Is nominal capacity the same as usable capacity?
Not necessarily. Battery specifications distinguish total/nominal capacity from the amount intended to be usable. Check the actual product specification.
Use consumption outside solar hours, likely surplus, reserve and efficiency to explore a sensible battery-capacity starting point.
Battery size should be driven by the energy you can realistically shift, not simply by buying the largest battery available. Consumption timing, solar surplus, tariffs, usable capacity, power and backup requirements all matter.
Outputs are simplified illustrations using the values you enter. They are not a prediction or guarantee of generation, savings, battery performance, charging cost or investment return.