The following calculator can be used to assess the level of carbonation resulting from adding a given amount of sugar for refermentation. Also, it shows how changes of temperature influence the saturation level and internal pressure.
As it does matter for the results, it can be selected whether the cider is initially saturated with CO2 as a result of storing/aging under an airlock until the moment it is poured into the bottle/keg, or not – e.g. all CO2 has been “lost” due to pasteurisation. The initial temperature and atmospheric pressure are there to estimate the amount of CO2 is initially present in the liquid.
It can also be selected whther the empty volume is filled with air or pure CO2, e.g. when the refermentation is done in a keg.
When refermenting in a keg, one need to apply some slight pressure to seal the lid – this can also be input to the calculations as the bigger the pressure, especially at larger empty volumes, the higher the target carbonation (which might explain why some claim refermentation in a keg results in higher saturation levels). Note, this is a one-time addition of CO2, not a constant inflow.
Total pressure is what is expected to be inside the bottle/keg (relative to the atmospheric pressure = on a gauge). Note that this is not only a CO2 pressure, but in certain cases can include also pressures of other gases – it is also shown.
The model used is slightly simplified: it does not account for vapour pressures, changes of volume of the liquid, and possibly other details I did not even think about :). Also, it uses Henry’s law directly, without accounting for a slightly increased solubility of CO2 in a mix of water and ethanol.
For more background information ref. link (in Polish though..)