Decibels Explained: dB, dBm and Why Engineers Use Them
A decibel (dB) is a way to write the ratio of two powers. You count how many times 10 is multiplied to make the ratio, then multiply that count by 10. Ten times the power is +10 dB, and 100 times is +20 dB. Twice the power is about +3 dB, and half is about −3 dB. Decibels turn multiplication into addition. Circuits and radio links have many stages that boost or weaken a signal, and with dB you can work them out in your head.
What you'll learn
- Where dB shows up (Wi-Fi signals, amplifiers, filters, noise, ADCs, sound)
- Why 10 times is +10 dB and 2 times is about +3 dB
- Why voltage alone uses a "20 times" formula, and what −3 dB means
- dBm, and how to estimate signal strength by adding numbers
Prerequisites: multiplication, and powers such as 10 × 10 × 10 = 1000 (middle-school math). A rough idea of what voltage, current and power are.
In everyday life
On a phone or laptop, you can open the details of the Wi-Fi network you are on. You may see a number such as "−55 dBm." It describes signal strength, yet it has a minus sign.
Datasheets for electronic parts use dB everywhere, too. An amplifier lists "20 dB," a filter "−3 dB," and an analog-to-digital converter "98 dB." Sound level meters also show dB.
All of these rest on the same idea. A dB value is not an amount by itself. It shows "how many times bigger," counted in powers of ten. This article first looks at what dB counts. Then it shows why dB is so handy for radio and circuit math.
How it works 1: counting a ratio by its zeros
Electronic circuits and radio deal with quantities of wildly different sizes at the same time. For example, say a Wi-Fi router sends out radio waves at 0.1 W (100 mW). A phone behind a wall may receive less than one ten-billionth of that.
If you write such a ratio as "1/10,000,000,000," it is easy to miscount the zeros. So instead, we count only how many times 10 is multiplied to make the ratio. 1000 is 10 multiplied 3 times, so it counts as "3." A million counts as "6." In math, this count is called the base-10 logarithm (from here on, just "logarithm").
A ratio written as a logarithm has a unit called the bel (B). It is named after Bell, famous for inventing the telephone. But the bel is a coarse scale, so we use one tenth of it: the decibel (dB). "Deci" means one tenth, as in decimeter. W. H. Martin announced the name in 1929, in the technical journal of the Bell System, a group of US telephone companies.
In short, a power ratio in dB is 10 times the logarithm. Ten times the power is +10 dB, 100 times is +20 dB, and 1000 times is +30 dB. Going the other way, one tenth is −10 dB and one thousandth is −30 dB. When the ratio is 1, meaning nothing changes, it is 0 dB.
How it works 2: why doubling is about 3 dB
Ten times was +10 dB. So how many dB is two times? Here we use a handy fact. If you multiply 2 by itself 10 times, you get 1024, which is close to 1000.
So doubling 10 times gives about 1000 times, or about +30 dB. Each doubling is a tenth of that: about 3 dB. The exact value is 3.01 dB, but people usually remember "doubling is about 3 dB." In the same way, 4 times is about 6 dB, 8 times is about 9 dB, and half is about −3 dB.
Decibels turn multiplication into addition. For example, 20 times is "10 times, then 2 times," so 10 dB + 3 dB gives about 13 dB. Multiply by 1000 and then halve, and you get 30 dB − 3 dB, about 27 dB. Math with long rows of zeros becomes adding and subtracting small numbers.
How it works 3: voltage in dB uses a "20 times" formula
So far we have looked at power ratios. Power is the electrical energy used or sent each second, measured in watts (W). In circuits, voltage is often easier to measure than power.
Suppose you put twice the voltage across the same resistor. The current also doubles. Power is voltage times current, so it becomes 2 × 2 = 4 times. If the voltage is 10 times, the power is 10 × 10 = 100 times. In other words, power is proportional to the square of the voltage.
When the voltage is 10 times, the power is 100 times, which is +20 dB. We want one change to have one dB value, whether we look at voltage or power. So for a voltage ratio, we take 20 times the logarithm. We write the logarithm as "log." Then a power ratio is dB = 10 × log(ratio), and a voltage ratio is dB = 20 × log(ratio).
By this rule, twice the voltage is about +6 dB (4 times the power), and 10 times is +20 dB. But this only matches exactly when the resistance is the same at the two points you compare. Between points with different resistance, the voltage ratio in dB and the power ratio in dB do not agree.
How many times an amplifier multiplies a signal is called its gain. Datasheets usually give gain in dB. An amplifier that multiplies the voltage by 100 has a gain of 40 dB.
How it works 4: −3 dB means "half the power"
A circuit that passes only the frequencies you need and weakens the rest is called a filter. Filter specs usually mark the edge of the range they pass as "the frequency where the output drops by 3 dB." This frequency is called the cutoff frequency.
−3 dB is about half the power. So what is it in voltage? Power is proportional to the square of the voltage. So at half the power, the voltage is multiplied by "the number that gives one half when squared." That is about 0.707 (1 divided by the square root of 2).
Half the voltage is not −3 dB but about −6 dB. When you remember "−3 dB = half," keep in mind that it is about power, and you will not mix them up. In a simple filter made of just a resistor and a capacitor, this frequency can be calculated from the time constant ("RC Time Constant Explained").
How it works 5: dBm means "dB compared with 1 mW"
A dB value alone only tells you "how many times." But if you fix a reference amount, dB can show an actual amount. Power written against a reference of 1 mW (one thousandth of a watt) is called dBm. The final m marks the milliwatt reference.
0 dBm equals the reference, 1 mW. 10 dBm is 10 mW, 20 dBm is 100 mW, and 30 dBm is 1 W. Going down, −30 dBm is 1 µW (one millionth of a watt), and −90 dBm is 1 pW (one trillionth of a watt). Any power below 1 mW is negative in dBm.
The Wi-Fi signal that reaches a phone has very little power. As a rough guide, it is about −30 dBm right next to the router. At the edge of a usable connection, it is about −90 dBm. Where the lines are drawn differs between devices and apps. For example, Apple says (as of 2026) that an iPhone starts looking for another router when the signal falls below −70 dBm. The "−55 dBm" from the start of this article is negative because it is far weaker than 1 mW.
There are other dB units with other references. dBi rates an antenna against an ideal antenna that sends equally strong waves in every direction. Sound levels in dB also have a fixed reference (explained later). The letters after dB tell you what the reference is. You can try conversions with the dB and dBm converter.
How it works 6: estimating signal strength by adding
Decibels really shine when many stages of boosting and weakening come one after another. As an example, let's estimate the signal strength at a phone 10 m from a Wi-Fi router. The numbers are only examples. To keep things simple, we assume there are no walls or reflections.
Say the router's transmitter puts out 20 dBm (100 mW). Assume the cable to the antenna loses half of that as heat. That is −3 dB.
An antenna does not have to send waves equally in all directions. It can focus them in certain directions. In those directions, the waves are stronger than from an ideal antenna. This ratio is called the antenna's gain, and here we take it as +3 dBi (about 2 times). Other directions get weaker, so the total energy does not grow.
How much weaker the signal gets in space
Radio waves leave the antenna and spread out like a growing sphere. The surface area of a sphere is proportional to the square of its radius. So the power caught by a fixed area falls to a quarter (−6 dB) at twice the distance. At 10 times the distance, it falls to a hundredth (−20 dB).
This weakening in space with no obstacles is called free-space path loss. Between two ideal antennas, the loss ratio is the square of "4 × pi × distance ÷ wavelength." The wavelength is the length from one peak of the wave to the next. It is in the formula because the area over which an ideal antenna collects waves depends on the wavelength (we won't go into that here).
Radio waves in the 2.4 GHz band have a wavelength of about 12.5 cm. For a distance of 10 m, 4 × 3.14 × 10 ÷ 0.125 is about 1000, and its square is about one million. One millionth has 6 zeros, so it is −60 dB. At 100 m, it is about −80 dB.
Putting it together by adding
Take the phone's antenna gain as 0 dBi (1 time). Then the strength that reaches the phone is 20 − 3 + 3 − 60 = −40 dBm. In power, that is 0.0001 mW, or one ten-millionth of a watt.
Doing the same math by multiplying gives 100 mW × 1/2 × 2 × 1/1,000,000. The answer is the same, but keeping track of the zeros is hard. With dB, the size of each number also shows at a glance which stage loses the most.
Adding up all the boosts and losses from sender to receiver like this is called a link budget. In a real home, walls, floors and people's bodies weaken the signal further. So designers leave plenty of margin above the strength that is needed.
Note that what you may add is "dBm + dB." Adding two dBm values together means nothing. For example, combining two 0 dBm (1 mW) signals gives 2 mW, which is about 3 dBm. It is not 0 + 0 = 0 dBm.
How it works 7: noise and signal-to-noise ratio
Inside a circuit, heat makes electrons move around at random. This always creates small wobbles in voltage. Such unwanted wobbles are called noise (a typical kind is thermal noise). If a signal is too weak, it gets buried in the noise and cannot be read.
So we look at how many times stronger the signal's power is than the noise's power. This ratio is called the signal-to-noise ratio (SNR), and it is given in dB. An SNR of 30 dB means the signal's power is 1000 times the noise's. The higher the SNR, the more clearly the signal can be read.
The "6 dB per bit" of an ADC
A circuit that turns a voltage into a number is called an analog-to-digital converter (ADC). An ADC rounds the voltage to one of a fixed set of steps and outputs that step as a number. The number of steps depends on the number of bits (digits that are 0 or 1). With 16 bits, there are 65,536 steps. The error from rounding (quantization error) is also a kind of noise.
Adding one bit makes the steps twice as fine, so the rounding error is half as large. A voltage ratio of 2 is about 6 dB, so each bit improves the SNR by about 6 dB. Suppose you feed an ideal ADC a sine wave (a smooth wave) that fills its whole input range. Its SNR is then about 6.02 × number of bits + 1.76 dB. The 1.76 dB is a small extra that comes from the shape of the sine wave (we skip the derivation).
For the 16 bits of a music CD, 6.02 × 16 + 1.76 gives about 98 dB. As a power ratio, that is about 6.4 billion times. Real ADCs fall below this because of other noise and distortion. Their real performance, converted into a number of bits, is the ENOB ("What Is an Analog Chip?", ADC SNR and ENOB calculator).
Sound in dB: the threshold of hearing is the reference
The dB on a sound level meter compares how much the air pressure wobbles (the sound pressure). The reference is 20 µPa (micropascals). For sounds near 1 kHz, that is about the smallest wobble a person can just barely hear.
In the same air, the square of the sound pressure is proportional to the sound intensity (the quantity that plays the role of power). This is the same relationship as for voltage. So sound pressure in dB also uses the 20 times formula. 0 dB does not mean "no sound." It means "the same wobble as the threshold of hearing."
A rule of thumb says that when sound intensity grows 10 times (+10 dB), people hear it as about twice as loud. This is not a law of physics. It is an average of how people perceive sound. How well it holds depends on the pitch and loudness of the sound.
Common misconceptions
Myth: 0 dB means "zero" or "nothing"
In fact, 0 dB means "a ratio of 1," the same as the reference. 0 dBm is a power of 1 mW, and 0 dB of sound is a sound right at the edge of hearing. Anything smaller than the reference goes negative, like −40 dBm. Just as 0 °C does not mean "no heat," the 0 on the scale only marks where the reference sits.
Myth: If the dB number doubles, the power doubles too
In fact, 10 dB is 10 times and 20 dB is 100 times. Doubling the dB number squares the ratio. Doubling the power is "+3 dB." dB is a scale that turns multiplication into addition, so the number on the scale is not proportional to the amount.
Myth: dB is a unit of quantity, like volts or watts
In fact, dB writes a ratio as a logarithm, and on its own it tells you no size. It is not a unit that measures a physical quantity itself, as the volt does. It is not a unit of the International System of Units (SI) either. Only when a reference is set, as in dBm, dBi or sound dB, can you tell a size. When you see dB in a datasheet, check what it is a ratio to.
Key numbers
| Example | dB | Ratio or amount |
|---|---|---|
| Transmit power (this article's example) | 20 dBm | 100 mW |
| Loss at 2.4 GHz over 10 m | −60 dB | One millionth |
| Same, over 100 m | −80 dB | One hundred-millionth |
| Rough lower limit for Wi-Fi reception | −90 dBm | 1 pW (one trillionth of a watt) |
| SNR of an ideal 16-bit ADC | About 98 dB | About 6.4 billion times in power |
1 W and 1 pW differ by 12 digits, or 120 dB. With dB, gaps of many digits like this become adding and subtracting numbers of three digits or fewer. That is why engineers in electronics and communications keep using dB.
Learn more
- Terms: link budget / free-space path loss / noise figure (NF) / Bode plot (a graph of gain in dB at each frequency)
- Try the numbers: dB and dBm converter / ADC SNR and ENOB calculator / op-amp gain calculator / Bode plot calculator
- Compare in a table: Wi-Fi vs Bluetooth vs LPWA
- Related explainers: "How Does Wi-Fi Work?" / "What Is 5G?" / "Fermi-Dirac vs Boltzmann Distribution in Semiconductors" (on counting the voltage that changes a current tenfold)