Convert between linear ratios and decibels. Essential for audio, power, and signal processing applications.
2026-03-28T00:00:00Z
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The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity, most commonly used for power and amplitude of sound. The logarithmic scale allows us to represent very large and very small ratios in a compact form. A 10 dB increase represents a 10x increase in power (or 3.16x increase in voltage/amplitude). The decibel scale is widely used in audio engineering, telecommunications, acoustics, and electronics because it closely matches how humans perceive changes in sound intensity and signal strength.
There are two common formulas for calculating decibels: for power ratios, we use dB = 10 log₁₀(P₂/P₁), and for voltage/amplitude ratios, we use dB = 20 log₁₀(V₂/V₁). The factor of 2 difference arises because power is proportional to the square of voltage. Understanding the relationship between linear ratios and decibels is essential for working with amplifiers, audio systems, signal processing, and telecommunications equipment. The decibel scale makes it much easier to work with exponential relationships and to visualize system behavior graphically.
Select "Power" for power ratios or "Voltage" for amplitude/voltage ratios. Power uses 10 log₁₀ while voltage uses 20 log₁₀ due to the power-voltage relationship.
Input the reference value (baseline or original measurement). This is the denominator in the ratio calculation and establishes your reference point for comparison.
Input the measured or compared value. This is the numerator in the ratio. It represents the value you want to compare against the reference.
The calculator displays the result in dB, linear ratio, and interpretation (gain or loss). Positive dB indicates an increase; negative dB indicates a decrease.
For common scenarios, use the quick-select buttons to instantly load standard ratios. This helps you understand typical dB values encountered in real applications.
An audio amplifier receives a 0.5 V input signal and outputs a 5 V signal. Calculate the voltage gain in dB.
The logarithmic scale compresses large ranges into manageable numbers. For example, power ranging from 1 mW to 1 kW (1,000,000x) becomes just 60 dB, making it easier to work with and visualize on graphs.
Power ratios use 10 log because power is directly proportional to the ratio. Voltage/amplitude ratios use 20 log because power is proportional to voltage squared. This compensates for the squared relationship.
0 dB means the two values are equal (ratio = 1). It represents no change or gain/loss. This is the reference point on the decibel scale.
For power: Ratio = 10^(dB/10). For voltage: Ratio = 10^(dB/20). This reverses the logarithmic conversion and gives you the linear multiplication factor.
Yes, negative dB indicates a decrease. For example, -3 dB represents approximately half the power (or 0.707x the voltage), which is very common in audio and signal processing.
Audio measurements often range from -120 dB (very quiet, near silence) to 0 dB (reference level) to +20 dB (loud). The human ear perceives a 3 dB change as a noticeable difference in loudness.
3 dB is approximately equal to doubling in power (2x). Since 10 log₁₀(2) = 3.01 dB, engineers often use 3 dB as a quick mental reference for "double the power."
The -3 dB point (half-power) is fundamental in filter design and frequency response analysis. It marks where power drops to 50% of the peak value, crucial for defining bandwidth and cutoff frequencies.
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