Decibel (dB) Calculator -- Power and Voltage

Power Ratio to dB Converter

Convert between power ratios and decibels. Formula: dB = 10 × log10(P1/P2)

Voltage Ratio to dB Converter

Convert between voltage (or current) ratios and decibels. Formula: dB = 20 × log10(V1/V2)

dBm / Watts Converter

Convert between dBm (power relative to 1 milliwatt) and watts. Common in RF engineering and telecommunications.

dB Addition Calculator

Add or subtract multiple dB values. Adding dB values multiplies their power ratios. This is useful for calculating total system gain or loss.

Common dB Reference Table

Quick reference for common decibel values and their corresponding power and voltage ratios.

Understanding Decibels

What is a Decibel?

A decibel (dB) is a logarithmic unit used to express ratios between two quantities. It was originally developed to measure losses in telephone cables but is now used across many fields including audio engineering, RF communications, acoustics, and electronics.

Why Use Logarithmic Scales?

Logarithmic scales compress very large ranges into manageable numbers. For example, a signal that varies from 1 microwatt to 100 watts represents a ratio of 100,000,000:1. In decibels, this is just 80 dB -- much easier to work with. Additionally, multiplication becomes addition: two 10 dB amplifiers in series give +20 dB total gain.

Power vs. Voltage Formulas

For power ratios: dB = 10 × log10(P1/P2)

For voltage or current ratios: dB = 20 × log10(V1/V2)

The factor of 20 for voltage accounts for the fact that power is proportional to voltage squared (P = V²/R). Both formulas give the same result when comparing equivalent signals.

Absolute vs. Relative dB Units

Plain "dB" is always a ratio -- it compares two values. Absolute measurements use a suffix to indicate the reference:

• dBm: Power relative to 1 milliwatt (0 dBm = 1 mW)
• dBW: Power relative to 1 watt (0 dBW = 1 W = 30 dBm)
• dBu: Voltage relative to 0.775 volts RMS (audio standard)
• dBV: Voltage relative to 1 volt RMS
• dBFS: Digital audio level relative to full scale

Common Applications

Audio Engineering: Decibels measure sound pressure levels, amplifier gains, and signal-to-noise ratios. The "3 dB point" is where power drops to half, commonly used for filter cutoff frequencies.

RF and Telecommunications: dBm is standard for measuring transmitter power, receiver sensitivity, and cable losses. Antenna gains are specified in dBi or dBd.

Acoustics: Sound pressure levels use dB SPL, referenced to 20 micropascals (threshold of human hearing). A whisper is about 30 dB SPL, normal conversation 60 dB SPL, and a rock concert can reach 120 dB SPL.

Key Rules for dB Calculations

• +3 dB = double the power (or 1.41x voltage)
• +6 dB = double the voltage (or 4x power)
• +10 dB = 10x the power (or 3.16x voltage)
• Adding dB values = multiplying power ratios
• Subtracting dB values = dividing power ratios
• Negative dB means a loss or attenuation

Frequently Asked Questions

What is a decibel (dB)?

A decibel (dB) is a logarithmic unit used to express the ratio between two values. For power, dB = 10 × log10(P1/P2). For voltage or current, dB = 20 × log10(V1/V2). Decibels make it easy to work with very large or very small ratios.

What is dBm?

dBm is decibels relative to 1 milliwatt. 0 dBm = 1 mW, 10 dBm = 10 mW, 20 dBm = 100 mW, 30 dBm = 1 W. The formula is dBm = 10 × log10(power_in_mW). dBm is an absolute power measurement, unlike plain dB which is a ratio.

How do I convert dBm to watts?

Watts = 10^(dBm/10) / 1000. For example, 30 dBm = 10^(30/10) / 1000 = 1000/1000 = 1 watt. Or equivalently, mW = 10^(dBm/10), then divide by 1000 for watts.

Why do we use 10 log for power but 20 log for voltage?

Power is proportional to voltage squared (P = V²/R). So when you double the voltage, power quadruples. 20×log10(V1/V2) = 10×log10((V1/V2)²) = 10×log10(P1/P2). The factor of 20 for voltage gives the same dB result as the factor of 10 for power.

What does +3 dB mean?

+3 dB represents a doubling of power. It corresponds to approximately 1.41x voltage (the square root of 2). This is also called the "half-power point" when measured as -3 dB (where power drops to 50%).

Can I add dB values together?

Yes, adding dB values is equivalent to multiplying their power ratios. For example, an amplifier with +20 dB gain followed by another +10 dB amplifier gives +30 dB total gain. This is one of the key advantages of using logarithmic scales.

What is the difference between dBm and dBW?

Both are absolute power measurements. dBm is referenced to 1 milliwatt, while dBW is referenced to 1 watt. To convert: dBW = dBm - 30. For example, 0 dBW = 30 dBm = 1 watt.

Why use dB instead of just power ratios?

Decibels compress huge ranges into manageable numbers, make multiplication into simple addition, and match how humans perceive sound and light (logarithmically). A million-fold power increase is just 60 dB, and cascaded gains/losses are easy to calculate.

Related Tools

• SWR Calculator -- Calculate standing wave ratio and reflection coefficient for RF systems
• Impedance Calculator -- Calculate electrical impedance for AC circuits
• Coax Cable Loss Calculator -- Determine signal attenuation in coaxial cables

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