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:
 $N=\sum_{k=0}^{n}N_{k}=2^{n}$