The term “pairwise lifting” in Excel refers to a special case of “lifting” – a built in calculation behavior whereby functions that don’t handle arrays natively are “lifted” and called once for each value in an array, returning in turn an array containing multiple results.

Pairwise lifting occurs when values in two or more arrays are combined pairwise to produce a different array holding the result of this operation.

Example

The example shown illustrates what happens if you call the SQRT function like this:

=SQRT({1;2;3}+{3;7;13})

Inside SQRT, two vertical arrays are added together with the addition symbol. The values in these arrays are combined pairwise, and result of this operation is a single array with 3 values:

=SQRT({4;9;16})

The SQRT function does not handle arrays natively, so the function is “lifted” and called three times, one for each value. The final result in an array with three values:

={2;3;4}

Handling with multiple results

When lifting occurs in a formula, there will be multiple results, and these need to handled in some way. One approach is to return all values to a worksheet in a multi-cell array formula. Alternatively, you can pass the result into another function like SUMPRODUCT:

=SUMPRODUCT(SQRT(C5:C7+E5:E7))

to return a final result of 9. SUMPRODUCT will handle arrays natively, so this formula does not require control + shift + enter.

The SUM function could be used as well, but would need to be entered with CSE .

The “Percentage” number format is one of the built-in number formats in Excel. In mathematics, a percentage is a number expressed as a fraction of 100. The word percent literally means “per one-hundred”. For example, 65% is read as “Sixty-five percent” and is equivalent to 65/100 or 0.65.

To apply the percentage number format to a number, first select the number(s), then use any of these methods:

  • Use the keyboard shortcut Control + Shift + Enter
  • Select “Percentage” from the dropdown on the home tab of the ribbon
  • Click the % button in the Number section on the home tab of the ribbon
  • Control + 1 > Number > Percentage

Applying percentage format does not change the number, only the display of the number. In the screen above, the numbers in column B are the same as the numbers in column D.

By default, Excel will display the number with the percent sign (%) and no decimal places. To adjust this format, open the Format Cells dialog box, select Percentage, then select Custom. There you can adjust the codes in the “Type” input area. For example:

0% // default, zero decimals
0.00% // two decimal places

For more information on custom number format codes see: Custom Number Formats .