Decibel (dB) Calculator
Decibel (dB) Calculator — Power and Voltage Ratios
Turn a ratio into decibels or decibels back into a ratio, with the right factor — 10 log₁₀ for power, 20 log₁₀ for voltage or current — plus the named reference levels (dBm, dBW, dBV, dBu, dBµV, dB SPL) and what your gain does to an absolute level.
decibel ratio
A ratio of 2 in power (an amplifier that doubles the watts)
The decibel, both ways round
ratio = 10L / 10 (power) ratio = 10L / 20 (amplitude) because P ∝ V², log P = 2 log V
- L
- the level difference in decibels; positive is a gain, negative a loss
- P1, P2
- the two powers, in the same unit
- V1, V2
- the two amplitudes — volts, amps or pascals — in the same unit
- 10 vs 20
- one rule, not two: doubling the voltage quadruples the power, so 6.02 dB of voltage is 6.02 dB of power
- 0 dB
- a ratio of one — no change. It does not mean nothing
Worked example
A ratio of 2 in power (an amplifier that doubles the watts)
The quantity is power, so the factor is 10: L = 10 log10(2)
log10(2) = 0.30103, so L = 3.0103 dB — the famous “3 dB”, which is 3.01 dB if you are being careful
Read the other way, 3 dB exactly is a power ratio of 100.3 = 1.9953, not quite 2
The same doubling in VOLTAGE would be 20 log10(2) = 6.0206 dB
With the absolute block set to dBm and 1 mW entered: 1 mW is 0.00 dBm, and 3.010 dB of gain takes it to 3.010 dBm — 2 mW
The decibels worth memorising
| Decibels | Power ratio | Amplitude ratio | Where you meet it |
|---|---|---|---|
| 0.5 dB | 1.1220 | 1.0593 | well below what anyone can hear |
| 1 dB | 1.2589 | 1.1220 | ×1.26 power — near the limit of what is audible |
| 2 dB | 1.5849 | 1.2589 | the smallest step most people notice on a loudspeaker |
| 3 dB | 1.9953 | 1.4125 | ≈ ×2 power — the half-power point, and a filter’s corner |
| 3.0103 dB | 2.0000 | 1.4142 | exactly ×2 power |
| 6 dB | 3.9811 | 1.9953 | ≈ ×2 voltage, and one bit of an ADC |
| 6.0206 dB | 4.0000 | 2.0000 | exactly ×2 voltage |
| 10 dB | 10.0000 | 3.1623 | exactly ×10 power |
| 20 dB | 100.0000 | 10.0000 | exactly ×10 voltage |
| 30 dB | 1,000.0000 | 31.6228 | ×1,000 power |
| 40 dB | 10,000.0000 | 100.0000 | ×10,000 power, ×100 voltage |
| 60 dB | 1,000,000.0000 | 1,000.0000 | ×1,000,000 power — a low-noise amplifier chain |
Named reference levels and what each is measured against
| Suffix | 0 dB is | Kind of quantity | Notes |
|---|---|---|---|
| dBm | 1 mW | power | The RF and audio workhorse. Into 50 Ω, 0 dBm is 0.2236 V RMS; into 600 Ω it is 0.7746 V — the same power, different voltage, which is why a dBm figure is meaningless without the impedance. |
| dBW | 1 W | power | Transmitter and radar power. 0 dBW = +30 dBm exactly. |
| dBV | 1 V RMS | voltage | Voltage only, no impedance implied. Consumer line level is −10 dBV = 0.3162 V RMS. |
| dBu | 0.7746 V RMS | voltage | The volts that would have dissipated 1 mW in 600 Ω, kept as a pure voltage reference after the 600 Ω line went away. Professional line level is +4 dBu = 1.2277 V RMS. |
| dBµV | 1 µV RMS | voltage | EMC and receiver work. 0 dBµV = −107 dBm in a 50 Ω system; a signal generator marked −73 dBm is 40 dBµV. |
| dB SPL | 20 µPa | pressure | Sound pressure in air, the reference being roughly the quietest audible tone at 1 kHz. Doubling the pressure is 6.0206 dB, doubling the acoustic power 3.0103 dB. |
Why power gets 10 and voltage gets 20
The decibel is defined on power. A level in decibels is ten times the base-10 logarithm of a power ratio, so ten decibels is a factor of ten in power, twenty decibels a factor of a hundred, and so on. The bel itself — one power decade — turned out to be too coarse a step for telephone work, which is why the deci- prefix stuck.
So where does 20 log come from? Voltage, current and sound pressure are not powers. In a resistor the power is V²/R, so doubling the voltage multiplies the power by four. Write that out: 10 log₁₀(V₂²/V₁²) = 20 log₁₀(V₂/V₁). The twenty is not a second definition of the decibel; it is the ten with the square pulled out of the logarithm. That is why the two rules agree exactly — as long as both voltages sit across the same impedance. Across different impedances they do not, and an amplifier with a voltage gain of 6.02 dB into a different load is not necessarily giving you that much more power.
The numbers to keep in your head. 3 dB is very nearly twice the power (exactly 1.9953×), and the exact doubling is 3.0103 dB. 6 dB is very nearly twice the voltage, and the exact doubling is 6.0206 dB. 10 dB is ten times the power exactly and 20 dB is ten times the voltage exactly, because those are the definitions. A filter’s corner frequency is the −3 dB point — the frequency at which half the power gets through, which is why it is also the 0.707 voltage point: √½ = 0.7071. Work those corners out with the RC and RLC filter calculator.
A dB on its own is a ratio; a dB with a suffix is a level. “The amplifier has 20 dB of gain” is a ratio and needs no reference. “The signal is −80 dBm” is an absolute power, because dBm names one: 1 milliwatt. dBW names a watt, dBV names a volt, dBu names 0.7746 V — the voltage that would have delivered 1 mW into the 600 Ω line of a telephone system — and dB SPL names 20 micropascals of sound pressure. The trap is that a power reference and a voltage reference are only interchangeable if you also state the impedance: 0 dBm is 0.224 V RMS in a 50 Ω system and 0.7746 V in a 600 Ω one. For the dBm-to-watts conversion with an impedance of your choosing, and the peak and peak-to-peak voltages that go with it, use the dBm to watts calculator; for the peak-to-RMS arithmetic behind those voltages, the RMS, peak and peak-to-peak converter.
Adding instead of multiplying. The reason engineers put up with logarithms at all is that a chain of gains and losses becomes a sum. An antenna at −65 dBm into 3 dB of cable loss, then a low-noise amplifier of 20 dB and a mixer with 7 dB of conversion loss, arrives at −65 − 3 + 20 − 7 = −55 dBm. Doing that as ratios means multiplying 3.16×10⁻¹⁰ by 0.5 by 100 by 0.2, and nobody does that reliably on a bench. Mismatch loss in that chain is a decibel figure too — see the VSWR and return loss converter.
Frequently asked questions
When do I use 10 log and when do I use 20 log?
10 log₁₀ for anything that is a power — watts, milliwatts, acoustic intensity, optical power. 20 log₁₀ for anything whose square is a power — volts, amps, sound pressure, field strength. They are the same rule: power goes as the square of the amplitude, and squaring inside a logarithm is the same as doubling outside it.
Is 3 dB exactly double the power?
No, but it is close. 3 dB is a power ratio of 1.9953; an exact doubling is 3.0103 dB. The same goes for 6 dB and a doubling of voltage, which is exactly 6.0206 dB. 10 dB and 20 dB, on the other hand, are exactly ten times the power and ten times the voltage — no rounding involved.
What is the difference between dB, dBm and dBu?
A plain dB is a ratio between two things you already have. dBm is an absolute power measured against 1 milliwatt. dBu is an absolute voltage measured against 0.7746 V RMS, which is the voltage that dissipates 1 mW in 600 Ω. dBm and dBu therefore agree numerically — and only — in a 600 Ω system.
Why does 0 dB not mean zero signal?
Because 0 dB is a ratio of one. log₁₀(1) = 0, so “0 dB of gain” means the output equals the input. A signal of genuinely zero amplitude has no decibel value at all: the logarithm of zero is minus infinity.
How do I add decibels together?
Gains and losses in a chain simply add, because a logarithm turns multiplication into addition. Two 10 dB amplifiers in series give 20 dB. What you cannot do is add the dB figures of two signals arriving at the same point — for that you convert both back to power, add the powers, and convert the total back to decibels.
Can I convert dBm to volts without knowing the impedance?
No. dBm is a power, and the voltage a given power produces depends on the resistance it flows through. 0 dBm is 0.224 V RMS into 50 Ω, 0.274 V into 75 Ω and 0.7746 V into 600 Ω. dBV and dBµV, by contrast, are voltage references and need no impedance at all.
Related calculators
References
- International Electrotechnical Commission. IEC 60027-3:2002, Letter symbols to be used in electrical technology — Part 3: Logarithmic and related quantities, and their units. The standard that defines the decibel and the neper, and the rule that a power quantity takes 10 log10 while a root-power (field) quantity takes 20 log10.
- Wikipedia contributors. Decibel — suffix table: dBV is “voltage relative to 1 volt, regardless of impedance”; “0 dBu is defined as the RMS voltage that would dissipate 0 dBm (1 mW) in a 600 Ω” load, about 0.7746 V; dB SPL is referenced to “20 micropascals”. Cross-checked against the same encyclopaedia’s dBm article, which gives 0 dBm as about 0.775 V into 600 Ω and about 0.224 V into 50 Ω.
- Horowitz P, Hill W. The Art of Electronics, 3rd ed. Cambridge University Press, 2015. §1.3.2 on the decibel and the two factors, and Appendix A on the oscilloscope — what a measured amplitude actually is.
- Bureau International des Poids et Mesures. The International System of Units (SI Brochure), 9th ed., 2019 — the speed of light fixed at exactly 299,792,458 m/s, which is where every wavelength on these pages comes from.