Dealing with Small Time Values

Zuzana has a need to perform calculations with very small time increments, such as thousandths of a second. She wonders how small of times Excel can deal with and how she can format for the display of the small increments.

Because of the way in which Excel stores times internally, it can theoretically deal with a time increment much smaller than a thousandth of a second. I say theoretically because there are a lot of factors that can negatively impact that precision.

As an example, consider that times and dates are stored in Excel such that full days are stored to the left of the decimal point and fractions of days are stored to the right. If you wanted to store a value as small as a hundred billionth of a second, you could conceivably do it. To store such a number in this format you end up with 1 day divided by 24 hours divided by 60 minutes divided by 60 seconds divided by 100,000,000,000. This results in a number that looks like this:

0.000000000000000115740740740741

Notice that there are a bunch of zeros followed by 15 significant digits. This is because Excel can only store a number that includes up to 15 significant digits. If you start doing anything else with this value, you ruin the value. For instance, you could add 3 to the value, signifying the addition of three days. Excel would then render this as the result:

3.000000000000000000000000000000

Notice that the small time increment disappeared. This happened because in the result of the addition, everything after the 3 became "significant," and Excel can only keep track of up to 15 significant digits, which was all zeros in the original number.

A thousandth of a second is a much longer duration than a hundred billionth of a second; it is represented in Excel's internal formatting as this:

0.0000000115740740740741

If you add three days to this value, you end up with this:

3.00000001157407

This is still accurate enough to render thousandths of a second just fine.

Of course, it doesn't do much good to store thousandths of a second internally if you can't display them in Excel. This is where custom formatting comes into play. You can create a custom format (as described in other issues of ExcelTips) that will display thousandths of a second just fine. Here's the format to use:

h:mm:s.000

If you try to use more zeros in the format (to display smaller increments of time), Excel will balk. The smallest increment you can display using custom formats is a thousandth of a second.

ExcelTips is your source for cost-effective Microsoft Excel training. This tip (9198) applies to Microsoft Excel 97, 2000, 2002, and 2003. You can find a version of this tip for the ribbon interface of Excel (Excel 2007 and later) here: Dealing with Small Time Values.