Let \(X\) be a smooth complete variety. The Segre number of \(X\) is defined as \(s_X= {\mathrm{deg}}\,c_{\mathrm{dim}X}(-T_X),\) where \(c_{\mathrm{dim}X}\) is the highest Chern class and \(T_X\) denotes the tangent bundle. The index \(n_X\) is the g.c.d. of the degrees of the closed points of \(X.\) The degree formula is the following relation in \({\mathbb Z}/2:\) \[ \frac{n_Y}{n_X}\cdot \frac{s_Y}{n_Y}={\deg}f \cdot \frac{s_X}{n_X} \,\, \mod 2, \] where \(f: Y\rightarrow X\) is a rational of smooth complete connected varieties and \(\deg f\) is defined to be zero when \(f\) is not dominant and the degree of the function field extension otherwise. One can prove the degree formula in various ways [A. Merkurjev, J. Reine Angew. Math. 565, 13–26 (2003; Zbl 1091.14006)], [M. Levine and F. Morel, Algebraic cobordism. Berlin: Springer (2007; Zbl 1188.14015)]. The author studies varieties with involution. He associates to each \(G\)-variety a cycle class \(\mathcal{S}_Y\) in the Chow group of its fixed locus. This class mod \(2\) is functorial and if one specializes to \(X\times X\) and the action of \(G\) by exchange, the class \(\mathcal{S}_{X\times X}\) can be identified with the total Segre class \(\mathrm{Sq}(X)\in \mathrm{CH}(X)\) of the tangent cone of \(X.\) The degree formula is then nothing other but functoriality of \(s_X\) of the component of degree zero of \(\mathrm{Sq}(X)\). It is worth noting that the proof given by the author works in arbitrary characteristic. Moreover the class \(\mathrm{Sq}(X)\) is expected to be the total homological Steenrod square of the fundamental class of \(X\).