There isn't an exact 'normal' figure for the number of cells in your blood (called your blood count). 'Normal' for a large man wouldn't be the same as for a small woman. But generally the normal white cell count is between about 4,000 and 11,000 cells per cubic millimetre of blood.here isn't an exact 'normal' figure for the number of cells in your blood (called your blood count). 'Normal' for a large man wouldn't be the same as for a small woman. But generally the normal white cell count is between about 4,000 and 11,000 cells per cubic millimetre of blood.