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.

Quick Examples

⚡ Power dB ∿ Voltage dB ⇄ dB to Ratio 📶 dBm / dBW

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

Power: $10^{dB/10}$ | Voltage: $10^{dB/20}$

P Power Value

$P_{dBm} = 10 \times \log_{10}(P_{mW})$ | $dBW = dBm - 30$

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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

Select a mode — Choose Power dB, Voltage dB, dB to Ratio, or dBm/dBW from the mode toggle.
Enter values — Input the required fields (e.g., P1 and P2 for power dB, or a dBm value for conversion).
Calculate — Click the "Calculate dB" button to run the computation.
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

Audio engineering — Sound levels are measured in dB SPL; 0 dB SPL is the threshold of hearing
RF/Telecommunications — Signal strength is expressed in dBm; link budgets are calculated in dB
Amplifier design — Gain specifications use dB for cascaded stage calculations (dB values add)
Fiber optics — Optical loss is measured in dB per kilometer of fiber
Antenna design — Gain is measured in dBi (relative to isotropic) or dBd (relative to dipole)

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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Decibel (dB) Calculator

About Decibel (dB) Calculator

What Is a Decibel?

Power dB vs. Voltage dB

dBm and dBW Reference Levels

How to Use This Calculator

The 3 dB Rule

Practical Applications

FAQ

What is a decibel (dB)?

What is the difference between power dB and voltage dB?

What is dBm and how does it differ from dBW?

What does 3 dB mean?

How do I convert dB back to a linear ratio?

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