Understanding and Measuring Loudness

This guide explains:

How products report how loud they are
How to measure how loud a sound is
How to play a sound at a specific loudness

The core ideas are kept accessible, but we also dive into technical details — including units, equations, and assumptions — for those who want a deeper understanding.

1. Product Loudness Ratings

Sound Power Level (SWL)

Products often report loudness using the Sound Power Level (SWL), usually in units of dB(A)^[1]. This measures the total sound energy emitted by the device, independent of distance or environment.

This differs from Sound Pressure Level (SPL)^[2], which varies depending on your distance from the source, reflections, and other room characteristics.

The “A” in dB(A) refers to A-weighting, a filter that mimics the human ear's sensitivity to different frequencies. It emphasizes mid frequencies and de-emphasizes very low or high frequencies to reflect how we perceive loudness.

2. Understanding Decibels

What is a Decibel?

A decibel (dB) is a logarithmic unit that expresses the ratio between two values. For power:

L = 10 × log₁₀(X / X₀)

For pressure-based sound levels like SPL:

L_p = 20 × log₁₀(p / p₀)

Where p is the measured sound pressure in pascals, and p₀ = 20 µPa is the reference pressure — the threshold of human hearing^[3].

Useful Rules of Thumb

+6 dB ≈ double the amplitude
+10 dB ≈ double the perceived loudness
+1 dB ≈ ~12% increase in amplitude

3. How to Measure Loudness in Practice

Digital Measurements: dBFS

In digital audio, measurements are often made using dBFS (decibels relative to full scale).

0 dBFS is the maximum possible digital level.
All real-world signals are negative (e.g. –20 dBFS).

This scale is unitless and does not correspond directly to real-world loudness.

Can You Convert dBFS to dB(A)?

Not directly — because dBFS depends on your digital system, while dB(A) is a physical loudness measure. The conversion depends on your device’s microphone, amplifier, and ADC characteristics.

How to Convert dBFS to dB(A) with Calibration

We use this formula:

dB(A) ≈ dBFS + offset

The offset is determined through calibration — comparing a known dB(A) reference to the digital reading.

Calibration Example:

You play a 70 dB(A) tone
Your system records –20 dBFS
So, offset = 70 - (-20) = 90

Future dB(A) estimates are made by adding this offset to any dBFS reading from the same setup.

Steps to Estimate dB(A) from Audio

Capture the raw digital signal
Apply an A-weighting filter
Smooth the data (e.g. RMS over 125 ms)
Convert to dBFS
Add your calibration offset

4. Assumptions & Limitations

Assumes consistent background noise level
Offset is constant across volume and frequency range
Requires no distortion or clipping in the signal

Under good conditions, accuracy is often within ±1–2 dB.

5. How This Site Handles Calibration

We use two methods:

Reference device calibration: Comparing your device to similar devices with known calibration in lab settings.
Assumed background noise: If calibration data is missing, we assume a typical indoor noise level (30–40 dB(A)) to estimate the offset.