The Peak is not the same as the Maximum Sound Level. The Peak, referred to as the Lpeak or sometimes Lpk, is the maximum value reached by the sound pressure. There is no time-constant applied and the signal has not passed through an RMS circuit or calculator. This is the true Peak of the sound pressure wave.
For a pure tone, the Peak will be 3 dB above the Maximum Sound Level. For varying signals there can be a huge difference and there is no way to calculate the Peak from the Max or any other measurement.
Unlike the Sound Level and the Leq, the Peak measurement is usually C-Weighted rather than A-Weighted. Some older meters used Linear, but C-weighting has replaced that in most standards, including the European Noise at Work regulations. The C-weighted Peak measurement is usually expressed as LCpeak in dB(C).
The LCpeak is used for occupational noise measurement where loud bangs are present. The Peak is not usually used for environmental noise measurement and is useless when any wind is present. A gust of wind will easily give very high LCPeak readings