Dissociation of pyrophosphoric acid  generates four anions, , where the charge k ranges from 1 to 4. The last one is pyrophosphate . The pyrophosphates are mostly water-soluble.
Likewise, tripolyphosphoric acid  yields at least five anions , where k ranges from 1 to 5, including tripolyphosphate . Tetrapolyphosphoric acid  yields at least six anions, including tetrapolyphosphate , and so on. Note that each extra phosphoric unit adds one extra P atom, three extra O atoms, and either one extra hydrogen atom or an extra negative charge.
Branched polyphosphoric acids give similarly branched polyphosphate anions. The simplest example of this is triphosphono phosphate  and its partially dissociated versions.
The general formula for such (non-cyclic) polyphosphate anions, linear or branched, is , where the charge k may vary from 1 to .  Generally in an aqueous solution, the degree or percentage of dissociation depends on the pH of the solution.