Returns the arccosine (inverse cosine) of a number, in radians. The result is an angle between 0 and π (0 and 180 degrees). Essential for trigonometry, engineering calculations, angle conversions, and solving equations involving cosine.
Master the fundamentals of Excel ACOS function
The ACOS function returns the arccosine (inverse cosine) of a number in radians. It is the inverse of the COS function: if y = COS(x), then x = ACOS(y). ACOS returns angles between 0 and π radians (0 to 180 degrees). Essential for trigonometry, engineering calculations, and solving equations where you know the cosine and need the angle.
Returns angle whose cosine is the number
Input must be between -1 and 1
Result is in radians (0 to π)
Always returns 0 to π range
Function-specific parameters
Function-specific return type
Find angles from cosine values
Calculate angles in engineering problems
Solve triangle angle problems
Perform scientific angle calculations
Exact matching required
Returns numeric position
Handles missing text gracefully
=ACOS(number)The cosine of the angle you want. Must be between -1 and 1 inclusive. The arccosine is the angle whose cosine is number.
The arccosine in radians (0 to π, or 0 to 180 degrees)
Description: Returns the arccosine (inverse cosine) of a number in radians
Calculate arccosine
Returns approximately 1.047 radians (60 degrees). ACOS(0.5) = 60° because cos(60°) = 0.5.
Use ACOS function in VBA
' Basic ACOS in VBA
Range("C1").Value = Application.WorksheetFunction.Acos(0.5)
' Returns: 1.047 (radians)
' Calculate angle in degrees
Sub CalculateAngleDegrees()
Dim cosineValue As Double
cosineValue = Range("A1").Value
Dim angleRadians As Double
Dim angleDegrees As Double
angleRadians = Application.WorksheetFunction.Acos(cosineValue)
angleDegrees = Application.WorksheetFunction.Degrees(angleRadians)
Range("B1").Value = angleDegrees
End Sub
' Calculate angle in triangle
Sub TriangleAngle()
Dim adjacent As Double, hypotenuse As Double
adjacent = Range("A1").Value
hypotenuse = Range("B1").Value
Dim cosine As Double
cosine = adjacent / hypotenuse
Dim angleDegrees As Double
angleDegrees = Application.WorksheetFunction.Degrees( _
Application.WorksheetFunction.Acos(cosine))
Range("C1").Value = angleDegrees
End Sub
' Validate input range
Sub SafeACOS()
Dim value As Double
value = Range("A1").Value
If value < -1 Or value > 1 Then
Range("B1").Value = "#NUM!"
Else
Range("B1").Value = Application.WorksheetFunction.Acos(value)
End If
End SubFind angle from cosine ratio
Convert cosine to angle in degrees
Calculate angles in engineering problems
Perform trigonometric analysis
ACOS returns #NUM! for values outside -1 to 1
=IF(AND(A1>=-1, A1<=1), ACOS(A1), "#NUM!")Solution: Ensure input is between -1 and 1. Cosine values are always in this range. Use IF to validate: =IF(AND(A1>=-1, A1<=1), ACOS(A1), "#NUM!").
ACOS returns radians but need degrees
=DEGREES(ACOS(A1))Solution: Wrap ACOS with DEGREES: DEGREES(ACOS(number)). This converts radians to degrees. Remember: π radians = 180 degrees.
ACOS results have many decimal places
=ROUND(DEGREES(ACOS(A1)), 2)Solution: Use ROUND for display: ROUND(ACOS(value), digits) or ROUND(DEGREES(ACOS(value)), digits) for degrees.
Uncertainty about ACOS vs COS relationship
ACOS(COS(60°)) = 60° (after converting)Solution: ACOS is inverse of COS: ACOS(COS(angle)) = angle (in radians). COS(ACOS(value)) = value (if value is between -1 and 1).