ASIN

Get the arcsine (inverse sine) of a number and return the angle in radians with ASIN.

Math & Trigonometry
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Excel All versions
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Google Sheets Supported

Spreadsheet editor

Syntax

=ASIN(number) Returns: Number

Arguments

Argument Required Description
number Yes The sine value for which you want the arcsine. Must be between -1 and 1.

About

The ASIN function returns the arcsine of a number, giving you the angle whose sine equals that number. The input must be between -1 and 1 (valid sine values), and the result is an angle in radians between -PI()/2 and PI()/2 (roughly -1.5708 to 1.5708).

Use ASIN when you know a sine ratio and need the original angle. This comes up in physics problems, engineering calculations, and geometry tasks. For example, if a sensor reading gives you a sine value of 0.5, =ASIN(0.5) returns about 0.5236 radians (30 degrees). To see the result in degrees, wrap it with the DEGREES function.

For the inverse of other trig functions, use ACOS for cosine or ATAN for tangent. If you need the forward operation instead, SIN converts an angle to its sine value.

Examples

Boundary values from -1 to 1

Try the full range of valid ASIN inputs. Edit the sine values in column A and watch the angles update. Notice that -1 and 1 map to -90° and 90°.

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Handling out-of-range inputs with IFERROR

See what happens when you pass a value outside -1 to 1. Column B shows the raw #NUM! error, while column C catches it with IFERROR. Change the values in column A to trigger or clear the errors.

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Calculating roof pitch angles

Use ASIN with a ratio to find real-world angles. Each row divides the roof rise by the rafter length, and ASIN converts that ratio into a pitch angle in degrees.

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Watch out for

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Input outside the -1 to 1 range

ASIN(2) returns a #NUM! error because 2 is not a valid sine value. Sine values only exist between -1 and 1.

→ Check that your input falls within -1 to 1 before passing it to ASIN. If you are dividing two lengths to get a ratio, make sure the denominator is the longer side.

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Forgetting the result is in radians

ASIN(0.5) returns 0.5236, which looks odd if you expected 30 degrees.

→ Wrap the formula with DEGREES to convert: =DEGREES(ASIN(0.5)) returns 30.

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Confusing ASIN with ASINH

Using ASINH by mistake gives the inverse hyperbolic sine, which is a different calculation and accepts inputs outside -1 to 1.

→ Use ASIN for standard trigonometric arcsine. ASINH is the hyperbolic version, used in different engineering contexts.

Tips & notes

ASIN is available in every version of Excel and in Google Sheets. The result is always in radians. Pair it with DEGREES when you need the angle in degrees.

Common questions

Does ASIN return degrees or radians?

ASIN always returns radians. To get degrees, wrap it: =DEGREES(ASIN(value)). For example, =DEGREES(ASIN(1)) returns 90.

What values can I pass to ASIN?

Only numbers between -1 and 1. Any value outside that range returns a #NUM! error because no angle has a sine greater than 1 or less than -1.

How is ASIN related to SIN?

They are inverses. SIN takes an angle and returns a ratio, while ASIN takes a ratio and returns the angle. So =ASIN(SIN(x)) gives back x (for x between -PI()/2 and PI()/2).