Electrical conversion

Decibel (dB) conversion

Convert power and amplitude ratios to decibels. Power: dB = 10·log₁₀(P₂/P₁). Amplitude/voltage: dB = 20·log₁₀(V₂/V₁). Runs locally in your browser.

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Result

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Inputs —

Mode —

Formula —

Formulas

Core equations used by this converter.

Power ratioL(dB) = 10 × log₁₀(P₂ / P₁)

iDC and resistive AC use PF = 1. Single-phase: multiply by PF. Three-phase line-to-line: include √3. Prefer RMS voltage and current for AC.

How to use

Decide whether you have a power ratio or an **amplitude*

Decide whether you have a **power** ratio or an **amplitude** ratio.

Divide the two levels (same units).

Take log₁₀ of the ratio.

Multiply by 10 (power) or 20 (amplitude).

Example conversions

Common values with formula and result.

Power doubles

10 × log₁₀(2) ≈ 3.01 dB ≈ +3 dB

Power ×10

10 × log₁₀(10) = 10 dB

10 dB

Voltage doubles (same Z)

20 × log₁₀(2) ≈ 6.02 dB ≈ +6 dB

Half power (−3 dB)

10 × log₁₀(0.5) ≈ −3.01 dB

Decibel (dB) conversion specification

Version 1.1.0 · Engine tested

Calculation status

Engine tested 4 published cases
Named expert review Not performed
Calculation version 1.1.0

Review policy

Definition: The **decibel** is a logarithmic unit for **ratios** — not an absolute SI base unit like the volt or watt. In electrical and audio work it commonly expresses power or voltage (amplitude) ratios: ``` 1 bel = 10 decibels
What it calculates: Convert power and amplitude ratios to decibels. Power: dB = 10·log₁₀(P₂/P₁). Amplitude/voltage: dB = 20·log₁₀(V₂/V₁). Steps, examples, and FAQ.
Inputs: Values required by the selected conversion mode
Outputs: Converted result in the target unit or format
Formula: L(dB) = 10 × log₁₀(P₂ / P₁)
db converter chart: Ratio Power dB Voltage dB
×0.5 ≈ −3 dB ≈ −6 dB
×1 0 dB 0 dB
×2 ≈ +3 dB ≈ +6 dB
×10 +10 dB +20 dB
×100 +20 dB +40 dB
Assumptions: Conversion runs locally in the browser; values are not uploaded.
Uses the formulas documented on this page.
Units: Amps × Volts
Boundary conditions: Empty or invalid input yields no valid result.
Out-of-range values may be rejected by the tool runtime.
Example: Power doubles → 10 × log₁₀(2) ≈ 3.01 dB ≈ +3 dB
Validation cases: Power doubles → 10 × log₁₀(2) ≈ 3.01 dB ≈ +3 dB
Power ×10 → 10 dB
Voltage doubles (same Z) → 20 × log₁₀(2) ≈ 6.02 dB ≈ +6 dB
Half power (−3 dB) → 10 × log₁₀(0.5) ≈ −3.01 dB
Sources: CalculatorX converter runtime
Standard unit / encoding definitions where applicable
Calculation version: 1.1.0

Ratio	Power dB	Voltage dB
×0.5	≈ −3 dB	≈ −6 dB
×1	0 dB	0 dB
×2	≈ +3 dB	≈ +6 dB
×10	+10 dB	+20 dB
×100	+20 dB	+40 dB

Background

Interpretation and common distinctions.

Use the converter tabs to switch direction when available. Results for Decibel (dB) conversion update locally in your browser.

Frequently asked questions

Key distinctions behind the conversion.

How do you convert using Decibel (dB) conversion?

Use W = A × V. Example: Power doubles → 10 × log₁₀(2) ≈ 3.01 dB ≈ +3 dB.

Can I switch direction?

Open the related reverse converter listed under Related tools.

Does this run online or locally?

Calculation runs locally in your browser. Values are not uploaded.

How precise are the results?

Results follow the formulas on this page. Round to the precision your use case needs.