Why does COS(1) return 0.5403 instead of a simple value like 0.5?

COS always interprets its input as radians. One radian ≈ 57.3 degrees, so COS(1) is not the cosine of 1 degree; it's the cosine of 57.3 degrees. To get the cosine of 1 degree, use =COS(1*PI()/180), which returns ≈0.9998.

How do I apply COS to model recurring patterns in campaign performance?

Map your time period (day, week, month) to a radian value using the formula angle = (period_number / total_periods) × 2π. Then apply =COS(angle) to get a multiplier. For monthly cycles, =COS((month_number/12)*2*PI()) gives the seasonal adjustment for that month.

What happens if I pass a very large number to COS, like COS(10000)?

COS cycles every 2π radians, so large inputs wrap around. COS(10000) is equivalent to COS(10000 mod 2π) ≈ COS(2.1), which returns ≈−0.505. The function always produces a valid result between -1 and 1.

Should I use COS or ABS(COS) for campaign adjustment factors?

Use COS alone if you want negative values to represent downturns or reversals in the cycle. Use ABS(COS) if you only care about the strength of the effect, regardless of direction. For budget adjustments, COS is often better because it naturally captures both boost and reduction phases.

COS function

COS returns the cosine of an angle in radians, producing values between -1 and 1; use it for cyclical calculations and trigonometric analysis.

=COS(number)

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Describe what you need. The generator will reach for COS where COS is the right tool, and tell you when it is not.

Arguments

How COS reads its arguments

Argument	Required	Description
number	Required	The angle in radians for which to calculate the cosine. Accepts any real number; negative values and values greater than 2π are valid and cycle appropriately.

Returns

A decimal number between -1 and 1 representing the cosine of the input angle.

Availability

Excel: All · Google Sheets: Supported

Worked examples

1. Calculate seasonal adjustment for Q3 campaign

Campaign	Channel	Spend	Clicks	Conversions
Q1 Social	Facebook	5000	245	12
Q2 Search	Google	6000	310	18
Q3 Email	Email	7000	425	25
Q4 Display	YouTube	8000	520	32

=COS(PI()/2)

Result: 0

Q3 represents π/2 radians—a quarter cycle through the year. COS(π/2) equals 0, marking the neutral point where seasonal forces balance. Use this multiplier to adjust campaign budgets: a zero factor means expected performance is at the median seasonal baseline, neither boosted nor diminished by cyclical trends.

2. Calculate performance phase factor from conversion angle

Campaign	Channel	Spend	Clicks	Conversions
Q1 Social	Facebook	5000	245	12
Q2 Search	Google	6000	310	18
Q3 Email	Email	7000	425	25
Q4 Display	YouTube	8000	520	32

=COS(0.0524)

Result: 0.9986

Converting 3 degrees to radians (≈0.0524) and applying COS gives 0.9986. Early in the campaign cycle, the small phase angle produces a value near 1, indicating near-full expected reach and engagement. As a multiplier, 0.9986 means expect minimal seasonal or cyclical drag on performance.

3. Find adjustment at campaign trough phase

Campaign	Channel	Spend	Clicks	Conversions
Q1 Social	Facebook	5000	245	12
Q2 Search	Google	6000	310	18
Q3 Email	Email	7000	425	25
Q4 Display	YouTube	8000	520	32

=COS(PI())

Result: -1

COS(π) = -1, the lowest point of any full cycle. When a campaign reaches this phase (often mid-year for annual cycles), the multiplier shows maximum negative impact. Use this value to downgrade ROI expectations by 100%, signaling time to redirect budget to fresh channels or refresh creative assets before entering the recovery phase.

Common errors

Which COS error are you seeing?

Error	Why it happens	How to fix it
#VALUE!	Passing a text string instead of a numeric angle, such as =COS("30 degrees") or =COS("π/4").	Ensure the argument is numeric. For degree inputs, convert first: =COS(0.5236) for radians, or use a conversion formula like =COS(degrees*PI()/180).
#NAME?	Misspelling the function name, such as =COSINE(0.5) or =COSIN(0.5), or omitting parentheses like =COS 0.5.	Use the exact function name COS with parentheses: =COS(number). Excel and Sheets do not include a COSINE variant.
#REF!	Referencing a cell that has been deleted, such as =COS(A1) when column A is later removed.	Restore the deleted column or edit the formula to reference an existing cell containing a numeric angle value in radians.

Tips and when to use something else

COS expects input in radians, not degrees. Convert degrees using the formula =COS(degrees*PI()/180). For example, =COS(90*PI()/180) returns 0 (the cosine of 90 degrees).
COS values repeat every 2π radians (≈6.28). COS(0)=1, COS(π/2)≈0, COS(π)=-1, COS(3π/2)≈0, COS(2π)=1. Use this cycle to model seasonal and recurring patterns.
For most campaign analysis, ROUND the COS result to 2–4 decimal places to keep spreadsheets readable: =ROUND(COS(angle),4).
If you need only the strength of a cyclical effect (not its sign), wrap COS with ABS: =ABS(COS(angle)) to always get a positive value between 0 and 1.

Related functions

ROUNDROUND returns a number rounded to a specified number of decimal places, using standard rounding rules (0.5 rounds up).ABSABS returns the absolute value of any number, removing the sign to show only magnitude, useful for comparing distances regardless of direction.IFThe IF function returns one value if a condition is true and another (or nothing) if it is false, letting you branch logic in a cell.PRODUCTReturns the product of all numeric values supplied as arguments, multiplying them together into a single result.INTINT rounds any number down to the nearest whole integer, always discarding decimal places and rounding toward negative infinity.

Frequently asked questions

Why does COS(1) return 0.5403 instead of a simple value like 0.5?: COS always interprets its input as radians. One radian ≈ 57.3 degrees, so COS(1) is not the cosine of 1 degree; it's the cosine of 57.3 degrees. To get the cosine of 1 degree, use =COS(1*PI()/180), which returns ≈0.9998.
How do I apply COS to model recurring patterns in campaign performance?: Map your time period (day, week, month) to a radian value using the formula angle = (period_number / total_periods) × 2π. Then apply =COS(angle) to get a multiplier. For monthly cycles, =COS((month_number/12)*2*PI()) gives the seasonal adjustment for that month.
What happens if I pass a very large number to COS, like COS(10000)?: COS cycles every 2π radians, so large inputs wrap around. COS(10000) is equivalent to COS(10000 mod 2π) ≈ COS(2.1), which returns ≈−0.505. The function always produces a valid result between -1 and 1.
Should I use COS or ABS(COS) for campaign adjustment factors?: Use COS alone if you want negative values to represent downturns or reversals in the cycle. Use ABS(COS) if you only care about the strength of the effect, regardless of direction. For budget adjustments, COS is often better because it naturally captures both boost and reduction phases.

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Reviewed 2026-09-17