Decibel (dB) Calculator

About the Decibel (dB) Calculator

The decibel is a logarithmic unit comparing a power or intensity to a reference. For sound intensity, the level in decibels is ten times the base-10 logarithm of the intensity ratio.

Enter the measured intensity and the reference intensity (the threshold of hearing I₀ = 1×10⁻¹² W/m² is the usual default). The level is returned in decibels (dB).

How to use this calculator

1. Enter the sound intensity value \(I\).
2. Enter the reference intensity \(I_0\).
3. Make sure both values use the same units.
4. Compute \(L = 10 \log_{10}\!\left(\frac{I}{I_0}\right)\).

The formula explained

The formula computes sound intensity level \(L\) in decibels by comparing an intensity \(I\) to a reference intensity \(I_0\). A ratio of \(10\) becomes \(10\) dB, and a ratio of \(100\) becomes \(20\) dB because of the base-10 logarithm.

• L = sound intensity level in decibels, \(\text{dB}\)
• I = sound intensity or power being measured
• \(I_0\) = reference intensity used for comparison

Step by step method

1. Find the ratio \(\frac{I}{I_0}\).
2. Take \(\log_{10}\) of that ratio.
3. Multiply the result by \(10\) to get \(L\) in decibels.

Worked example

Problem. A sound has intensity \(I = 2.5 \times 10^{-6}\) and the reference intensity is \(I_0 = 1.0 \times 10^{-12}\). Find the decibel level.

1. Compute the ratio, \(\frac{I}{I_0} = \frac{2.5 \times 10^{-6}}{1.0 \times 10^{-12}} = 2.5 \times 10^{6}\).
2. Take the base-10 logarithm, \(\log_{10}(2.5 \times 10^{6}) \approx 6.398\).
3. Multiply by \(10\), so \(L \approx 63.98\,\text{dB}\).

Tips and common mistakes

• Use the same units for \(I\) and \(I_0\), because the ratio only works correctly then.
• If \(I = I_0\), the level is \(0\,\text{dB}\), and if the ratio is less than \(1\), the result is negative.

Frequently asked questions