Hochster and Huneke defined quasilength for any $I$-torsion modules, generalizing the notion of length to any non-maximal ideal $I$. Based on quasilength, we develop a new numerical invariant for ideals, called "size". It is invariant up to taking radicals and bounded between the arithmetic rank and height of the ideal. We will present some results in low dimensions and discuss a lot of open questions related to "size" and asymptotical behaviors of quasilength. Speaker(s): Zhan Jiang (University of Michigan)