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Analysis of Excel dates

This weekend I set out on an exercise that consisted of fill an Excel table with dates and times randomly increased. Trivial thing at first! Or not?

What was my surprise when I found a problem that I did not expect with the decimal number formats representing the date and time. Insignificant thing if you're not very meticulous! Or not?

The fundamental premise with dates in Excel is that the day is stored as an integer serial number and time is the decimal part of the day. Drawer thing! Or not?

My discovery tells me that dates stored as decimals do not always correspond to the dates displayed in date format. Thing never seen before! Or not?

Date and time format in Excel (see link here):

Displays date and time serial numbers as date values, according to the type and locale (location) that you specify. Date formats that begin with an asterisk (*) respond to changes in regional date and time settings that are specified in Control Panel. Formats without an asterisk are not affected by Control Panel settings.

What a mess I've gotten myself into! Or not?

Format and value of dates and times

In A2 cell I write the date: 03/20/2021  23:59:58

Its decimal value is displayed with 15 digits: 44275.9999768519

The integer part is the serial number representing the number of days since January 1, 1900. The integer number corresponds to the day 03/20/2021: 44275

The decimal part is the fraction of a day. The decimal value 0.9999768519 is equivalent to 23:59:58 in hh:mm:ss format, with hh:hours; mm: minutes; ss: seconds.

Decimal accuracy

Excel can display the time as a decimal number with 15 digits significant, as we're going to see by adding up the decimal part of the hours, minutes and seconds:

• 0.958333333333333 = 23/24 it's 23 hours.
• 0.0409722222222222 = 59/60/24 it's 59 minutes.
• 0.000671296296296296 = 58/60/60/24 it's 58 seconds.

The sum of these 3 decimal numbers gives:

• 0.999976851851852 = (23 + (59 + 58 / 60) / 60) / 24
• it's 23 hours, 59 minutes and 58 seconds as a decimal part of a day.

If you like numbers like me, you'll see that sum with 15 digits 0.999976851851851 being the last figure being 1 in place of a 2. This is because Excel represents 15 digits but secretly stores 17 significant digits, what the calculated sum will be:

• 0.95833333333333333000 it's 23 hours.
• 0.04097222222222222200 it's 59 minutes.
• 0.00067129629629629629 it's 58 seconds.

The sum of the previous 3 decimal places with 17 digits of precision is the decimal:

• 0.99997685185185184 which is represented as the time 23:59:58 and that is rounded to 15-digit display: 0.999976851851852

Bill Jelen, one of Excel's top gurus, known worldwide as MrExcel, wrote an excellent article warning of some of the problems derived from the internal accuracy of the Excel calculation engine. Access the following link in English to study it:

www.mrexcel.com - 17 or 15 digits of precision

On this important issue of Excel's internal accuracy, I will return to talk below. Keep reading this article to the last one to find out more about the accuracy of dates. Case you're interested in it! Or not?

Random dates and times

In A3 cell I write the following formula and drag it down:

=A2+RAND()/100000

What I do is add a very small random value to a date and time, divided by one hundred thousand, so that the date and time increment is minimal.

In this image you can see the result obtained in the 'Random' sheet, which you can download below:

We look at the cells marked with red background color, in which we are calculated the integer part of the date. Unexpected thing! Or not?

You can verify that the day represented in column A does not match, the 03/21/2021, with day 03/20/2021 in column B, which is equivalent to the integer part of the date, equal to 44275. This problem occurs 2 times in this random execution, but can occur several more times. Undesirable thing! Or not?

Problem with inaccurate dates

When dates are randomly generated, the decimal part of a date close to one, makes the format of date numbers in Excel overflows, showing the next day, when the integer part of the serial number of the date corresponds to the previous day. Inexplicable thing! Or not?

The following image shows the decimal accuracy of various formats dates that generate overflow in the 'Dates' sheet.

In red background color are marked the dates shown for those that do not agrees on its corresponding day, i.e. date serial number which is integer part . Unforgivable thing! Or not?

Accuracy of the numerical date format

If you've read Bill Jelen's article:

www.mrexcel.com - 17 or 15 digits of precision

you've seen that Excel's calculation engine stores and calculates decimal places more accurately (17 digits) than the one represented (15 digits). You already knew that! Or not?

With the decimals of the dates the same thing also happens. Dates can have more decimal places than the dates displayed, which creates a problem when decimal digits are close to the unit, as we can see with this example:

• 44275.9999999999 with the serial number of 5 figures 44275, represents the day 03/20/2021
• but shows the day 03/21/2021, due to internal rounding of Excel's numeric date format. Dangerous thing! Or not?

Proposed solution for overflowing dates

The solution proposed by Bill Jelen, in his article on the internal accuracy of the Excel calculation engine, can also be applied to this new problem with date format.

The problem can be solved by rounding the date down to 5 decimal places, with this formula:

=ROUNDDOWN([@Date],5) = 44275.99999

with only 10 digits of precision, 5 for the day and another 5 for the decimal part of the day, which is displayed as the correct date and time: 03/20/2021 23:59:59 Desired thing! Or not?

Overflow dates template

Download the template I've written this article with since Microsoft OneDrive, or play with the template embedded in my blog from here:

Inexplicably the 4 buttons on the bottom right of the embedded Excel have not responded for a few days, so the file cannot be downloaded with the Download button. I have filed an issue incident to the Microsoft Support and and I have commented about in the Microsoft Excel Tech Community here, but we already know that things at the palace are going slowly... Truth or not truth?

Finally the buttons respond! It's been 11 days with no response due to poor OneDrive service with the embedded workbooks into blogs or webs. The issue has lasted from January 5 to January 16, 2023. It will happen again? Surely yes!

ATTENTION: Excel Online does not allow recalculating with the F9 key. In the 'Random' sheet, you can modify the A2 cell and it will recalculate everything. Better thing! Or not?

NOTE: Microsoft Excel is designed around the IEEE 754 specification, and the IEEE 754 specification has some limitations.

The limitations of this problem and the solution to the problem can be found in the following article:

Floating-point arithmetic may give inaccurate result in Excel - Office | Microsoft Learn

I'll soon publish the randomly generated date table and see what motivated this simple exercise. Curious thing! Or not?

You can now read the blog post that inspired me when I detected the problem with overflowed dates when I was preparing a macro to randomly fill a million visits to my blog.

Post in Spanish easily translatable into more than 100 languages with the Google box at the top left of this post:

Buscar rápida y eficazmente en Excel | #ExcelPedroWave