ACOS Function
Returns the angle (in radians) whose cosine is the supplied number.
Syntax
Parameters
| Parameter | Description | Required |
|---|---|---|
| number | The cosine of the angle you want, which must be a real number between -1 and 1 inclusive. | Required |
Basic Example
Find the angle whose cosine is -1
=ACOS(-1)The arccosine of -1 is π radians (180°), the angle whose cosine equals -1.
Advanced Examples
Example 1: Convert the result to degrees
An engineering problem needs the angle in degrees.Wrap ACOS in DEGREES to read the angle in degrees.
=DEGREES(ACOS(0.5))Example 2: Angle of a right triangle
Given adjacent/hypotenuse = 0.6, find the angle.Use the ratio directly as the argument.
=DEGREES(ACOS(0.6))How ACOS Works
ACOS is the inverse of COS. For an input x in [-1, 1] it returns the unique angle θ in [0, π] (radians) such that cos(θ) = x. It uses the principal value only.
Important Notes & Limitations
The argument must be between -1 and 1; outside that range the function returns #NUM!.
The result is always in radians, never degrees, so apply DEGREES for degree output.
ACOS returns only the principal value, so it cannot produce angles outside the [0, π] range.
Common Errors & Fixes
#NUM!The argument is less than -1 or greater than 1.Fix: Ensure the value is a valid cosine between -1 and 1.
#VALUE!The argument is non-numeric text.Fix: Supply a numeric value or a cell that contains a number.
Download Practice File
ACOS
acosPractice ACOS with Real Data
Download a sample CSV file with pre-populated data and practice exercises for the ACOS function. Works in both Excel and Google Sheets.
File format: CSV (comma-separated values) - opens in Excel, Google Sheets, and all spreadsheet apps