ABS

Returns the absolute value of a number.

Syntax:

ABS(number)

number is the number whose absolute value is to be calculated. The absolute value of a number is its value without the +/- sign.

Example:

ABS(-56)

returns 56.

ABS(12.3)

returns 12.3.

ABS(0)

returns 0.

Application:

Tracking Temperature Deviations

Imagine a manufacturing process that requires a specific component to be produced at a target temperature of 200°F. During a production run, a quality control engineer takes temperature readings at various stages. The goal is to identify any readings that deviate significantly from the target, regardless of whether they are too hot or too cold.

Here is a table of the temperature readings:

	Reading ID	Actual Temperature (°F)	Target Temperature (°F)	Temperature Deviation (Actual - Target)	Absolute Deviation (\|Actual - Target\|)
	A	B	C	D	E
1	1	205	200	205−200=5	\|5\|=5
2	2	198	200	198−200=−2	\|-2\|=2
3	3	202	200	202−200=2	\|2\|=2
4	4	195	200	195−200=−5	\|-5\|=5
5	5	200	200	200−200=0	\|0\|=0

Explanation:

Temperature Deviation: The "Temperature Deviation" column shows the simple difference. A positive number means the temperature was above the target, and a negative number means it was below. While this is useful, it doesn't give a consistent measure of "how far off" the reading is. A deviation of 5° seems worse than a deviation of −2°, but it's not immediately clear how a deviation of 5° compares to a deviation of −5°.
Absolute Deviation: The "Absolute Deviation" column uses the ABS function. It takes the absolute value of the "Temperature Deviation" column. This gives a clear, positive number that represents the distance from the target temperature.
- For Reading 1, the absolute deviation is |5|=5.
- For Reading 2, the absolute deviation is |−2|=2.
- For Reading 4, the absolute deviation is |−5|=5.

By using the absolute value, the quality control engineer can easily see that Readings 1 and 4 have the same magnitude of error (5°), even though one was too hot and the other was too cold. This allows them to set a single tolerance limit (e.g., any reading with an absolute deviation greater than 3 needs to be flagged for review) without having to check for both positive and negative extremes separately.