Integral geometry on the octonionic plane A basis of the space of Spin(9) invariant translation invariant continuous valuations on the octonionic plane is presented in terms of invariant differential forms. Furthermore the canonical algebra structure on this space is determined in terms of generators andexplicit relations. As a result the Principal kinematic formula on the octonionic plane is computed by means of our basis. A bi product of the notion of octonion valued forms upon which our construction heavily depends is a new simple algebraic formula for the canonical Spin(9) invariant 8 form. Finally motivated by our results we conjecture a version of the Hodge Riemann bilinear relations for smooth translation invariant valuations.