Calculators
Decibel Calculator
Convert relative power and amplitude ratios to and from decibels.
Convert relative power or amplitude ratios to decibels, or convert a dB difference back to its corresponding ratio.
Decibels
10 dB
This is a relative dB calculator, not a dBm, dBW, dBV, SPL, or measurement-calibration tool. The 20 log rule for voltage/current-like amplitudes requires compatible reference and impedance conditions.
About This Tool
Decibels express a ratio on a logarithmic scale, making very large or small changes easier to compare. They are common in electronics, communications, audio, controls, and signal analysis. This calculator handles relative decibel relationships: power ratio to dB, amplitude ratio to dB, and the inverse conversions from a dB difference back to a ratio. It deliberately keeps relative dB separate from reference-based units such as dBm, dBW, dBV, and sound pressure level.
How To Use It
- Choose whether you are converting a power ratio, an amplitude ratio, or converting a dB difference back to a ratio.
- For ratio-to-dB modes, enter a positive ratio. A ratio above 1 produces positive dB, 1 produces 0 dB, and a ratio below 1 produces negative dB.
- For dB-to-ratio modes, enter any finite dB value, including negative values for attenuation.
- Use the amplitude form only when the compared voltage/current-like amplitudes share the conditions that make power proportional to amplitude squared, such as equal impedance.
Examples
Ten times the power
A power ratio of 10 corresponds to 10 dB because 10 log₁₀(10) = 10.
Twice the voltage amplitude
With equal impedance, an amplitude ratio of 2 corresponds to about 6.0206 dB because 20 log₁₀(2) ≈ 6.0206.
A -3.0103 dB power change
A power difference of about -3.0103 dB corresponds to a power ratio of 0.5, meaning the second power is half the reference power.
Useful Notes
Power ratio formula
For powers P₂ and P₁ measured in the same unit, dB = 10 log₁₀(P₂/P₁). The ratio must be positive. A ratio of 1 is 0 dB, 10 is 10 dB, 100 is 20 dB, and 0.1 is -10 dB.
Amplitude ratio formula
For compatible amplitudes, dB = 20 log₁₀(A₂/A₁). The factor 20 appears because power is proportional to the square of amplitude under the required matching conditions: 10 log₁₀[(A₂/A₁)²] = 20 log₁₀(A₂/A₁).
Converting dB back to a ratio
Invert the logarithm to recover a linear ratio. Power ratio = 10^(dB/10), while amplitude ratio = 10^(dB/20). Therefore +20 dB means 100× power or 10× compatible amplitude; -20 dB means 0.01× power or 0.1× amplitude.
Gain and attenuation
A positive relative dB value means the numerator is larger than the reference; a negative value means it is smaller. In a signal chain, gains and losses expressed in dB can often be added, while their equivalent linear ratios would be multiplied.
When 20 log is valid
Do not automatically apply 20 log to arbitrary voltage or current readings. The relationship assumes the amplitude ratio maps to a power ratio through consistent conditions, commonly equal impedances. If impedances differ, calculate the relevant powers or use a formula that explicitly includes impedance.
Relative dB versus referenced dB units
Plain dB is dimensionless and expresses a ratio. Units such as dBm, dBW, and dBV define a specific reference level, while acoustic SPL has its own reference convention. This tool calculates relative ratios only and does not convert those absolute referenced units.
FAQ
What ratio equals 0 dB?
A ratio of exactly 1 equals 0 dB. The compared quantities are equal under the selected power or amplitude relationship.
Why are there 10 log and 20 log formulas?
Power ratios use 10 log₁₀ directly. When compatible amplitude is squared to obtain a proportional power quantity, the exponent of 2 turns the coefficient into 20.
Is +3 dB exactly double power?
No. Exactly double power is 10 log₁₀(2), approximately 3.0103 dB. The common +3 dB statement is a useful approximation.
Can dB be negative?
Yes. Negative relative dB means the numerator quantity is below its reference. For example, a power ratio of 0.1 is -10 dB.
Does this calculator convert dBm to watts?
No. dBm is referenced to 1 milliwatt and is an absolute referenced level. This calculator intentionally covers only relative dB ratios.
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