What is the difference between degrees and radians?

Degrees divide a circle into 360 parts; radians divide it into 2π parts (~6.28). Radians are standard in mathematics, physics, and APIs because they relate arc length directly to calculus. Most spreadsheet trigonometric functions operate in radians.

Why does SIN(45) return 0.85 instead of 0.707?

Because SIN expects radians, not degrees. The input 45 represents 45 radians (~2,578°), whose sine is ~0.85. For 45 degrees, use =SIN(RADIANS(45)), which returns 0.707 (approximately √2/2).

Can RADIANS handle negative angles or angles larger than 360?

Yes. RADIANS converts any numeric angle. Negative angles return negative radians, and angles >360° convert proportionally—for example, 450° becomes 7.854 radians (2π + π/4), useful for multi-rotation calculations.

How do I visualize radians to understand the output?

A full circle is 2π radians (~6.28). Key angles: 0° = 0 rad, 90° = π/2 rad (~1.571), 180° = π rad (~3.14159), 270° = 3π/2 rad (~4.712). Verify with =DEGREES(RADIANS(90)), which returns 90.

RADIANS function

RADIANS converts an angle in degrees to its equivalent in radians, returning a numeric value useful for trigonometric and circular calculations.

=RADIANS(angle)

Generate a RADIANS formula

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

Arguments

How RADIANS reads its arguments

Argument	Required	Description
angle	Required	A number representing an angle in degrees; can be positive, negative, or zero. Text values and blank cells return #VALUE!.

Returns

A number representing the radian equivalent of the input angle in degrees.

Availability

Excel: All · Google Sheets: Supported

Worked examples

1. Convert campaign rotation angle to radians

Campaign	Channel	Spend	Clicks	Conversions	Angle
EmailQ1	Email	5000	1250	150	45
SocialQ1	Social	3000	900	45	90
DisplayQ1	Display	2000	600	24	180

=RADIANS(F2)

Result: 0.785398

The EmailQ1 campaign uses a 45-degree creative rotation angle. Converting 45 degrees to radians yields approximately 0.785398 radians (π/4), which is the standard unit required by trigonometric functions and most charting libraries for circular positioning and visualization.

2. Convert all campaign angles to radians

Campaign	Channel	Spend	Clicks	Conversions	Angle
EmailQ1	Email	5000	1250	150	45
SocialQ1	Social	3000	900	45	90
DisplayQ1	Display	2000	600	24	180

=RADIANS(F2:F4)

Result: 0.785398, 1.5708, 3.14159

Applying RADIANS to the range F2:F4 converts each campaign's degree angle to radians. The three results—π/4, π/2, and π radians—represent 45°, 90°, and 180° respectively, enabling direct mapping to polar plots and circular performance dashboards where radians are required.

3. Calculate average campaign angle in radians

Campaign	Channel	Spend	Clicks	Conversions	Angle
EmailQ1	Email	5000	1250	150	45
SocialQ1	Social	3000	900	45	90
DisplayQ1	Display	2000	600	24	180

=RADIANS(AVERAGE(F2:F4))

Result: 1.8324

The average of the three campaign angles (45°, 90°, 180°) is 105°. Converting to radians yields 1.8324 radians, useful for determining the mean directional position of campaigns on circular visualizations or analyzing overall rotation distribution across channels.

Common errors

Which RADIANS error are you seeing?

Error	Why it happens	How to fix it
#VALUE!	The angle argument is text (e.g., =RADIANS("45") or a cell containing '45° instead of a numeric 45), or a non-numeric value like TRUE.	Ensure the angle is a pure number. If it's text, convert it: =RADIANS(VALUE(A1)). If it contains a degree symbol, remove it first with SUBSTITUTE or TRIM.
#NAME?	The function name is misspelled (e.g., =RADIAN(45) without the S, or the function is not recognized in your spreadsheet application).	Verify the exact spelling: RADIANS (plural, with an S at the end). Use autocomplete by typing =RA... to confirm your application recognizes it.
#DIV/0!	RADIANS itself cannot produce #DIV/0!, but a formula using its result can if division by zero occurs (e.g., =RADIANS(45)/0 or =SIN(RADIANS(A1))/(A2-A3) where A2 equals A3).	Review arithmetic operations after RADIANS. Verify no denominators are zero. Optionally wrap with IFERROR: =IFERROR(expression, default_value).

Tips and when to use something else

RADIANS and DEGREES are inverses: =DEGREES(RADIANS(45)) returns 45. Use DEGREES to convert radians back to degrees for human-readable output.
Most spreadsheet trigonometric functions (SIN, COS, TAN) require radians, not degrees—always wrap degree inputs: =SIN(RADIANS(30)) returns 0.5, while =SIN(30) returns ~−0.988.
For small angles, radians ≈ degrees × π/180 ≈ degrees × 0.01745. RADIANS performs this calculation automatically with full precision.
If you only need to display or store angles in degrees, skip RADIANS. Use it only when feeding angles into trigonometric functions, circular geometry calculations, or APIs that expect radians.

Related functions

DEGREESConverts an angle measured in radians to degrees, making trigonometric or sensor data more readable and interpretable for practical applications.SINSIN returns the sine of an angle in radians, a decimal value between -1 and 1 representing the trigonometric sine ratio.COSCOS returns the cosine of an angle in radians, producing values between -1 and 1; use it for cyclical calculations and trigonometric analysis.ROUNDROUND returns a number rounded to a specified number of decimal places, using standard rounding rules (0.5 rounds up).

Frequently asked questions

What is the difference between degrees and radians?: Degrees divide a circle into 360 parts; radians divide it into 2π parts (~6.28). Radians are standard in mathematics, physics, and APIs because they relate arc length directly to calculus. Most spreadsheet trigonometric functions operate in radians.
Why does SIN(45) return 0.85 instead of 0.707?: Because SIN expects radians, not degrees. The input 45 represents 45 radians (~2,578°), whose sine is ~0.85. For 45 degrees, use =SIN(RADIANS(45)), which returns 0.707 (approximately √2/2).
Can RADIANS handle negative angles or angles larger than 360?: Yes. RADIANS converts any numeric angle. Negative angles return negative radians, and angles >360° convert proportionally—for example, 450° becomes 7.854 radians (2π + π/4), useful for multi-rotation calculations.
How do I visualize radians to understand the output?: A full circle is 2π radians (~6.28). Key angles: 0° = 0 rad, 90° = π/2 rad (~1.571), 180° = π rad (~3.14159), 270° = 3π/2 rad (~4.712). Verify with =DEGREES(RADIANS(90)), which returns 90.

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Reviewed 2026-09-17