How to calculate the percentage of a year up to a date is of the whole?

Question

Given a date, I need to calculate the percentage of its position in the year. So that 31-12-2015 would return 1, or 100%, because it's the 365th day of 365 days in that year. And 1-1-2015 would return 0,274% (1/365).

I have a long formula solution

=MINUS(
  A1;
  DATE(YEAR(A1)-1;12;31)
) / MINUS(
  DATE(YEAR(A1);1;1);
  DATE(YEAR(A1)+1;1;1)
)

Basically it counts the day of the year of the date given in A1 and divides that by the number of days in that year.

Is there a way to do this with a shorter formula?

Answer 1

Here is a shorter formula that is equivalent to yours, using yearfrac:

=yearfrac(date(year(A1), 1, 1), A1, 1)

However, the formula you have is inconsistent with your description, since it returns 0 for 1-1-2015, representing that at the beginning of that day, no time has elapsed since the beginning of the year. To have 1/365 for 1-1-2015 and 1 for 12-31-2015, add 1 to the date, to calculate each day's end:

=yearfrac(date(year(A1), 1, 1), A1+1, 1)

Answer 2

Short answer

Besides the use of other functions, like YEARFRAC() as was suggested by Live Forever, usually the way to get the shorter formula is to use a custom function.

Example

A Custom function

/**
 * Calculates the progress of the year for the date provided.
 * 
 * @param {DATE(2015,1,1)} input - The date to calculate the progress of the year.
 * @customfunction
 */
function YEARPROGRESS(adate) {
  if(adate instanceof Date){   
    var start = new Date(adate.getFullYear(), 0, 0);
    var day = Math.floor(adate - start);
    var end = new Date(adate.getFullYear(), 11, 31)
    var days = Math.floor(end - start);
    return day/days;
  } else {
    throw new Error('adate should be a valid date' );
  }
}

Use examples

=YEARPROGRESS(A1)  
=YEARPROGRESS(DATE(2015,1,1))

Use the cell formatting options to display the result as percentage.

Custom function names

If you want to save even more characters, you could name your function as short as a single alphabetic character (A..Z) but this is not a good practice as this could make a bit harder to remember how was named.

From the reference

Naming

In addition to the standard conventions for naming JavaScript functions, be aware of the following:

• The name of a custom function must be distinct from the names of built-in functions like SUM().
• The name of a custom function cannot end with an underscore (_), which denotes a private function in Apps Script.
• The name of a custom function must be declared with the syntax function myFunction(), not var myFunction = new Function().
• Capitalization does not matter, although the names of spreadsheet functions are traditionally uppercase.

References

• Custom functions - Guides - Google Apps Script