 mW | 0.001 W | Reference point; signal generator output |
| 10 dBm | 10 mW | 0.01 W | QRP transmitter milestone |
| 20 dBm | 100 mW | 0.1 W | Low-power stage output |
| 30 dBm | 1000 mW | 1 W | Legal QRP power level |
| 37 dBm | 5012 mW | ~5 W | Typical handheld transceiver |
| 40 dBm | 10 000 mW | 10 W | Low-power HF operation |
| 43 dBm | 20 000 mW | 20 W | Portable HF transceiver |
| 50 dBm | 100 000 mW | 100 W | Typical HF station (legal limit many countries) |
| 53 dBm | 200 000 mW | 200 W | Mid-range HF amplifier |
| 60 dBm | 1 000 000 mW | 1 kW | High-power HF amplifier |
Notice the pattern: every +10 dBm multiplies the power by 10, and every +3 dBm approximately doubles it (because 100.3 ≈ 2). These two facts alone let you work out most dBm values mentally once you know a single reference point.
Key reference points on the dBm scale. The 30 dBm steps (−120, −90, −60, −30, 0, 30, 60) each represent a factor of 1000 in power.
View LargerConverting between watts and dBm
The conversion steps are:
- Convert the power to milliwatts (multiply watts by 1000).
- Take log10 of the milliwatt value.
- Multiply by 10.
100 W = 100 000 mW
log10(100 000) = 5
P(dBm) = 10 × 5 = 50 dBm
PmW = 10(−110/10) = 10−11 = 0.000 000 000 01 mW
= 10 picowatts (pW)
dBW — decibels relative to 1 watt
dBW uses exactly the same formula as dBm, but the reference is 1 watt instead of 1 milliwatt:
which simplifies to:
P(dBW) = 10 × log10(PW)
The key relationship between dBm and dBW is straightforward: since 1 watt = 1000 mW = 30 dBm, every dBW value is exactly 30 dB higher in milliwatt terms:
or equivalently:
dBm = dBW + 30
Example: 1 kW = 60 dBm = 60 − 30 = 30 dBW
Watts / dBm / dBW Calculator
Watts to dBm and dBW
Enter a power in watts to convert it to dBm and dBW.
dBm to Watts and dBW
Enter a power level in dBm to convert it to milliwatts, watts and dBW.
dBi — gain relative to an isotropic antenna
An isotropic antenna is a theoretical ideal that radiates equally in all directions, forming a perfect sphere around itself. No real antenna can do this, but it is a useful mathematical reference point. The gain of a real antenna over this ideal is expressed in dBi (decibels relative to isotropic).
A half-wave dipole in free space has a gain of approximately 2.15 dBi. This means it concentrates its radiation slightly more than the theoretical isotropic — not because it amplifies the signal, but because it does not radiate equally in all directions. The energy "saved" from the blind spots (the ends of the antenna) is redirected to the broadside directions.
More directive antennas have higher dBi figures:
- Isotropic antenna: 0 dBi (by definition)
- Half-wave dipole: 2.15 dBi
- 3-element Yagi: approximately 7–8 dBi
- 5-element Yagi: approximately 9–10 dBi
- High-gain dish (microwave): 30–50 dBi or more
dBd — gain relative to a dipole
Because the isotropic antenna does not exist in practice, many antenna manufacturers rate their antennas against the more familiar half-wave dipole. This gives dBd (decibels relative to a dipole).
A dipole has 0 dBd by definition. A Yagi that is rated at 5.85 dBd has 5.85 dB more gain than a simple half-wave dipole pointed in the same direction.
Relationship between dBi and dBd
Since a dipole itself has 2.15 dBi, the conversion between the two units is simply:
dBd = dBi − 2.15
dBd = 8.15 − 2.15 = 6 dBd
Always check which reference unit a manufacturer uses. Quoting 8.15 dBi sounds more impressive than 6 dBd, but they refer to the same antenna. This is not deceptive when stated clearly, but it can cause confusion when comparing specifications from different sources.
Radiation pattern comparison. The isotropic radiates equally in all directions; the dipole concentrates energy broadside; a Yagi focuses it further in one direction. dBi and dBd express the gain relative to each reference.
View LargerWhen each unit is used
| Unit | What it measures | Typical use |
|---|---|---|
| dBm | Absolute power (ref: 1 mW) | Receiver sensitivity, signal levels at connectors, handheld transmitter power, component datasheets |
| dBW | Absolute power (ref: 1 W) | High-power transmitters, satellite and microwave link budgets, broadcast stations |
| dBi | Antenna gain (ref: isotropic) | Technical specifications, antenna modelling software, engineering documents |
| dBd | Antenna gain (ref: dipole) | Commercial antenna datasheets, antenna comparisons in ham radio publications |
In a radio link budget, you will typically mix these units. For example: transmitter power in dBm, cable losses in dB, antenna gain in dBi, path loss in dB, and received signal level back in dBm. As long as you keep track of what each number references, the arithmetic stays simple.
Frequently Asked Questions
What does −73 dBm mean in ham radio?
−73 dBm is the traditional S9 signal level for HF receivers. It corresponds to approximately 50 nanovolts across a 50-ohm input, or about 50 nanowatts of power. The S-meter scale was standardised so that each S-unit above S9 represents +6 dB, meaning S9+10 dB is −63 dBm and S9+20 dB is −53 dBm.
Why do receiver sensitivity specs use negative dBm numbers?
Because the signal levels involved are far below 1 milliwatt. A typical HF receiver might have a sensitivity of −130 dBm for a 10 dB signal-to-noise ratio. That is 10−13 milliwatts, or 0.1 femtowatts — an inconveniently small number to write out. The negative dBm value is much easier to work with and makes comparisons straightforward.
Can a passive antenna have gain?
Yes — passive antenna gain is real, but it works by concentration, not amplification. A directive antenna focuses its energy in one direction rather than spreading it equally in all directions. You gain in some directions at the expense of others. The total radiated power is the same (minus losses); it is just more concentrated. This is the kind of gain described by dBi and dBd.
Which unit should I quote when reporting my station's effective radiated power?
Effective Radiated Power (ERP) is normally quoted in watts or dBW when dealing with regulators and licence conditions. Some authorities use ERP (referenced to a dipole, the older convention) and others use EIRP (referenced to an isotropic, the more modern convention). EIRP = ERP + 2.15 dBW. Always check which reference your local regulations use.
Test Your Knowledge
Answer the questions below to check your understanding of this lesson. Every answer can be found in the lesson above.