Solutions and methods are disclosed for the extraction and quantification of cellulose derived from cellulosic biomass samples. Improved extraction yields and selectivities are provided through the use of an extraction solvent mixture comprising an aprotic solvent such as DMSO, a quaternary ammonium salt such as TBAF, and an quaternary ammonium base such as TBAOH. The extracted cellulose can be optionally precipitated using disclosed precipitation solutions to further improve cellulose purity. Extracted cellulose can be measured by hydrolyzing the cellulose to glucose or cellobiose, or by using disclosed spectrophotometric assays of cellulose-salt complexes.