If you want to find the angle whose sine equals a given value in Google Sheets, the ASIN function is what you need. You pass it a number between -1 and 1, and it returns the matching angle in radians.
In this article, I’ll show you how ASIN works, where its limits are, and four short examples you can drop into your own sheet.
ASIN Function Syntax in Google Sheets
The ASIN function takes a single input.
=ASIN(value)
- value is the sine value you want the angle for. It must be between -1 and 1, inclusive.
One number in, one angle out.
When to Use ASIN Function
Here are a few times ASIN earns its place.
- Recovering an angle from a known sine ratio.
- Trigonometry and geometry problems that start from a side ratio.
- Physics or engineering formulas that rely on inverse trig functions.
- Reversing a SIN result to get back to the original angle.
Example 1: Arcsine of a Column of Values
Let’s start by running ASIN down a column of values.
Below is the dataset with a single column of numbers between -1 and 1.
The goal is to get the arcsine of each value in column A.
Here is the formula:
=ASIN(A2)
ASIN returns the angle in radians, always between -pi/2 and pi/2. So -1 returns about -1.5708, 0 returns 0, and 1 returns about 1.5708. Negative inputs give negative angles.
Pro Tip: To run ASIN on a whole column at once, wrap it in ARRAYFORMULA: =ARRAYFORMULA(ASIN(A2:A6)). One formula instead of filling down.
Example 2: Convert the Result to Degrees
Radians work for math, but degrees are easier to recognize.
Below is the dataset, a column of common sine values.
The goal is to read each arcsine as an angle in degrees.
Here is the formula:
=DEGREES(ASIN(A2))
DEGREES converts the radian output into degrees. So 0.5 returns 30 degrees, about 0.7071 returns 45 degrees, and 1 returns 90 degrees. These are the familiar angles from a trig table.
Example 3: Boundary Inputs Return Plus or Minus pi/2
This example shows what happens at the edges of what ASIN accepts.
Below is the dataset, running from -1 up to 1.
The goal is to see the output at the two extreme valid inputs.
Here is the formula:
=ASIN(A2)
The lowest valid input is -1, which returns about -1.5708 (that’s -pi/2). The highest is 1, which returns about 1.5708 (pi/2). Anything outside the -1 to 1 range returns an error instead of a number.
Pro Tip: If your data might stray outside -1 to 1, guard it with an IF check like =IF(ABS(A2)<=1, ASIN(A2), “out of range”) so one bad value doesn’t break the column.
Example 4: Round Degrees for a Clean Angle
Stacking ASIN, DEGREES, and ROUND together gives you a tidy whole-degree result.
Below is the dataset, a couple of sine values to convert.
The goal is to return each angle in degrees, rounded to two decimal places.
Here is the formula:
=ROUND(DEGREES(ASIN(A2)), 2)
This nests three functions. ASIN finds the angle in radians, DEGREES converts it, and ROUND trims it. So 0.5 returns 30 and about 0.8660 returns 60, clean angles with no trailing decimals.
Tips & Common Mistakes
- Inputs outside -1 to 1 cause an error. Sine only ranges from -1 to 1, so ASIN rejects anything beyond that. Check your data if values might fall outside the range.
- The result is in radians. Don’t read the raw output as degrees. Wrap it in DEGREES when you need a degree angle.
- Don’t mix up ASIN with ASINH. ASIN is the regular inverse sine bounded to -1 through 1. ASINH is the hyperbolic version that accepts any real number.
ASIN is a one-argument function that returns the angle whose sine equals your value, always in radians between -pi/2 and pi/2. You saw how to run it down a column, convert to degrees, handle the boundaries, and round for a clean result.
Stay inside the -1 to 1 range and ASIN is simple to work with.
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