What is the syntax for COS in Excel?

The syntax for COS is: =COS(number)

What are common errors with COS?

Argument must be in radians, not degrees

How do I calculate the x-coordinate of a point on a circle?

Use =radius*COS(angle). For a point at 45° on a circle with radius 10: =10*COS(RADIANS(45)) = 7.07. Combined with SIN for y-coordinate, you can plot any point on a circle: x=r*COS(θ), y=r*SIN(θ).

What is the relationship between SIN and COS?

COS and SIN are phase-shifted by 90°: COS(x) = SIN(x + π/2). Also, SIN²(x) + COS²(x) = 1 always (Pythagorean identity). COS starts at 1 when angle is 0, while SIN starts at 0.

How do I use COS for direction calculations?

For movement in a direction: x_move = speed*COS(RADIANS(angle)), y_move = speed*SIN(RADIANS(angle)). At 0°, COS=1 and SIN=0, so movement is purely horizontal. At 90°, COS=0 and SIN=1, so movement is purely vertical.

Math & Trig

COS Function in Excel

Returns the cosine of an angle specified in radians.

Syntax

=COS(number)

Arguments

number (required): Angle in radians

Examples

=COS(0) - Cosine of 0 - Result: 1
=COS(PI()) - Cosine of 180 degrees - Result: -1

COS in reporting workflows

Use absolute references when copying formulas across rows.
For conditional totals see [SUMIF](/functions/sumif/) and [SUMIFS](/functions/sumifs/).
Filtered lists may need [SUBTOTAL](/functions/subtotal/) instead of SUM on visible cells only.

Common errors

Argument must be in radians, not degrees

Use cases

Trigonometry
Circular motion
Engineering calculations

Frequently asked questions

How do I calculate the x-coordinate of a point on a circle? Use =radius*COS(angle). For a point at 45° on a circle with radius 10: =10*COS(RADIANS(45)) = 7.07. Combined with SIN for y-coordinate, you can plot any point on a circle: x=r*COS(θ), y=r*SIN(θ).
What is the relationship between SIN and COS? COS and SIN are phase-shifted by 90°: COS(x) = SIN(x + π/2). Also, SIN²(x) + COS²(x) = 1 always (Pythagorean identity). COS starts at 1 when angle is 0, while SIN starts at 0.
How do I use COS for direction calculations? For movement in a direction: x_move = speed*COS(RADIANS(angle)), y_move = speed*SIN(RADIANS(angle)). At 0°, COS=1 and SIN=0, so movement is purely horizontal. At 90°, COS=0 and SIN=1, so movement is purely vertical.

Editorial review

Reviewed by Excel.Directory Editorial Team. Updated May 2026.