Decibel Calculator
Convert between power ratios and decibels, voltage ratios and decibels. Compute gain/loss for cascades. Includes dBm, dBu, dBV reference conversions.
How to Use
- Pick conversion direction: ratio to dB, or dB to ratio.
- Select type: power (10·log) or voltage (20·log).
- Use dBm/dBu/dBV presets to reference absolute power/voltage levels.
- For cascaded stages, add dB values directly — no multiplication needed.
Worked Example
A preamp takes a 0.1 V signal and outputs 2 V. The voltage ratio is 2 ÷ 0.1 = 20, so the gain is 20 × log₁₀(20) = 26.0 dB. If input and output see the same impedance, the power ratio is 20² = 400, and 10 × log₁₀(400) gives the same 26.0 dB.
Rules of thumb: +3 dB doubles power, +6 dB doubles voltage, +10 dB is 10× power, +20 dB is 10× voltage (100× power).
The common mistake: 10·log on a voltage ratio. 10 × log₁₀(20) = 13.0 dB understates the gain by half. Use 20·log for voltage, current or sound pressure, and 10·log for power or energy.
Show Work
Formulas
Reference Scales
| Scale | Reference | Use |
|---|---|---|
| dBm | 1 mW | RF, telecom |
| dBW | 1 W | Transmitter power |
| dBV | 1 V RMS | Consumer audio |
| dBu | 0.775 V RMS | Pro audio |
| dBSPL | 20 µPa | Acoustic sound pressure |
| dBi | Isotropic radiator | Antenna gain |
History of the Decibel
In 1924 Bell System engineers introduced the "transmission unit" to measure signal losses on long telephone lines. In 1928 it was renamed the decibel: a tenth of a bel, the unit for a tenfold change in power, named after Alexander Graham Bell. W. H. Martin of Bell Labs explained the change in a 1929 paper. One decibel is close to the smallest change in loudness most people can notice.
The logarithmic scale matches the natural psychophysics of human perception. Gustav Fechner's 1860 Weber-Fechner law established that perceived intensity of sound, light, and pressure is proportional to the logarithm of the physical stimulus — so plotting loudness, brightness, or pressure on a log scale gives approximately linear perceived changes. This is why decibels and musical octaves (which are log2) both work so well for describing sensory phenomena.
The distinction between 10·log (for power) and 20·log (for voltage or current) comes from the fact that power = V²/R, so a factor-of-2 voltage change corresponds to a factor-of-4 power change. Both express the same physical change — 10·log(4) = 20·log(2) ≈ 6.02 dB — so the two conventions give identical results for identical physical situations. Engineers use whichever matches their measurement (voltmeter → 20·log; wattmeter → 10·log).
About This Calculator
Pick conversion direction (ratio → dB or dB → ratio) and measurement type (power 10·log vs voltage 20·log). The tool converts between linear ratio and decibels, also showing the equivalent in the other unit type (e.g., 20 dB voltage = 100× voltage = 10,000× power). Use quick presets for common benchmarks (2×, 10×, 100×).
Reference tables below show common absolute-reference decibel scales: dBm (mW), dBW (W), dBV (1 V RMS), dBu (0.775 V RMS), dBSPL (20 µPa for acoustic sound), dBi (isotropic radiator for antennas). When you see "dBm," "dBV," etc., that's an absolute reference — plain "dB" is just a ratio. Everything runs client-side; no values leave your browser.
Frequently Asked Questions
Why use decibels?
Decibels convert multiplicative ratios into additive values. A 100× power gain followed by a 50× power gain is 5,000×; in dB that is simply 20 + 17 = 37 dB. Adding beats multiplying for large ratios. Also lets us describe signals spanning billions in range with reasonable numbers.
Why 10·log for power but 20·log for voltage?
Both give the same dB value for the same physical change. Power = V²/R, so doubling voltage quadruples power. 20·log(2) = 6.02 dB for voltage doubling; 10·log(4) = 6.02 dB for the corresponding power quadrupling. Same answer.
What's dBm?
dB referenced to 1 mW. 0 dBm = 1 mW. +30 dBm = 1 W. −30 dBm = 1 µW. Common in RF and telecom. Always specifies absolute power, unlike plain dB (which is a ratio).
dBu vs dBV?
dBV: referenced to 1 V RMS (consumer audio: −10 dBV = 0.316 V). dBu: referenced to 0.775 V RMS (pro audio: +4 dBu = 1.23 V). Both are absolute voltage scales.
How do dB add up?
For cascaded stages, add the dB values: amplifier +20 dB, cable −3 dB, attenuator −10 dB = +7 dB overall. In power ratios that is 100 × 0.5 × 0.1 = 5×, and 10·log(5) = 7 dB. In voltage ratios the same stages are 10 × 0.708 × 0.316 = 2.24×, and 20·log(2.24) = 7 dB too. Just don't mix a power ratio with the 20·log formula.
How do I use the Decibel Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Audio Amp Gain
Pre-amp adds 20 dB, mic pre adds 60 dB, headphone amp adds 10 dB. Total gain = 90 dB = 10^(90/20) = 31,623× voltage.
RF Link Budget
TX power +20 dBm, antenna +2 dBi, free-space loss −60 dB, RX antenna +2 dBi. Received signal: −36 dBm. If noise floor is −100 dBm, link margin is 64 dB.
Acoustic Sound Level
SPL (sound pressure level) is dB re 20 µPa. Quiet room: 30 dB. Conversation: 60 dB. Rock concert: 110 dB. Each 10 dB is 10× the sound intensity, which listeners hear as roughly twice as loud.
Fiber Optic Attenuation
Single-mode fiber: 0.2 dB/km at 1550 nm. 100km run = 20 dB loss. Amplifiers every 80km compensate.
Cable Loss
RG-58 at 100 MHz loses about 16 dB per 100 m, so a 25 m run loses 4 dB: only 10−0.4 = 40% of the power arrives and 60% is lost.
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