Sound levels expressed in decibels describe ratios of intensity using a logarithmic scale. When two sources are combined, you cannot simply add their decibel values. Instead, you must convert each level back to linear intensity, add those intensities together, and then convert the sum back to decibels. This calculator performs that sequence for up to five independent sound sources.
The intensity associated with a decibel level is 0, where 0 is the reference intensity, typically 1 × 10−12 W/m². After summing the individual intensities, the combined level is \text{total}
Imagine two identical machines each producing 70 dB at a certain location. If you run both simultaneously, the resulting level is not 140 dB. Instead, converting each 70 dB to intensity gives about 1 × 10−5 W/m². Adding them yields 2 × 10−5 W/m². Converting back, the level becomes approximately 73 dB. Thus doubling the number of identical sources raises the sound level by only about 3 dB.
Engineers designing factories and concert venues often need to estimate overall noise from multiple machines or instruments operating at once. Summing sound levels helps determine whether ear protection or acoustic treatment is required. In environmental studies, regulators evaluate how highway traffic combines with industrial sources to affect nearby residents. The principles of addition also apply in audio production when layering tracks and balancing their perceived loudness.
Our ears respond roughly logarithmically to sound intensity, which is why the decibel scale aligns better with perception than a simple watt-per-square-meter measurement. A 10 dB increase is typically perceived as about twice as loud, though this varies with frequency and individual sensitivity. Summing levels accurately ensures you don't underestimate the impact of multiple moderate noises, which together could become harmful over long exposure times.
This tool accepts up to five decibel levels. Leave unused fields blank. When you click the button, the script converts each provided level to intensity, sums them, and displays the total in decibels. Because everything runs locally, you can experiment freely—try adding a loud outdoor event to the background noise of an office, or combine several small appliances to gauge overall impact in a kitchen.
As a reference, here is a table showing how doubling identical sources changes the combined level:
| Number of Sources | Combined Level |
|---|---|
| 1 | L |
| 2 | L + 3 dB |
| 4 | L + 6 dB |
| 8 | L + 9 dB |
This calculator assumes the sound sources are incoherent and uncorrelated. If they are phase-aligned or deliberately combined, as with certain speaker arrays, the increase can be greater. Additionally, reflections and room acoustics may raise or lower the measured level relative to the ideal case. Nevertheless, summing intensities provides a reasonable approximation for many real-world scenarios.
When levels differ significantly, the loudest source dominates the sum. For instance, adding 40 dB to 70 dB changes the result by less than 0.5 dB. This rule of thumb helps prioritize mitigation efforts on the noisiest equipment. Conversely, similar levels require more detailed calculations, which the tool handles automatically.
The decibel originates from early telephone engineering as a convenient way to express ratios of power. It evolved from the bel, named after Alexander Graham Bell. Today, decibels appear in audio equipment specifications, acoustic regulations, and even radio communications. Understanding how to combine levels correctly ensures these specifications yield accurate expectations in practice.
The Sound Level Addition Calculator illustrates why decibels behave differently from ordinary numbers. By converting between logarithmic and linear units, you obtain an accurate total level that reflects true sound energy. Use this tool to predict noise levels in workplaces, plan safe listening environments, or balance audio sources in a recording. Because it functions entirely in your browser, no data is stored or transmitted, allowing you to experiment with various scenarios to better appreciate how multiple sound sources interact.
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