ConverterHub

Decibel Ratio Calculator

Enter the ratio and choose whether it is a power or amplitude ratio.

How it is calculated

You enter one dimensionless ratio R (output ÷ input, or measured ÷ reference) and pick its type. For a power ratio the tool computes dB = 10 × log10(R); for an amplitude ratio (voltage, current, sound pressure) it computes dB = 20 × log10(R). The ratio must be greater than zero, because the logarithm of zero or a negative number does not exist. A ratio above 1 gives a positive decibel value (gain), a ratio below 1 a negative one (loss), and exactly 1 gives 0 dB. Results are rounded to two decimals. Any unrecognised type is treated as power.

Worked example

A stage doubles the signal voltage, so the amplitude ratio is 2. Using the 20 factor: 20 × log10(2) = 20 × 0.30103 = 6.02 dB. If the ratio 2 had been a power ratio, the 10 factor would give 3.01 dB. That difference is the reason to choose the type carefully: doubling voltage into the same load quadruples power, and 10 × log10(4) is also 6.02 dB. A ratio of 0.5 as power would give −3.01 dB.

Try this example →

Common mistakes

  • Choosing power for a voltage or sound-pressure ratio (or amplitude for watts). This halves or doubles the decibel value, e.g. 3.01 dB instead of 6.02 dB for a ratio of 2.
  • Entering the two values as a difference or in dB already. The field wants a plain ratio such as 2 or 0.5, not 6 or −3.
  • Entering the ratio the wrong way round. Output over input gives gain; input over output gives the same size with the opposite sign.
  • Forgetting that a ratio of zero or less has no logarithm, so the tool shows nothing for it. Silence or total loss cannot be expressed in finite dB.
  • Treating the decibel as an absolute level. A plain dB figure is only a ratio; dBm, dBV or dB SPL need a stated reference.

About this calculator

The decibel is a logarithmic unit for expressing a ratio, and the formula depends on whether the quantity being compared is a power quantity or a field (amplitude) quantity. For power ratios — such as watts of electrical or acoustic power — the conversion is dB = 10 · log10(P2/P1). For amplitude ratios — such as voltage, current, sound pressure or field strength — it is dB = 20 · log10(A2/A1), with the extra factor of two because power is proportional to amplitude squared, so both formulas agree when applied to the same physical change.

This is exactly why audio engineers use 20·log10 for voltage/gain ratios on a mixing console, RF and telecom engineers use 10·log10 for power ratios in a link budget, and acoustic measurements of sound pressure level also use the 20·log10 form. This calculator converts a ratio you enter into decibels using whichever formula matches the type you select, power or amplitude.

Was this helpful?

You can pick up to 3 reactions.

Comments (0)

  • Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators