Decibel (dB) Calculator

Perform various decibel calculations for power, amplitude, and combining sources.

Select a calculation type and enter your values to begin. The calculator supports converting ratios to dB, dB to ratios, and combining multiple dB sources.

Practical Examples

See how the Decibel Calculator is used in real-world scenarios.

Amplifier Power Gain

ratioToDb

Calculate the power gain of an amplifier that outputs 20W from a 10W input signal.

Calculation: Ratio to dB

Quantity: Power (e.g., Watts)

Reference: 10

Measured: 20

Voltage Gain

ratioToDb

Calculate the voltage gain in dB for a circuit where input is 5V and output is 10V.

Calculation: Ratio to dB

Quantity: Amplitude (e.g., Volts)

Reference: 5

Measured: 10

Signal Attenuation

dbToRatio

A signal is attenuated by -6 dB. Find the resulting amplitude ratio.

Calculation: dB to Ratio

Quantity: Amplitude (e.g., Volts)

dB Value: -6 dB

Combining Sound Sources

combineDb

Calculate the total sound level when one machine produces 80 dB and another produces 85 dB.

Calculation: Combine dB Values

Values to Combine: 80, 85

Other Titles
Understanding the Decibel (dB): A Comprehensive Guide
Explore the fundamentals, applications, and calculations related to the decibel, a key unit in science and engineering.

1. What is a Decibel (dB)?

  • The Logarithmic Scale
  • Power vs. Amplitude Quantities
  • Common Reference Levels
The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity, often power or intensity. Instead of representing a fixed value, it represents a relationship. The logarithmic scale is convenient for representing very large or very small numbers in a more manageable way, which closely corresponds to how humans perceive stimuli like light and sound.
Power vs. Amplitude Quantities
The dB calculation differs based on whether the quantity is related to 'power' or 'amplitude'. Power quantities (like power, energy, intensity) are proportional to the square of amplitude quantities (like voltage, current, sound pressure). This distinction leads to two main formulas:

Core Formulas:

  • For Power Quantities: dB = 10 * log10(P2 / P1)
  • For Amplitude Quantities: dB = 20 * log10(A2 / A1)

2. Step-by-Step Guide to Using the dB Calculator

  • Converting Ratios to dB
  • Converting dB back to a Ratio
  • Combining Multiple dB Values
Converting a Ratio to Decibels (dB)
1. Select 'Ratio to dB' as the calculation type. 2. Choose whether you are measuring a 'Power' or 'Amplitude' quantity. 3. Enter your 'Reference Value' (the 'before' or denominator value, X1) and your 'Measured Value' (the 'after' or numerator value, X2). 4. Click 'Calculate' to see the result in dB.
Combining Multiple dB Values
1. Select 'Combine dB Values'. 2. In the input field, enter the different dB values you wish to combine, separated by commas (e.g., '60, 65, 62'). This is for combining incoherent sources, such as multiple independent machines running at once. 3. Click 'Calculate' to find the total logarithmic sum.

Example Scenario:

  • If you measure a sound source at 90 dB and a second one at 90 dB, the combined level is not 180 dB. The calculator will correctly show the total is approximately 93 dB.

3. Real-World Applications of Decibels

  • Acoustics and Audio Engineering
  • Electronics and Telecommunications
  • Environmental Science
Acoustics and Audio Engineering
In audio, dBs are indispensable. They are used to measure Sound Pressure Level (SPL), set levels on mixing consoles, and specify the signal-to-noise ratio (SNR) of equipment. For example, a quiet library might be around 40 dB SPL, while a rock concert could exceed 110 dB SPL.
Electronics and Telecommunications
Engineers use dB to quantify the gain of amplifiers, the attenuation of signals in cables, and the strength of radio signals. Reference units like dBm (relative to 1 milliwatt) and dBV (relative to 1 volt) are standard in this field.

Application Example:

  • An antenna with a gain of 3 dB provides double the power compared to an isotropic antenna.

4. Common Misconceptions and Correct Methods

  • Decibels are Not Absolute Units
  • You Cannot Add dB Values Directly
  • A 3 dB Increase Means Double the Power
Myth: You Can Add Decibel Values Like Regular Numbers
A common mistake is to arithmetically add dB values. For instance, two 60 dB sound sources do not create a 120 dB sound level. Because dB is logarithmic, the powers of the sources must be converted from dB, added together, and then converted back to dB. Our calculator's 'Combine dB Values' feature does this correctly, showing that two 60 dB sources result in a 63 dB total.
Fact: A 3 dB Increase is a Big Deal for Power
A +3 dB change corresponds to a doubling of power or intensity. Conversely, a -3 dB change means the power has been halved. For amplitude, the equivalent is ±6 dB for doubling or halving the value.

Quick Reference:

  • +3 dB ≈ 2x Power
  • +10 dB = 10x Power
  • +6 dB ≈ 2x Amplitude
  • +20 dB = 10x Amplitude

5. The Mathematical Formulas Behind Decibels

  • The Core Logarithmic Formulas
  • Formula for Combining Decibels
  • Derivation for dB to Ratio Conversion
Ratio to Decibel Formulas
The conversion from a linear ratio to a logarithmic decibel value is the foundation of all dB calculations. The specific formula depends on the nature of the quantity being measured.
For Power Quantities: dB = 10 ⋅ log₁₀(X₂/X₁)
For Amplitude Quantities: dB = 20 ⋅ log₁₀(X₂/X₁)
Formula for Combining Decibel Values
To combine multiple incoherent sources (L₁, L₂, L₃, ...), you must convert each dB value back to a linear power-like quantity, sum them up, and then convert the total back to dB. The formula is:

Combination Formula

  • L_total = 10 ⋅ log₁₀(10^(L₁/10) + 10^(L₂/10) + ...)