Decibel Calculator

This calculator converts a ratio of two values into decibels, handling both power ratios and amplitude, or field, ratios. The decibel is a logarithmic unit used to express how much larger or smaller one quantity is than another, and it appears throughout sound, electronics, optics and communications. Its logarithmic nature is what makes it so useful: human senses, especially hearing, respond roughly logarithmically, and quantities in engineering can span an enormous range, so compressing them onto a decibel scale keeps the numbers manageable. A key subtlety trips many people up: there are two decibel formulas. For power-like quantities, such as acoustic or electrical power and intensity, the decibel value is ten times the base-ten logarithm of the ratio. For amplitude-like quantities, such as voltage, current or sound pressure, it is twenty times the logarithm, because power is proportional to amplitude squared. This calculator lets you choose the right one. You enter the measured value and the reference value it is compared against, pick power or amplitude mode, and it returns the result in decibels, positive for a gain and negative for a loss. It also shows the underlying ratio. The results update as you type, so you can build a feel for the scale: a power ratio of ten is ten decibels, a hundred is twenty, and a thousand is thirty. Use it for audio and acoustics, for signal gain and attenuation in electronics, or for any logarithmic comparison. Remember that a decibel is always relative to a reference, so the reference you choose defines what the figure means. The calculation is rounded for display.

Power ratios use 10 log10; amplitude/voltage ratios use 20 log10. Positive is a gain, negative a loss. The reference defines the meaning. Rounded for display.