# ABS Function in Microsoft Excel

## Part 1: Introduction

### Definition

The ABS function in Excel is a mathematical function that returns the absolute value of a number.

### Purpose

The purpose of the ABS function is to return the absolute value of a number, which is the number without its sign. This can be useful in various scenarios where you want to consider only the magnitude of a number without regard to its character.

### Syntax & Arguments

The syntax for the ABS function is as follows:

syntax
```ABS(number) ```

The ABS function has only one argument:

• Number: This is the actual number you want the absolute value.

### Return Value

The ABS function returns the absolute value of the number provided as the argument.

### Remarks

The ABS function ignores the sign of the number, so it always returns a positive value or zero. The ABS function returns the number itself if the argument is positive or zero. If the argument is a negative number, the ABS function returns the positive counterpart of the number.

## Part 2: Examples

Let’s look at some examples of using the ABS function in business.

### Example 1

Purpose: To calculate the absolute value of sales differences.

ABCD
1Sales Last MonthSales This MonthSales Difference (Formula)Sales Difference (Result)
250006000`=ABS(A2-B2)`1000
370006500`=ABS(A3-B3)`500
480007500`=ABS(A4-B4)`500

Explanation: In this example, we calculate the absolute value of the difference in sales between last month and this month. This can be useful when we want to measure the magnitude of change without considering whether it’s an increase or decrease.

### Example 2

Purpose: To calculate the absolute value of profit differences.

ABCD
1Profit Last QuarterProfit This QuarterProfit Difference (Formula)Profit Difference (Result)
22000025000`=ABS(A2-B2)`5000
33000028000`=ABS(A3-B3)`2000
44000042000`=ABS(A4-B4)`2000

Explanation: Here, we calculate the absolute value of the difference in profit between the last quarter and this quarter. This can be useful when we want to measure the magnitude of change without considering whether it’s a profit increase or decrease.

### Example 3

Purpose: To calculate the absolute value of inventory differences.

ABCD
1Inventory Last WeekInventory This WeekInventory Difference (Formula)Inventory Difference (Result)
2100120`=ABS(A2-B2)`20
3150140`=ABS(A3-B3)`10
4200190`=ABS(A4-B4)`10

Explanation: In this example, we calculate the absolute value of the difference in inventory between last week and this week. This can be useful when we want to measure the magnitude of change without considering whether it’s an inventory increase or decrease.

### Example 4

Purpose: To calculate the absolute value of temperature differences.

ABCD
1Temperature Yesterday (°C)Temperature Today (°C)Temperature Difference (Formula)Temperature Difference (Result)
22025`=ABS(A2-B2)`5
33028`=ABS(A3-B3)`2
43533`=ABS(A4-B4)`2

Explanation: Here, we calculate the absolute value of the difference in temperature between yesterday and today. This can be useful when we want to measure the magnitude of change without considering whether it’s a temperature increase or decrease.

### Example 5

Purpose: To calculate the absolute value of exchange rate differences.

ABCD
1Exchange Rate Last MonthExchange Rate This MonthExchange Rate Difference (Formula)Exchange Rate Difference (Result)
21.201.25`=ABS(A2-B2)`0.05
31.301.28`=ABS(A3-B3)`0.02
41.351.33`=ABS(A4-B4)`0.02

Explanation: In this example, we calculate the absolute value of the difference in exchange rates between last month and this month. This can be useful when measuring the magnitude of change without considering whether it’s an exchange rate increase or decrease.

📌 Example 6:

• Purpose: Determining the absolute difference between budgeted and actual sales.
• Data tables and formulas:
ABCD
1Budgeted SalesActual SalesAbsolute Difference FormulaResult
2\$5,000\$4,800=ABS(A2-B2)\$200
3\$6,000\$6,500=ABS(A3-B3)\$500
4\$7,000\$6,900=ABS(A4-B4)\$100
• Explanation: In business, comparing budgeted figures with actual results is crucial. Here, we’re using the `ABS` function to determine the absolute difference between budgeted and solid sales, giving a clear picture of deviations without considering if the actual sales were over or under the budget.

📌 Example 7:

• Purpose: Using the `ABS` function with `IF` to determine if sales targets were met.
• Data tables and formulas:
ABCD
1Target SalesActual SalesTarget Met FormulaResult
2\$10,000\$9,500=IF(ABS(A2-B2)<=500, “Met”, “Not Met”)Met
3\$12,000\$11,200=IF(ABS(A3-B3)<=500, “Met”, “Not Met”)Met
4\$15,000\$14,200=IF(ABS(A4-B4)<=500, “Met”, “Not Met”)Not Met
• Explanation: Businesses often have a tolerance range to determine if sales targets are met. Here, we’re using the `ABS` function nested within a `IF` statement to check if the absolute difference between target and actual sales is within a \$500 range.

📌 Example 8:

• Purpose: Calculate the sum of absolute differences between forecasted and actual expenses.
• Data tables and formulas:
ABCD
1Forecasted ExpensesActual ExpensesAbsolute Difference FormulaResult
2\$2,000\$2,100=ABS(A2-B2)\$100
3\$3,000\$2,900=ABS(A3-B3)\$100
4\$4,000\$4,200=ABS(A4-B4)\$200
5Total=SUM(D2:D4)\$400
• Explanation: Forecasting expenses is a common practice in businesses. By using the `ABS` function combined with the `SUM` function, we can calculate the total absolute difference between forecasted and actual expenses, providing a clear picture of the overall accuracy of the forecasts.

📌 Example 9:

• Purpose: Using `ABS` with `VLOOKUP` to find the absolute difference between a product’s listed price and its sale price.
• Data tables and formulas:
ABCD
1ProductListed PriceSale PriceAbsolute Difference Formula
2Widget A\$50\$45=ABS(B2-VLOOKUP(A2,E:F,2,FALSE))
3Widget B\$60\$58=ABS(B3-VLOOKUP(A3,E:F,2,FALSE))
4Widget C\$70\$65=ABS(B4-VLOOKUP(A4,E:F,2,FALSE))
EF
1ProductSale Price
2Widget A\$45
3Widget B\$58
4Widget C\$65
• Explanation: Businesses often have a list of products with their respective prices. When products go on sale, it’s helpful to determine the absolute difference between the listed price and the sale price. Here, we’re using the `ABS` function nested with `VLOOKUP` to fetch the sale price and calculate the difference.

📌 Example 10:

• Purpose: Using `ABS` with `AVERAGE` to find the average absolute deviation from the mean.
• Data tables and formulas:
ABC
1DataAbsolute Deviation FormulaResult
25=ABS(A2-AVERAGE(A\$2:A\$4))1.67
36=ABS(A3-AVERAGE(A\$2:A\$4))0.67
48=ABS(A4-AVERAGE(A\$2:A\$4))1.33
• Explanation: In statistics, the average absolute deviation measures the dispersion of data points. By using the `ABS` function nested with `AVERAGE`, we can determine how far each data point deviates from the mean on average.

📌 Example 11:

• Purpose: Using `ABS` with `MAX` to find the maximum absolute deviation from a target.
• Data tables and formulas:
ABC
1DataAbsolute Deviation FormulaResult
210=ABS(A2-15)5
314=ABS(A3-15)1
416=ABS(A4-15)1
5Max Deviation=MAX(C2:C4)5
• Explanation: When tracking performance against a target, knowing the maximum deviation is useful. Here, we’re using the `ABS` function nested with `MAX` to find the most significant absolute deviation from a target of 15.

📌 Example 12:

• Purpose: Using `ABS` with `MIN` to find the minimum absolute deviation from a baseline.
• Data tables and formulas:
ABC
1DataAbsolute Deviation FormulaResult
250=ABS(A2-55)5
354=ABS(A3-55)1
456=ABS(A4-55)1
5Min Deviation=MIN(C2:C4)1
• Explanation: In some scenarios, knowing the slightest deviation from a baseline is essential. Here, we’re using the `ABS` function nested with `MIN` to find the most minor absolute deviation from a baseline of 55.

## Part 3: Tips and Tricks

1. The ABS function can be combined with other functions to perform more complex calculations.
2. Remember that the ABS function always returns a positive value or zero, so it’s unsuitable for situations where you need to preserve the sign of the number.
3. The ABS function can be used on various cells with the Excel array formula functionality.
4. If you want to calculate the absolute value of differences, like in the examples above, you can use the ABS function in combination with the subtraction operator (-).
5. The ABS function can be used in financial calculations where the magnitude of numbers is essential, such as in risk analysis or variance analysis.