A blade is a term often used to describe a basis entity in the space defined by a geometric algebra. Since a geometric algebra is a multi-graded space, the basis entities also have multiple grades. To distinguish the various graded entities, the blades are often prefixed by their grade. For example a grade-$k$ basis entity would be called a $k$ blade.

The number of linearly independent $k$ blades in a particular geometric algebra is dependent on the number of dimensions of the manifold on which the algebra is defined. For an $n$ dimensional manifold, the number of $k$ blades is given by the binomial coefficient. $$ N_k = \left( \begin{array}{c} n \\ k \end{array} \right) $$ The total number of basis blades of all grades in a geometric algebra defined on an $n$ manifold is then: $$ N = \sum_{k=0}^n N_k = 2^n $$