Excel serial date to Day, Month, Year and vise versa

Introduction

For a little project of mine, I needed to convert a serial date number to day/month/year (DMY) and vise versa. The serial number came from date field in a converted Paradox database and seemed to be exactly the same as the serial date in Microsoft Excel, hence the article name. After some googling I learned that the Excel serial date is related to Julian date, and found a speedy algorithm to convert these numbers to DMY and vise versa.

Excel Serial Date Number

Now what is an Excel serial date number? 37477 is a serial date number and is the number of days since 1-1-1900. 37477 actually translates to Aug 9, 2002, the date of writing this article.

The number of days since 1-1-1900 isn't that hard to calculate of course, once you know the leap years. Microsoft Excel however contains a bug with its date calculation: it considers 29-02-1900 as a valid date, but 1900 isn't a leap year! 29-02-1900 is not a valid date!

According to the stories, Microsoft decided to duplicate this date bug from Lotus 123, which was the dominating spreadsheet application at the time Excel was being written. This allowed Excel to open Lotus 123 spreadsheets without date problems.

(Note that a serial date number may also contain a fraction that denotes the time. It's actually the percentage of 24 hours, but that's not for this article.)

Mac Excel Serial Date number

Excel on the Apple Mac uses a slightly different Serial Date number base: the number of days since 1-1-1904. That's why Excel also features a "1904 Date System" checkbox in its Options (Calculation tab). I won't go into this futher.

Translating Serial Date Number to DMY

First of all, credit where credit is due. I got the basic algorithm from http://serendipity.magnet.ch/hermetic/cal_stud/jdn.htm. It's about converting a Julian date to DMY using integer calculations. I won't bore you with the theory (following the above hyperlink), but the original Julian has a different base date.

With an addition of a certain number, the algorithm comes close to the Excel serial date. And when the 29-02-1900 issue is handled, we've got an Excel serial date to Day, Month, Year calculation!

void ExcelSerialDateToDMY(int nSerialDate, int &nDay, 
                          int &nMonth, int &nYear)
{
    // Excel/Lotus 123 have a bug with 29-02-1900. 1900 is not a

    // leap year, but Excel/Lotus 123 think it is...

    if (nSerialDate == 60)
    {
        nDay    = 29;
        nMonth    = 2;
        nYear    = 1900;

        return;
    }
    else if (nSerialDate < 60)
    {
        // Because of the 29-02-1900 bug, any serial date 

        // under 60 is one off... Compensate.

        nSerialDate++;
    }

    // Modified Julian to DMY calculation with an addition of 2415019

    int l = nSerialDate + 68569 + 2415019;
    int n = int(( 4 * l ) / 146097);
            l = l - int(( 146097 * n + 3 ) / 4);
    int i = int(( 4000 * ( l + 1 ) ) / 1461001);
        l = l - int(( 1461 * i ) / 4) + 31;
    int j = int(( 80 * l ) / 2447);
     nDay = l - int(( 2447 * j ) / 80);
        l = int(j / 11);
        nMonth = j + 2 - ( 12 * l );
    nYear = 100 * ( n - 49 ) + i + l;
}

DMY to Excel Serial Date

Calculate an Excel serial date from Day, Month, Year. The function assumes that the day, month and year are valid date numbers.

int DMYToExcelSerialDate(int nDay, int nMonth, int nYear)
{
    // Excel/Lotus 123 have a bug with 29-02-1900. 1900 is not a

    // leap year, but Excel/Lotus 123 think it is...

    if (nDay == 29 && nMonth == 02 && nYear==1900)
        return 60;

    // DMY to Modified Julian calculatie with an extra substraction of 2415019.

    long nSerialDate = 
            int(( 1461 * ( nYear + 4800 + int(( nMonth - 14 ) / 12) ) ) / 4) +
            int(( 367 * ( nMonth - 2 - 12 * ( ( nMonth - 14 ) / 12 ) ) ) / 12) -
            int(( 3 * ( int(( nYear + 4900 + int(( nMonth - 14 ) / 12) ) / 100) ) ) / 4) +
            nDay - 2415019 - 32075;

    if (nSerialDate < 60)
    {
        // Because of the 29-02-1900 bug, any serial date 

        // under 60 is one off... Compensate.

        nSerialDate--;
    }

    return (int)nSerialDate;
}