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ACOS Function

Excel 2007+

Summary

The Excel ACOS function returns the arccosine (inverse cosine) of a number, providing the angle in radians whose cosine equals the input value. It handles trigonometric calculations where you need the angle from a known cosine value within the valid range.

Syntax

ACOS(number)

Parameters

Parameter	Type	Required	Description
number	`Number`	Yes	The cosine value representing the angle you want to find, ranging from -1 to 1

Using the ACOS Function

ACOS is vital for mathematical modeling, physics calculations, engineering analysis, and geometry problems in Excel. Use it when working backwards from cosine ratios to find actual angles in radians, commonly paired with other trig functions for comprehensive analysis.

Common ACOS Examples

Basic Arccosine Calculation

=ACOS(-0.5)

Returns approximately 2.0944 radians (120 degrees), the angle whose cosine is -0.5.

Convert to Degrees

=ACOS(-0.5)*180/PI()

Converts arccosine result to degrees, showing 120 degrees.

Using DEGREES Function

=DEGREES(ACOS(-0.5))

Simplified degree conversion using the DEGREES helper function, returns 120.

Frequently Asked Questions

ACOS requires numbers between -1 and 1 inclusive. Values outside this range return a #NUM! error.

ACOS always returns radians (0 to π). Multiply by 180/PI() or use DEGREES() for degree output.

Inputs < -1 or > 1 produce #NUM! errors. Non-numeric inputs cause #VALUE! errors.

Common Errors and Solutions

#NUM! Error

Cause: Input number is less than -1 or greater than 1

Solution: Ensure input value is within the valid cosine range [-1, 1]

#VALUE! Error

Cause: Input is not a valid number

Solution: Verify the input cell contains numeric data

Notes

Output range is always 0 to π radians (0 to 180 degrees)
For degree output, use DEGREES(ACOS(number)) or ACOS(number)*180/PI()
Perfect cosine inputs: ACOS(1)=0, ACOS(0)=π/2, ACOS(-1)=π
Combine with COS for angle-cosine verification: COS(ACOS(x))=x for x in [-1,1]

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in:

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+