Why ABS Function Behavior Appears Different with Direct Formula vs. Cell References

The ABS function consistently returns the absolute value of any input. The apparent difference in behavior between direct formulas and cell references arises from how the subtraction is calculated before ABS is applied.

Direct Formula: Calculation of Absolute Difference

When using direct formulas, the subtraction occurs between fixed numbers, potentially producing a negative result that ABS converts to positive.

Example:

=ABS(10-25) → 15,
(the formula directly subtracts 25 from 10, resulting in -15).
=ABS(-15) → 15,
the ABS function then converts -15 to its absolute value, 15.
=ABS(25-10) → 15

💡Key Point: The subtraction is straightforward, and the ABS function simply removes the negative sign from the result.

Cell References: Resolving Negative Input

When using cell references, if one cell contains a negative value, the subtraction operation follows the mathematical rule that subtracting a negative number is the same as adding its positive value.

Example:

if A4 = 10 (positive number) and A5 = -25 (negative number)
The formula =ABS(A4 - A5) becomes:
- When we subtract a negative number, it’s the same as adding its positive value
- This is because: a - (-b) = a + b
- Think of it as “removing a negative” which makes it positive
  =ABS(10 - (-25))
  = ABS(10 + 25) ____// Subtracting a negative is the same as adding
  = ABS(35) _______/ First resolve what’s inside the parentheses
  = 35 __________// Since 35 is already positive, ABS doesn’t change it

💡Key Point: The presence of a negative value in A5 leads to a positive result during the subtraction step, so the ABS function does not modify it.

This creates a positive intermediate result that ABS doesn’t need to modify. In both cases, the ABS function itself works identically – the difference lies in when and how the subtraction is resolved before ABS processes the final value.

Conclusion:

The ABS function always returns the absolute value of the input. The perceived difference in behavior arises from the difference in how the subtraction is computed before ABS is applied:

In Example 1, subtraction produces a negative result.
In Example 2, the subtraction involves a double negative, producing a positive result