This article uses Clifford algebra of positive definite signature to derive octonions and the Lie exceptional algebra \(\textrm{G2}\) from calibrations using \(\mathrm{Pin(7)}\) . This is simpler than the usual exterior algebra derivation and uncovers a subalgebra of \(\mathrm{Spin(}7)\) that enables \(\textrm{G2}\) and an invertible element used to classify six new power-associative algebras, which are found to be related to the symmetries of \(\textrm{G2}\) in a way that breaks the symmetry of octonions. The 4-form calibration terms of \(\mathrm{Spin(7)}\) are related to an ideal with three idempotents and provides a direct construction of \(\textrm{G2}\) for each of the 480 representations of the octonions. Clifford algebra thus provides a new construction of \(\textrm{G2}\) without using the Lie bracket. A calibration in 15 dimensions is shown to generate the sedenions and to include one of the power-associative algebras, a result previously found by Cawagas.
