Decibels as Percentages

The Basics

Manufacturer data sheets can sometimes express improvements in decibels as percentages. This can lead to the belief that something is better than it really is by the uninformed reader.

This article will try to help clarify some confusion that can arise from expressing decibels as percentages.

Lets start at the very beginning, as simply as possible. Decibel values, with respect to acoustics, will usually relate to either Sound Power Level (L_w), or Sound Pressure Level (L_p).

A product, system or data sheet may refer to an acoustic performance as providing, for example, a 50% reduction in noise.

The data sheet for a noisy machine, perhaps a jack-hammer, may state that it produces L_w 100dB.

Or it may, on the other hand, state that it produces an L_p of 90dB at 1m, or even at 3m.

What does this actually mean in a real world experience ?

History of the Decibel

The unit was originally invented by Bell Telephone Labs as the Bel and given its name after Alexander Graham Bell credited as the inventor of the telephone. The decibel is 1/10th of a Bel. The Bel was defined as a ratio of power levels of 10:1. (Ten times the power or one tenth the power).

In telephone systems, the amplifiers are driving speakers often over very long cable or ‘lines’. To drive the speakers there needs to be a power transfer. The business of driving speakers requires analysis of how much power is available and how much power is lost in getting the original signal down the cable to the speaker at the other end.

More power means more volume can be achieved at the receiving end. However, these two factors don’t directly relate.

Volume is related to the amount of Sound Pressure available as the human ear is a pressure sensitive organ. However, power in an electrical system is not just the pressure but also the flow rate.

With electricity the pressure is the voltage and the amount of flow is the current. For example, if you push twice as much voltage into a light bulb there would be twice as much current. Therefore, because both the voltage and current are doubled the power will be multiplied by a factor of four.

In order to double the sound pressure wave out of a speaker we need four times the amplifier power to drive it.

Adding decibels represents a multiplication of levels as they are logarithmic. 10dB + 10dB = 13dB and not 20dB.

The Human Ear

The ear is a pressure sensitive organ and many studies have been done regarding how changes in perceived volume (or loudness) relate to changes in dB. The problem encountered with these studies was that it is a subjective experience so the opinions of many listeners were taken into account, and averaged, to produce usable data. The studies demonstrated that perceived loudness from one person to the next can vary up to 30% depending on the initial volume, the frequency or the complexity of the sound being listened to.

During these studies it was also discovered that many listeners could detect a certain amount of dB increase much easier than they could detect the same amount of dB decrease. An interesting phenomenon.

That said, to date, the generalisation is that a 10dB change in level is twice (or half) the perceived volume. Furthermore, as mentioned below, 6dB is a doubling or halving of sound pressure and often, when listening to full range music, this is found to be the case instead of 10dB.

0dB does not actually mean there is no sound at all. It simply defines the faintest sound an average, young, healthy, sensitive human ear can detect. It is the base reference that other decibels are related to. In acoustic terms decibels are the ratio of a measured sound pressure level with respect to this baseline.

One may wonder why we don’t just use Pascals (Pa) as this is a simple measurement of scientific pressure. This is because the human ear does not react to sound in a linear fashion (like Pascals). It responds to intensity in a logarithmic manner.

Sound Power Level vs Sound Pressure Level

Sound Power (L_w) is always a larger figure than Sound Pressure (L_p).

Doubling or halving of sound power equates to a difference of ±3dB.

Doubling or halving of sound pressure equates to a difference of ±6dB.

Decibels as Percentages

The decibel scale is logarithmic. It is exponential. It is not a linear scale like percentages are.

To be able to work out a percentage we need to know the maximum value and the given value within that maximum. It is possible to convert a decibel to a decimal number with respect to the aforementioned 0dB reference value but 100% would equate to an infinite number of decibels.

For example, in the table below you can see just how crazy things can get:

% loss	Lw dB	Lp dB
99.9999	-60	-120
99.999	-50	-100
99.99	-40	-80
99.9	-30	-60
99	-20	-40
90	-10	-20
80	-7	-14
70	-5	-10
60	-4	-8
50	-3	-6
25	-1.25	-2.5
12	-0.56	-1.11

A 50% reduction could be equated to a Sound Power reduction of 3dB, or a Sound Pressure reduction of 6dB or a subjective loudness reduction of 10dB but we can never get to 100%.

A certain percentage change in sound pressure level will always be the same amount of change in decibels.

Pretty confusing stuff, hence why expressing decibels as percentages, other than 50%, doesn’t really make any usable sense. Anything less than 25% is negligible. Anything more than 50%….well you can see what happens.

Footnote

It is also worth noting that the human ear is more sensitive to higher frequency sound over lower frequency sound.

At 1kHz going from 40dB to 50dB may be perceived as being twice as loud as, but at a lower frequency of say 50Hz we have to increase the same level to around 65dB for the sound to appear twice as loud to the average ear. This phenomena is covered by our blog on equal loudness contours and Phons.