Basic calculator that calculates result based on operands using a class
There is no need to manually raise ZeroDivisionError. Python will do it for you anyway.
Rather than inspecting an operand with the bunch of ifs, create a dictionary of operand, lambda:

ops = {
    '+': lambda x,y: x + y,
    ....
}


and calculate the result as

ops[operand](value1, value2)


Such dictionary (initialized in a constructor) is the only justification for making a class. It doesn't feel right to make an operator and values class members. Consider

r = calculator()
r.calculate(1, 2, '+')
r.calculate(3, 4, '*')


etc.