Decibel Calculator
Convert a ratio of powers or amplitudes into decibels and back — the logarithmic scale behind sound levels, signal gain and attenuation.
Turn "twice as loud" or "half the signal" into decibels.
How the decibel calculator works
A decibel expresses a ratio on a logarithmic scale. For power quantities (watts, sound intensity) the level is 10 × log₁₀(P₂ ÷ P₁); for amplitude or field quantities (volts, sound pressure, current) it is 20 × log₁₀(A₂ ÷ A₁), because power goes with the square of amplitude. Doubling power is +3 dB; doubling voltage or pressure is +6 dB; ×10 power is +10 dB.
Enter the ratio to get decibels, or the decibels to get the ratio back.
Formula: dB = 10 log₁₀(P₂ ÷ P₁) for power · 20 log₁₀(A₂ ÷ A₁) for amplitude
Worked examples
| Inputs | Result | Note |
|---|---|---|
| Power ratio 2 | 3.01 | +3.01 dB |
| Voltage ratio 2 | 6.021 | +6.02 dB |
| 20 dB of power gain → ratio | 100 | ×100 |
| Power ratio 1,000 | 30 | 30 dB |
FAQFrequently asked questions
Why 10 log for power but 20 log for voltage?
Power is proportional to voltage squared, and log(x²) = 2 log(x). Using 20 for amplitudes keeps the decibel figure the same whichever quantity you measure.
How much louder is +10 dB?
Ten times the sound power, and roughly twice as loud to the ear. +3 dB is double the power but only just noticeable.
What are dBm and dB SPL?
Decibels relative to a fixed reference: 1 milliwatt for dBm, 20 µPa for sound pressure level. The arithmetic is the same with P₁ or A₁ fixed.
Can decibels be negative?
Yes — a ratio below 1 is a loss. Halving the power is −3 dB; an attenuator marked −20 dB passes 1% of the power.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.