Why you can't just add decibels

Decibels measure sound level on a logarithmic scale, which means you cannot simply add them like ordinary numbers — two sounds of equal loudness do not combine to twice the decibel figure. This adds sound levels correctly, accounting for the logarithmic maths.

The surprising result

Here is the counterintuitive heart of it: combining two sources of equal level adds only about three decibels, not double the number.

This is because the decibel scale is logarithmic, so each step of ten decibels represents a tenfold increase in sound energy, and adding levels means combining the underlying energies and converting back, not adding the decibel numbers.

Why the logarithmic scale exists

Decibels are logarithmic because human hearing spans an enormous range of sound intensities — the loudest sounds we can bear carry trillions of times the energy of the quietest we can detect — and a logarithmic scale compresses that vast range into manageable numbers, while also matching how we perceive loudness, which is itself roughly logarithmic. This is why every ten decibels sounds roughly twice as loud to us, and why the maths of combining sounds is not simple addition. Understanding this matters in acoustics, audio engineering and noise control, where getting the combination of sound sources right — whether adding machines in a room or speakers in a system — depends entirely on treating decibels as the logarithmic quantities they are, not as ordinary numbers that you can simply sum.

Decibel Addition Calculator FAQ

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