How To Convert Between Linear & Logarithmic Audio Scales

The following scale below is designed for those using audio systems, where they would like to convert a relative audio voltage back & forth between a linear audio scale in percentages and a logarithmic audio scale in decibels (dB).

It's really a reference guide from whatever volume level you're currently at. For example, if you're recording something and the audio level is peaking at -8 dB on the digital meter (with 0 dB being the full scale clip point), you can look on the conversion chart and see that you can raise the level by 2.5X (250%) before it will start to clip. Likewise if you recorded some narration and kept it well below the clip point to prevent spike overloads, but you found that it still wasn't loud enough, you could do an analysis in an audio program (like Sound Forge) and find that maybe you still had 8 dB of headroom, so you'd know from the conversion scale the factor by which you could still raise the volume (in this case from 100 to 250%).

In the case of this scale, 0 dB doesn't necessarily represent the clipping point of 0dBfs (0 dB full scale) of digital audio, but rather the arbitrary voltage level below clipping that you recorded your audio at, or that you're seeing on the digital meter. Therefore, if the sound program you are using says that you have 3.52 dB headroom before clipping, that means that your volume is 2/3rds (66.7%) of its maximum potential & you'll know that means you cannot raise the volume more than 50% (to 150%) without clipping. Conversely, if you want to lower your volume to half (50%), that would mean a 6.02 dB drop.

Our ears hear in a logarithmic fashion, but we often choose to describe audio in linear terms. Even though the standard method of audio measurement uses logarithmic dBs, which mimic the way our ears & brain work in perceiving audio volume, some computer programmers choose to use percentages for linear audio levels (because it's easier for them & those unfamiliar with the dB scale), hence the need for a conversion scale like this.

This conversion scale is for audio VOLTAGE levels used on "volume meters", not for POWER levels (wattage) used for volume (sound pressure level or acoustic power) used on "loudspeakers" . On a POWER conversion scale, a 200% increase would be a 3 dB increase (not 6 dB).

Conversion Scale of audio voltages from % to dB

By Doug Hembruff.