Unlocking the Power of ACOS in Excel: A Complete Guide with Examples & VBA

Remember trigonometry from high school math? It's still useful today, especially for engineers and data analysts. The ACOS, or ArcCosine, is a powerful function in Excel.

Let's dive into how to use it and add some VBA magic to it!

🔍 What Is the ACOS Function in Excel?

ACOS(number) finds the arccosine (inverse cosine) of a number. It returns the result in radians between 0 to π.

Syntax:

=ACOS(number)

• number must be between -1 and 1. Any value outside this range will cause a #NUM! error.
• The result is the angle (in radians) whose cosine is the specified number.

✅ Basic Examples of ACOS in Excel

A	B
Cos Value	Arccos (in Radians)
1	=ACOS(A2) → 0
0.5	=ACOS(A3) → 1.047198 (≈60°)
0	=ACOS(A4) → 1.570796 (≈90°)
-0.5	=ACOS(A5) → 2.094395 (≈120°)
-1	=ACOS(A6) → 3.141593 (≈180°)

To convert the result into degrees, use the DEGREES() function:

=DEGREES(ACOS(A2))

📈 Real-World Use Case: Calculating Angles from Cosine Values

Imagine working on a robotics project and needing to find joint angles from cosine values. Excel's ACOS is great for this.

Let's say you have a cosine value from sensor data. You can use ACOS to find the angle in radians or degrees.

🔧 Using VBA to Work with ACOS

Let's automate angle calculations with VBA. We'll create a custom function and a routine that applies ACOS to a range of values.

🧩 Example 1: A Custom VBA Function

Function ArcCosine(val As Double) As Double
    If val >= -1 And val <= 1 Then
        ArcCosine = WorksheetFunction.Acos(val)
    Else
        ArcCosine = CVErr(xlErrNum)
    End If
End Function

How to use:

1. Press ALT + F11 to open the VBA Editor.
2. Insert a new module.
3. Paste the above code.
4. Use it like a formula in Excel:CopyEdit=ArcCosine(A2)

🧩 Example 2: ACOS with Degrees in VBA

Want results in degrees? Here’s an updated version:

Function ArcCosineDeg(val As Double) As Variant
    If val >= -1 And val <= 1 Then
        ArcCosineDeg = WorksheetFunction.Degrees(WorksheetFunction.Acos(val))
    Else
        ArcCosineDeg = CVErr(xlErrNum)
    End If
End Function

Use in a cell like this:

=ArcCosineDeg(A2)

📊 Example 3: Looping Through a Range to Apply ACOS

Let’s say you have a column of cosine values. You want to fill the next column with the angle in degrees.

Sub ApplyACOS()
    Dim rng As Range
    Dim cell As Range

    Set rng = Range("A2:A10") ' Adjust your range

    For Each cell In rng
        If IsNumeric(cell.Value) Then
            If cell.Value >= -1 And cell.Value <= 1 Then
                cell.Offset(0, 1).Value = WorksheetFunction.Degrees(WorksheetFunction.Acos(cell.Value))
            Else
                cell.Offset(0, 1).Value = "Invalid Input"
            End If
        End If
    Next cell
End Sub

This script checks each value in A2:A10. It calculates the arccosine in degrees if valid. Then, it writes the result to column B.

🚫 Common Errors and Troubleshooting

Error	Cause
#NUM!	Value is outside the range -1 to 1
#VALUE!	Non-numeric input
"Invalid Input" (custom VBA)	Caught in script

🎯 Final Thoughts

The ACOS function is great for trigonometric calculations. It's useful in geometry, physics, and advanced robotics. With DEGREES() and VBA, you have a powerful toolkit ready to use!