Quick Answer

ACOS Function

Returns the angle (in radians) whose cosine is the supplied number.

✓ Excel✓ Google SheetsExcel All versions

Syntax

ACOS
(number)

Parameters

ParameterDescriptionRequired
numberThe 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)
Result3.141592654

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))
Result: 60
ACOS(0.5) returns π/3 radians (about 1.047), and DEGREES converts that to 60°.

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))
Result: 53.13010235
ACOS(0.6) is the angle whose cosine is 0.6, about 53.13°.

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.

1
Pick the cell
Select the cell where you want the angle.
2
Enter the formula
Type =ACOS(number) where number is between -1 and 1.
3
Press Enter
The angle in radians appears; use DEGREES for degrees.

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

Practice 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.

Works in Google SheetsCompatible with ExcelIncludes exercises

File format: CSV (comma-separated values) - opens in Excel, Google Sheets, and all spreadsheet apps

Frequently Asked Questions

Does ACOS return degrees?
No. ACOS returns radians. Multiply by 180/PI() or wrap with DEGREES to get degrees.
What range of values does ACOS return?
It returns angles from 0 to π radians, i.e. 0° to 180°.
What if I need a full-circle angle for a point?
Use ATAN2(x, y) instead, which returns angles across the full -π to π range using both coordinates.