dBFS / Audio Level Calculator mechanism

Model scope

The two logarithmic formulas are algebraically correct under their respective amplitude and power assumptions. Final implementation and labeling require an explicit dBFS reference convention, peak-versus-RMS behavior, headroom sign convention, over-full-scale policy, and zero/invalid-input behavior.

• The amplitude formula dB=20log10(A1/A2) and power formula dB=10log10(P1/P2) are standard, but the specification does not define whether dBFS uses peak amplitude, RMS amplitude, voltage, or power normalization.
• The meaning of headroom is not defined. A standard convention is headroom_dB=0-dBFS, which is positive below full scale and negative above full scale.
• The statement that full-scale equals 1.0 is ambiguous for power: it must specify whether full-scale power is normalized to 1.0 and whether the reported power dBFS is intended to be comparable to amplitude dBFS.
• The specification does not state whether values above full scale are allowed, rejected, or reported as positive dBFS/negative headroom.
• The empty honest_label field omits important labeling such as peak versus RMS dBFS and the treatment of inter-sample peaks.

Units and conventions

• A1 and A2 are quantities of the same amplitude type and unit, such as two voltage values in volts or two normalized linear amplitudes; their ratio is dimensionless.
• P1 and P2 are quantities of the same power unit; their ratio is dimensionless.
• For normalized dBFS, full-scale amplitude is assumed to be 1.0 and the input amplitude is normalized to that same full-scale reference.
• For power dBFS test cases, full-scale power is assumed to be 1.0 in normalized units.
• Headroom is assumed to mean 0 dBFS minus the computed dBFS level.
• log10 requires a strictly positive ratio; zero amplitude or power produces negative infinity and negative inputs are invalid unless magnitude handling is explicitly specified.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "reference_type": "amplitude",
    "amplitude": 0.5,
    "full_scale_amplitude": 1
  },
  "expected_outputs": {
    "dBFS": -6.020599913,
    "linear_ratio": 0.5,
    "headroom_dB": 6.020599913
  },
  "working": "A1/A2=0.5/1.0=0.5. log10(0.5)=-0.3010299957. dBFS=20*(-0.3010299957)=-6.020599914 dBFS. Headroom=0-(-6.020599914)=6.020599914 dB."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero reference value produces a division-by-zero before the logarithm, so the instrument must reject the input or explicitly return an undefined result. Exact zero signal amplitude also reaches the logarithm boundary and must be represented as -Infinity rather than a finite dB value.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json