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Decibel (dB) Calculator

Calculate power and voltage gain or loss in decibels, convert between dB and linear scale, and analyze signal levels with dBm and dBW conversions.

Decibel (dB) Calculator
Quick Examples
P1 Input Power
P2 Output Power
\(dB = 10 \times \log_{10}(P_2 / P_1)\)
V1 Input Voltage
V2 Output Voltage
\(dB = 20 \times \log_{10}(V_2 / V_1)\)
dB Decibel Value
dB
Power: \(10^{dB/10}\)  |  Voltage: \(10^{dB/20}\)
P Power Value
\(P_{dBm} = 10 \times \log_{10}(P_{mW})\)  |  \(dBW = dBm - 30\)

Embed Decibel (dB) Calculator Widget

About Decibel (dB) Calculator

The Decibel (dB) Calculator converts between decibels and linear ratios for both power and voltage signals. It supports four calculation modes: power dB, voltage dB, dB to ratio conversion, and dBm/dBW power level conversion. Each calculation includes step-by-step MathJax formulas and a common reference table for quick lookup.

What Is a Decibel?

A decibel (dB) is a logarithmic unit that expresses the ratio of two values on a base-10 scale. Originally developed for telephone engineering by Bell Labs, it compresses enormous dynamic ranges into manageable numbers. For example, a ratio of 1,000,000:1 is just 60 dB.

$$\text{dB} = 10 \times \log_{10}\left(\frac{P_2}{P_1}\right) \quad \text{(power)}$$
$$\text{dB} = 20 \times \log_{10}\left(\frac{V_2}{V_1}\right) \quad \text{(voltage/amplitude)}$$

The factor of 20 for voltage arises because power is proportional to the square of voltage (\(P \propto V^2\)). Applying the log rule: \(10 \times \log_{10}(V^2) = 20 \times \log_{10}(V)\).

Power dB vs. Voltage dB

When comparing power levels (watts, milliwatts), use the 10× factor. When comparing voltage or amplitude levels (volts, sound pressure), use the 20× factor. The result in dB is the same for equivalent systems — a system with 2× voltage gain has 4× power gain, both equaling 6 dB.

dBm and dBW Reference Levels

dBm (decibels relative to 1 milliwatt) and dBW (decibels relative to 1 watt) are absolute power measurements rather than ratios. They provide a standardized way to express signal power levels in telecommunications, RF engineering, and audio systems.

$$P_{dBm} = 10 \times \log_{10}\left(\frac{P_{mW}}{1\text{ mW}}\right) \qquad P_{dBW} = P_{dBm} - 30$$

How to Use This Calculator

  1. Select a mode — Choose Power dB, Voltage dB, dB to Ratio, or dBm/dBW from the mode toggle.
  2. Enter values — Input the required fields (e.g., P1 and P2 for power dB, or a dBm value for conversion).
  3. Calculate — Click the "Calculate dB" button to run the computation.
  4. Review results — See the dB value, gain/loss indicator, equivalent ratios, common reference table, and step-by-step derivation.

The 3 dB Rule

One of the most fundamental concepts in electronics: 3 dB equals a doubling (or halving) of power. This comes from \(10 \times \log_{10}(2) \approx 3.01\). For voltage, 3 dB corresponds to a factor of \(\sqrt{2} \approx 1.414\). The −3 dB point is used to define filter cutoff frequencies, amplifier bandwidth, and half-power beamwidths in antenna design.

Practical Applications

FAQ

What is a decibel (dB)?

A decibel is a logarithmic unit used to express the ratio between two values, commonly power or voltage. Because it uses a logarithmic scale, decibels can represent very large or very small ratios with manageable numbers. For example, a 1,000,000:1 power ratio is simply 60 dB.

What is the difference between power dB and voltage dB?

Power dB uses the formula dB = 10 × log10(P2/P1), while voltage dB uses dB = 20 × log10(V2/V1). The factor of 20 for voltage accounts for the squared relationship between power and voltage (P ∝ V²). Both yield the same dB result for equivalent systems.

What is dBm and how does it differ from dBW?

dBm is decibels relative to 1 milliwatt, and dBW is decibels relative to 1 watt. Since 1 watt = 1000 milliwatts, dBW = dBm − 30. For example, 0 dBm = 1 mW = −30 dBW, and 30 dBm = 1 W = 0 dBW.

What does 3 dB mean?

A 3 dB increase represents approximately doubling the power (ratio of about 2). A 3 dB decrease means halving the power. This is known as the "3 dB rule" and is one of the most important reference points in electronics. For voltage, 3 dB corresponds to a factor of about 1.414.

How do I convert dB back to a linear ratio?

For power ratio: ratio = 10(dB/10). For voltage ratio: ratio = 10(dB/20). For example, 20 dB = 100× power ratio or 10× voltage ratio.

Reference this content, page, or tool as:

"Decibel (dB) Calculator" at https://MiniWebtool.com/decibel-db-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Mar 18, 2026

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