Cosine similarity measures the angular closeness of two vectors irrespective of their magnitudes. For document vectors $\vec{u}$ and $\vec{v}$ it is defined as $\cos(\vec{u},\vec{v})=\dfrac{\vec{u}\cdot\vec{v}}{\|\vec{u}\|_2\,\|\vec{v}\|_2}=\sum_t \dfrac{u_t}{\|\vec{u}\|_2}\,\dfrac{v_t}{\|\vec{v}\|_2}$. The value lies in $[0,1]$ for non-negative term-weight vectors, with $1$ when the two documents have identical term-weight distributions (up to scale) and $0$ when they share no terms. Length normalization makes the score insensitive to absolute document length, so a short and a long document with the same relative term emphasis are scored as highly similar.