Yes, database is really necessary, but for a simple calculator database won't be needed.
So you are going to use C# right??
Start with designing the form(i mean designing the calculator)
Now, begin with functionalities one by one.
Say begin with Addition, then move to Subtraction, then Multiplication, Division etc.
After the basic functionalities gets completed, move to advanced functionalities like Square Root, Percentage, Square(^2), MR, MS etc.