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formula consist of one or more functions (sometimes no functions at all, only operators)
A function is an instruction already set in MS-Excel that can not be tampered with. For Example; Sum() is a function that adds the columns in between it and it can not be tampered with.
Where as, a formula in MS-Excel is said to any instruction or command given in the sheet to be done that can be;
1). User Made,
2). Easy and Complex, and
3). made by1 function or a number functions together.
Moreover, a formula in MS-Excel always start with =
For Example; ={Sum() / ( -)}*2 .
This formula contains functions of addition, division, multiplications, brackets etc.
Both function and formulas mostly gives an outcome or a result.
A formula is statement written by the user to be calculated. Formulas can be as simple or as complex as the user wants. A formula can contain values, references to cells, defined names, and functions.
All formulas must start with the equals sign. =1+2+3
A function is a piece of code designed to calculate specific values and are used inside formulas. Functions to sum values, calculate a trigonometric cosine, and to calculate the current time are built into excel. Additional functions can be defined using Visual Basic.
Functions are typed alongside parenthesizes, where in the arguments if any are listed in between. To use functions in a formula, for example
=COS(3.14) will return the calculated cosine. =NOW() returns the current time. =SUM(1+2+3) *2 will multiply the sum by 2
A function is a built-in operation, such as SUM(), AVERAGE(), etc. A formula is something that the user defines, and can use/refer to various functions in it. They are similar in that both return a result based on the calculations that each performs. The difference is that a function is a built-in calculation, while a formula is a user-defined calculation. A formula could just use a single function.
http://superuser.com/questions/166008/what-is-the-difference-between-function-and-formula-in-excel