In the literature this somewhat depends on the method you use to measure phytoplankton cell size. If you use conventional particle counter e.g. Coulter Counter or Elzone, the instrument expresses the cell size as "equivalent spherical volume". If you measure the linear dimensions of the cells (e.g., length and width) by microscopy or other means (e.g. imaging device), you can calculate the volume using simple geometry. This works well for cells of simple shapes (e.g. cylindrical and spherical), but more challenging for others (e.g. cells with complex morphology). Cell volume is usually expressed in cubic micrometers.
the question you raised is always actual and of extra interest for hydrobiologists. the father of the approaches - Hans Loman (1908) worked with marine algae.
In my book – From energy budget of small hydrobionts to the flow of energy through hydroecosystem. (can find in RG), Chapter 3 devoted completely for methods of identidication of ind mass/weight of small hydrobionts. But this book is in Russian. Today I'm working on translation into English, so I attach for this case my unpublished English text (draft, but useful) of Chapter 3. Illustrations and formulas you can find in the original book, as well with enough good list of Reference in the problem.
Note, that today nobody is calculating the biomass manually. Exist good PC programm equipment with perfect databases...