We present the G2 Mass Formula: a single algebraic expression that predicts all twelve Standard Model particle masses to within 1.7%, with an average error of 0.58%. The formula is m = v × ^n × ε (op_num/op_den), where v = 246 GeV is the electroweak vacuum expectation value, = 1/42 = 1/(6×7) is ε the structural suppression parameter derived in Paper III (acting as the Froggatt-Nielsen flavourbreaking parameter), n is an integer index encoding the coupling distance from the electroweak scale, and op_num/op_den is a ratio of two operator values established in Paper I. The electroweak VEV is itself recovered from the top-quark relation v = m_top × ALM/N to 0.03%, so the twelve Standard Model mass parameters are reduced to a derived suppression parameter, a set of integer indices, and operator values fixed in Paper I. The operator pairings follow a systematic pattern: single-letter operators appear in numerators, multi-letter operators in denominators. A neutrino mass scale of approximately 50 meV follows from n=7, consistent with the seesaw mechanism. The explicit derivation of the integer indices n from G2 representation theory is identified as the central open problem. All structural integers cited in the body are drawn from the corpus database of Paper I; their sources are tabulated in the Appendix. Keywords: particle masses, G2 algebra, mass formula, Froggatt-Nielsen mechanism, operator ratios, Higgs mechanism, neutrino masses, flavour hierarchy