I re-researched this every fall when it came time to backsweeten the previous year’s cider, so I wrote this guide to future me.
If you add sugar to hard cider and don’t want that addition to restart fermentation (which would increase alcohol and leave the cider even drier), you’ll need to stabilize it. The most common method in home cidermaking is to add both potassium sorbate and potassium metabisulfite (“K-Meta”). This guidance from BYO magazine on backsweetening provides background on the approach.
Tl;dr
For each gallon of cider, use 1/2 tsp of potassium sorbate and 1/2 tsp of 10% sulfite solution (an extra step, but worth making – the solution is easier to work with than dry potassium metabisulfite).
Longer version
How much potassium sorbate?
Winemakers say…
Winemakers talk more about sorbic acid, the relevant chemical; potassium sorbate is 74% sorbic acid. There are legal limits of 0.2 g/L (Europe) and 0.3 g/L (America); the sensory level for perceiving this chemical’s flavor is reported at 0.135 g/L.
Adjusting these from sorbic acid -> potassium sorbate (what a homebrewer weighs) gives legal limits of 0.26 g/L and 0.4 g/L, respectively, with a taste threshold of 0.18 g/L.