Converting Amplitude Representations

This is a tutorial on how to convert between different amplitude scales.

Convert dBFS to a percentage

Use the following formula (where x is dBFS):

10^(x/20)

For example:

10^(-6dBFS/20) = 0.5

This shows that -6dBFS is 0.5, or 50% of the maximum level of a digital system.

Convert a percentage to dBFS

Use the following (where x is a percentage written as a decimal):

20 * log₁₀(x)

For example:

20 * log₁₀(0.5) = -6dBFS

This illustrates that 0.5 equates with -6dBFS.

Note:

• 1 is 0dBFS, or 100% of the maximum level of a digital system, and 0 corresponds with -∞dBFS.
• If a signal level exceeds 1 (i.e., 0dBFS) the result is distortion of the signal (i.e., it is clipped at the maximum amplitude).
• The image above is one period of a 1Hz sine wave at 0dBFS, -6dBFS, and +6dbFS (or 1, 0.5, and 2).