ACOS Function in Excel: Angle From a Cosine

ACOS Function in Excel: Angle From a Cosine featured illustration

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⏱ 2 min readUpdated 5 October 2026

MathLevel: ExpertAvailable in: Excel 2007+

In this article
  1. Syntax
  2. Examples
  3. Example 1
  4. ACOS in practice
  5. Where you will use it
  6. Worked example
  7. Mistakes people make
  8. Related functions
  9. Continue learning

ACOS is the inverse of COS. It appears in the formula for distance between two places on Earth.

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Syntax

=ACOS(number)
Argument What it means
number Between −1 and 1.

Examples

Example 1

=6371*ACOS(COS(RADIANS(90-B2))*COS(RADIANS(90-B3))+SIN(RADIANS(90-B2))*SIN(RADIANS(90-B3))*COS(RADIANS(C2-C3)))

Approximate km between two latitude/longitude points.

ACOS in practice

Where you will use it

  • Angle between two vectors (cosine similarity to degrees)
  • Angle of a triangle from three sides
  • Navigation bearings

Worked example

CosineFormulaResult
0.5=ROUND(DEGREES(ACOS(A2)),2)60
0=ROUND(DEGREES(ACOS(A3)),2)90
-1=ROUND(DEGREES(ACOS(A4)),2)180

Results calculated in Excel.

Mistakes people make

MistakeWhat to do instead
Value outside -1..1#NUM!; floating point can give 1.0000001, so wrap in MIN(1,MAX(-1,x))
Expecting degreesACOS returns radians; use DEGREES

COS · RADIANS

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📎 Practice files for this article

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    Practice workbook: Math & rounding24 tasks on realistic sales data — type your formula, the Check column turns green when it is right. Answers sheet included.
    ⬇ XLSX · 35 KB

Free to use for learning. Files with macros (.bas) are plain text — import them with Alt+F11 → File → Import File, and always test on a copy.

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