Creating a calculation field to add up interactive buttons

Yes and No, as Try states, buttons don't have a value.

Do you have to use buttons?

If so then the values for the calculation could be stored in a JS object that matches the button name to a value. 

The best way to do this is to use group naming with the buttons,i.e., "Score.Button1" "Score.Button2" etc. then a generic script can be written to loop through the buttons, adding up the values for the ones that are visible. 

If the buttons can be replace with somthing that does have a value, like a field, then the same technique applies, only you don't need the JS object for mapping values. 

Buttons don't have values. However, you can write a script that will check the visibility property of the button fields and if they are visible it will assume they have a value and use it to calculate a sum.