Decibel Ratio Calculator
Convert the ratio of two values into decibels. Because decibels differ for power and for amplitude quantities, this tool reports both the power interpretation (10·log) and the voltage/amplitude interpretation (20·log), along with the plain linear ratio.
Enter Values
How to use this calculator
- Enter the reference value (value 1) — the baseline you are comparing against.
- Enter the measured value (value 2) — the level you want to express in dB.
- Read the power dB, the voltage/amplitude dB, and the linear ratio; pick the row that matches your quantity.
How it works
The linear ratio is value 2 divided by value 1. For power quantities such as watts or acoustic intensity, decibels are 10 × log₁₀ of that ratio. For field or amplitude quantities such as voltage or sound pressure, decibels are 20 × log₁₀ of the ratio, because power is proportional to the square of amplitude. Both values must be positive because the logarithm of zero or a negative number is undefined.
Worked example
Worked example. Doubling a value (value 1 = 1, value 2 = 2) gives a linear ratio of 2: 10·log₁₀(2) = 3.0103 dB of power, or 20·log₁₀(2) = 6.0206 dB of voltage/amplitude.
Common mistakes
- Using 20·log for a power quantity (watts) or 10·log for a voltage/SPL quantity — pick the formula that matches what you are measuring.
- Entering zero or a negative value; decibel ratios are only defined for positive numbers.
- Swapping value 1 and value 2, which flips the sign of the result.
Frequently asked questions
When do I use 10·log versus 20·log?
Use 10·log₁₀ for power-like quantities (electrical power, acoustic intensity). Use 20·log₁₀ for amplitude-like quantities (voltage, current, sound pressure). The 20·log form is just 10·log applied to the squared amplitude, which is why the same physical change reads as twice the dB.
Why is doubling +3 dB sometimes and +6 dB other times?
Doubling the power of a signal is +3.01 dB, while doubling its voltage or pressure is +6.02 dB. They describe the same event from different quantities: doubling voltage quadruples power, and 10·log₁₀(4) equals about 6 dB.
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Tip: Enter any known values to calculate the remaining results.
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