Decibel Calculator

Calculate decibel values for power and voltage ratios. Convert between dB, dBm, dBW, and linear units.

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1. Select the calculation mode - power ratio to dB, voltage ratio to dB, or unit conversion (dBm, dBW, dBV). 2. For ratio calculations, enter the two values (input and output power, or input and output voltage). 3. For unit conversions, enter a value in one dB unit and select the target unit to convert to. 4. Use the dB addition tool to correctly combine multiple signal levels (e.g., adding two sound sources). 5. Review the results showing both the logarithmic dB value and the equivalent linear ratio.

About This Tool

Decibels (dB) are a logarithmic unit used throughout engineering, audio, telecommunications, and acoustics to express ratios of power, voltage, or sound intensity. Because the decibel scale is logarithmic, it compresses enormous ranges into manageable numbers - making it much easier to work with signals that span many orders of magnitude.

This calculator handles all common decibel operations. Convert between linear ratios and decibels for both power (10 x log10) and voltage/amplitude (20 x log10) quantities. Add and subtract dB values, convert between absolute reference units like dBm (referenced to 1 milliwatt), dBW (referenced to 1 watt), dBV (referenced to 1 volt), and dBu (referenced to 0.775 volts).

Whether you are designing an audio signal chain and need to calculate gain staging, working with RF link budgets for wireless systems, measuring sound pressure levels for noise compliance, or analyzing any system where signal levels matter, this calculator keeps the math simple and accurate.

Formula / How It Works

dB (power) = 10 x log10(P1/P2) | dB (voltage) = 20 x log10(V1/V2) | dBm = 10 x log10(P / 0.001) | dBW = 10 x log10(P / 1)

Frequently Asked Questions

A decibel is a logarithmic unit that expresses the ratio between two values. For power ratios, dB = 10 x log10(P1/P2). For voltage or amplitude ratios, dB = 20 x log10(V1/V2). The logarithmic scale means that 3 dB represents a doubling of power, 10 dB represents a tenfold increase, and 20 dB represents a hundredfold increase.
Plain dB is a relative ratio with no fixed reference. dBm uses 1 milliwatt as the reference point (0 dBm = 1 mW), making it an absolute power level commonly used in RF and telecommunications. dBW uses 1 watt as the reference (0 dBW = 1 W). To convert: dBW = dBm - 30.
Decibels are used because they compress huge ranges into small numbers (a signal varying from 0.001 to 1000 watts is simply -30 to +30 dBW), they allow multiplication to become addition (cascading gains and losses are simply added), and they align more closely with human perception of sound and light intensity.
Sound pressure levels (dB SPL) give a sense of loudness: 0 dB SPL is the threshold of hearing, 30 dB is a whisper, 60 dB is normal conversation, 85 dB is heavy traffic (hearing damage with prolonged exposure), 100 dB is a motorcycle, 120 dB is a rock concert, and 140 dB is the threshold of pain.
You cannot simply add dB values numerically because they are logarithmic. To add two power levels in dB, convert each to linear power, add the linear values, then convert back to dB. For example, adding two equal 90 dB sources gives approximately 93 dB (not 180 dB). This calculator handles the conversion automatically.

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