Decibel Calculator

About the Decibel (dB) and Ratios

The decibel (dB) is a logarithmic unit used to express ratios—for example, how much louder one sound is than another, or how much more power an amplifier delivers. Because human perception and many physical systems respond logarithmically, dB is widely used in audio, acoustics, communications, and signal processing. This calculator converts between dB and linear ratios for both power and amplitude (e.g. voltage or sound pressure).

Power vs. Amplitude

For power ratios (e.g. electrical power, acoustic power), the definition is dB = 10·log₁₀(P₂/P₁). For amplitude ratios (e.g. voltage, current, sound pressure), the definition is dB = 20·log₁₀(A₂/A₁). The factor of 20 comes from the fact that power is proportional to amplitude squared; so 10·log(amplitude²) = 20·log(amplitude). Always choose the mode that matches your quantity: power or amplitude.

How to Use This Calculator

Select Power ratio or Amplitude ratio, then choose dB → Ratio or Ratio → dB. Enter the value you have (dB or ratio); the other is computed. For example, 3 dB (power) corresponds to a ratio of about 2; 6 dB (power) to about 4. For amplitude, 6 dB corresponds to a ratio of 2. Results are for the same reference (e.g. P₁ or A₁); no absolute unit (like watts) is implied.

Common Reference Points

In audio, 0 dB often means “no change” (ratio = 1). +3 dB (power) is roughly a doubling of power; −3 dB is half. +10 dB (power) is a factor of 10; +20 dB (amplitude) is a factor of 10 in amplitude. These relationships help when interpreting levels and gains in sound systems and signal chains.

Where dB Is Used

Decibels are used for sound level (e.g. dB SPL), gain and loss in amplifiers and filters, signal-to-noise ratio, antenna and cable loss, and acoustic and RF measurements. This tool does not compute absolute levels (e.g. dBm or dB SPL); it only converts between dB and a dimensionless ratio. For absolute levels, use the appropriate reference and unit.

How the Conversion Is Computed

For dB → ratio: if the mode is power, ratio = 10^(dB/10); if amplitude, ratio = 10^(dB/20). For ratio → dB: if power, dB = 10·log₁₀(ratio); if amplitude, dB = 20·log₁₀(ratio). The factor of 20 for amplitude comes from power ∝ amplitude², so 10·log(A²) = 20·log(A). The calculator uses base-10 logarithms. Negative dB means the ratio is less than 1 (attenuation); positive dB means gain. This tool works with dimensionless ratios only—it does not compute absolute levels like dBm or dB SPL, which require a reference value.

How to Use This Decibel Calculator

Enter a ratio (power or amplitude, depending on the mode) or a dB value. The Decibel Calculator converts between the two. For power: dB = 10 log10(ratio). For amplitude: dB = 20 log10(ratio). Choose whether you are entering a power ratio or an amplitude (voltage, pressure) ratio so the formula matches. Use it to interpret gain, attenuation, or level differences in audio, RF, or signal processing. A positive dB means the output is larger than the reference; negative dB means smaller.

When Decibels Matter

Decibels compress a wide range of ratios into a manageable scale. In audio, +6 dB (amplitude) is roughly double the level; in RF, dB is used for link budget and cable loss. This calculator is for dimensionless ratios only; for dB SPL, dBm, or dBi, you need the correct reference. For critical design, verify formulas and references in your field.

Limitations

This calculator converts only between dB and a dimensionless ratio. It does not compute absolute sound levels (dB SPL), power levels (dBm, dBW), or antenna gain (dBi). For those, you need the correct reference and formula. Ratio must be positive; zero or negative ratios are invalid. For safety (e.g. hearing protection) or regulatory compliance, use appropriate standards and calibrated measurements. This tool is for informational and educational use only.

Tips for Use

Choose power for electrical power, acoustic power, or intensity ratios; choose amplitude for voltage, current, sound pressure, or field strength. Remember: +3 dB (power) ≈ double power; +6 dB (amplitude) ≈ double amplitude. For cascaded gains, add dB values. For critical audio or RF design, verify formulas and references in your field. Pair with an absolute level calculator if you need dBm, dB SPL, or similar. In audio, doubling the power is +3 dB; doubling the voltage or pressure is +6 dB. In RF, link budget calculations often add or subtract dB for gains and losses. This tool is for informational and educational use only; for safety or compliance, use calibrated equipment and applicable standards.

Disclaimer

This tool is for informational and educational use only. It does not compute absolute physical levels. For safety (e.g. hearing) or compliance, use appropriate standards and measurements.