5 Ways to Calculate Inverse Sine in Microsoft Excel

Are you a student of mathematics or working on a data analytics project that deals with trigonometry? Wondering if you can use Excel to calculate the inverse sine function? Yes, you can!

Besides data analytics and visualization, Excel is also a suitable software to solve problems of mathematics and statistics. Microsoft Excel comes with more than 50 formulas to solve mathematical and trigonometrical problems.

Besides built-in formulas, you can create custom functions and programs to do inverse sine in Excel using Excel VBA, Power Query, Office Scripts, etc.

If you need to solve a complex problem involving arcsine or you just want to build an inverse sine calculator, you’ve come to the right place.

Keep reading to explore more about the sine inverse function, when you might need it, and several intuitive methods to do sine inverse in Excel.

What Is Sine Inverse Function?

The inverse sine function is the mathematical operation to find the angle whose sine value matches a given number. It’s commonly denoted as sin^(-1) or arcsin. In simple language, it’s the inverse of the sine function.

For a given value between -1 and 1, the sine inverse function returns the angle (in radians or degrees) whose sine equals that value. Mathematically, if y = sin^(-1)(x), then sin(y) = x.

You may want to note that the sine inverse function has a principal value between -π/2 and π/2 radians or -90° and 90° in degrees.

Reasons to Calculate Sine Inverse

Here’s why you might want to do an inverse sine calculation:

  1. You want to find the angle in degrees or radians whose sine value matches a given number.
  2. Sine inverse calculation helps you in solving problems in physics, engineering, and math that involve angles and waves.
  3. If you’re working on designing and analyzing mechanical systems with rotating components you might need to calculate inverse sine sometimes.
  4. This function also helps in understanding oscillatory behavior and periodic phenomena in different disciplines.
  5. If you’re into computer graphics and game development to manipulate angles and rotations
  6. Inverse sine is also important in navigation and astronomy for celestial calculations and positioning.
  7. In signal processing, when you need to calculate phase angles to understand waveforms, you often need to calculate arcsine.

So far, you learned the definition of inverse sine and its applications in mathematics and real-life scenarios. Now, explore below how to do inverse sine in Excel.

Calculate Inverse Sine Using a Formula

The ASIN function in Excel formulas helps you to calculate inverse sine in Excel. If you got a right-angle triangle, the sine value of that angle will be the ratio of the length of the opposite and hypotenuse.

The sine function oscillates between -1 and 1 as the angle changes from 0 to 90 degrees (or 0 to π/2 radians) in a right-angled triangle. Thus, you can calculate the sine of any given number between 1 and -1. For example, 0.7.

The sine inverse or arcsine is the angle between the opposite and hypotenuse. If the sine is the given number 0.7, then its arcsine is 0.775397496610753, and the angle is in radians.

If you convert it to degrees, which is a more common unit for angles, you get 44.4270040008057° or 44.42°.

Suppose you got a table of a right angle triangle height and hypotenuse values. You must find the corresponding sine inverse values. Find below the quick steps to use the ASIN function in Excel:

Using ASIN to do inverse sine in Excel
  1. Highlight the first cell of the table where you need to populate the arcsine value.
  2. Double-click and enter the following formula:
=ASIN(A2/B2)
  1. Hit Enter and you get the arcsine value in radians.
Getting ASIN value in degrees
  1. If you need to get the sine inverse values in degrees, enter the following formula instead:
=DEGREES(ASIN(A2/B2))
  1. The above formulas generate values in multiple decimal numbers. Use the Decrease Decimals or Increase Decimals tool in the Home tab on the Excel ribbon menu to reduce or increase the decimal numbers.
Decreasing decimals of arcsine
  1. Once you’re done generating the sine inverse value for the first cell in the table, use the fill handle to calculate the sine inverse for the rest of the sine values.
Using the fill handle to calculate sine inverse in Excel

Need to modify the above formula so it works in your own worksheet? Follow these instructions:

  • A2 should be the height of the right-angle triangle
  • B2 should be the hypotenuse of the triangle

Suppose, you simply have the ratios of opposite sides and hypotenuse of a few right-angle triangles and need to calculate the inverse sine in Excel. Here’s how to put the ASIN formula in the target cell:

=DEGREES(ASIN(0.5))

In the above formula, 0.5 is the sin number given in the mathematical engineering problem.

Calculate Sine Inverse Using Power Query

In Power Query, you can utilize the Number.ASIN and Number.PI functions to calculate sine inverse from sine numbers. Find below the detailed instructions:

  1. Highlight the entire column where you got the sine numbers that need conversion to inverse sine.
  2. Click the Data tab and then click the From Table/Range button.
  3. Now, click OK on the Create Table dialog box.
Load data to Power Query
  1. Your dataset will load into the Power Query Editor tool.
  2. There. click the Add Column button on the ribbon menu and click Custom Column.
  3. In the New column name field, type Arcsine Radians.
  4. Inside the Custom column formula field, type the following formula:
=Number.Asin([Sine values])
  1. Click OK to add the new column with inverse sine values in radians.
Apply new column formula
  1. To convert the radians value to degrees, again add a custom column and use the following formula:
Converting radians to degrees
=[Arcsine Radians]*(180/Number.PI)
  1. You should now see the calculated column for inverse sine in degrees.
How to do inverse sine in Excel using Power Query
  1. Click File and choose the Close & Load To option.
Import data to the worksheet
  1. On the Import Data dialog box, choose the Existing worksheet option and select the cell where you want to import the columns.
inverse sine calculator

How to Do Inverse Sine in Excel Using Power Pivot

In Power Pivot, you can perform the inverse sine (arcsine) calculations using the DAX (Data Analysis Expressions) language.

Adding data to the data model in the power pivot

Suppose you have already imported your data into Power Pivot. If not, you can go to the Power Pivot menu by clicking on the Power Pivot tab and then selecting Add to Data Model to import your data.

Once you added the source data column to Power Pivot, follow these steps:

  1. You should now see the Power Pivot window on the workbook.
  2. Double-click the Add column text and rename it to Arcsine Degrees.
  3. Click the formula bar and copy and paste the following formula into it:
=ASIN([Sine])*(180/PI())
  1. Select the calculated column.
  2. Right-click and choose Copy.
  3. Close the Power Pivot window.
Calculating inverse sine in power pivot
  1. Select the cell where you’d like to paste the column from Power Pivot.
  2. Hit Ctrl + Alt + V and choose CSV.
Select CSV
  1. Click OK to import the calculated column in the worksheet.
Imported power pivot columns to the worksheet

You’ll find the Power Pivot as a tab in modern Excel desktop apps like Excel for Microsoft 365, Excel 2021, Excel 2019, etc. In older Excel desktop editions, you’ll find Power Pivot in Developer > Excel Add-ins.

Use Excel VBA to Calculate Sine Inverse in Excel

Don’t want to manually calculate the arcsine values for a large dataset? Use the following Excel VBA scripts. Also, you’ll find the steps to use the code effortlessly:

  1. Click the Developer tab on the Excel ribbon menu.
  2. Select the Visual Basic button to bring up the Excel VBA Editor interface.
Open Excel VBA Editor
  1. Click Insert and choose Module.
  2. Inside the new module, copy and paste the following Excel VBA script:
Sub Calculatearcsin()
    Dim ws As Worksheet
    Dim heightRange As Range, hypotenuseRange As Range, resultRange As Range
    Dim i As Long

    Set ws = ThisWorkbook.Worksheets("Sheet2")
    
    Set heightRange = ws.Range("A2:A4")
    Set hypotenuseRange = ws.Range("B2:B4")
    Set resultRange = ws.Range("C2:C4")
    
    For i = 1 To heightRange.Rows.Count
        If IsNumeric(heightRange.Cells(i, 1).Value) And IsNumeric(hypotenuseRange.Cells(i, 1).Value) And hypotenuseRange.Cells(i, 1).Value <> 0 Then
            resultRange.Cells(i, 1).Value = WorksheetFunction.Degrees(WorksheetFunction.Asin(heightRange.Cells(i, 1).Value / hypotenuseRange.Cells(i, 1).Value))
        Else
            resultRange.Cells(i, 1).Value = "Error: Invalid input"
        End If
    Next i
End Sub
  1. Click the Save button.
  2. Close the Excel VBA Editor tool.
Create arcsin calculation in VBA
  1. Hit Alt + F8 to open the Macro dialog box.
  2. There, select the Calculatearcsin macro and click Run to execute the VBA script.

If you got a few right-angle triangle heights from A2:A4 and hypotenuse in B2:B4, then the above code will automatically calculate the arcsine values in degrees in the cell range C2:C4.

If your dataset is bigger and the values are in different cell ranges than those mentioned in this tutorial, you must modify the script. Here are the instructions for script modifications:

  • "A2:A4": This cell range should contain triangle height data, modify it accordingly.
  • "B2:B4": Similarly, you should enter triangle hypotenuse data in this cell range or modify it according to your own dataset.
  • "C2:C4": This is the cell range where Excel will populate inverse sine values. If needed, modify this cell range as well.
  • "Sheet2": It’s the worksheet on which the macro would work. Change it according to your workbook.

Suppose, you only got sine values in your dataset and you need to get the corresponding sine inverse values or angles. Here’s the VBA script you can use:

Sub CalculateInverseSineInDegrees()
    Dim ws As Worksheet
    Dim sineRange As Range, resultRange As Range
    Dim i As Long
    
    Set ws = ThisWorkbook.Worksheets("Sheet2")
    Set sineRange = ws.Range("A2:A10")
    Set resultRange = ws.Range("B2:B10")
    
    For i = 1 To sineRange.Rows.Count
        If IsNumeric(sineRange.Cells(i, 1).value) Then
            Dim value As Double
            value = sineRange.Cells(i, 1).value
            If value >= -1 And value <= 1 Then
                resultRange.Cells(i, 1).value = WorksheetFunction.Degrees(WorksheetFunction.Asin(value))
            Else
                resultRange.Cells(i, 1).value = "Error: Value not in range [-1, 1]"
            End If
        Else
            resultRange.Cells(i, 1).value = "Error: Invalid input"
        End If
    Next i
End Sub
VBA script for sine to arcsine

In the above code, the cell range "A2:A10" has the sine numbers to be converted to inverse sine. The inverse sine calculator will populate results in "B2:B10". The code calculates inverse sine in Excel in degrees.

Arcsine by VBA in degrees

Create an Inverse Sine Calculator Using Office Scripts

Do you often need to calculate the sine inverse in Excel for the web app by following manual steps for the ASIN function?

Stop wasting time by learning how to do inverse sine in Excel using Office Scripts. The method also works on Excel for Microsoft 365 desktop app when connected to the internet. Here are the steps you must follow:

Using Office Scripts to calculate sine inverse
  1. Click the Automate tab in the Excel ribbon.
  2. Select the New Script button.
  3. In the Code Editor interface, copy and paste the following script:
function main(workbook: ExcelScript.Workbook) {
	let selectedSheet = workbook.getActiveWorksheet();
	// Set range C2 on selectedSheet
	selectedSheet.getRange("C2").setFormulaLocal("=DEGREES(ASIN(A2/B2))");
	// Paste to range C3:C4 on selectedSheet from range C2 on selectedSheet
	selectedSheet.getRange("C3:C4").copyFrom(selectedSheet.getRange("C2"), ExcelScript.RangeCopyType.all, false, false);
	// Set number format for range C2:C4 on selectedSheet
	selectedSheet.getRange("C2:C4").setNumberFormatLocal("0.00");
}
  1. Click the Save script option to save your script.
  2. Hit the Run button to execute the Office Scripts code.

If you got height and hypotenuse values in cells A2:B4, then the above code will populate inverse sine in degrees in the cell range C2:C4. The code will also reduce the decimals to two digits after the decimal symbol.

Here’s how you should personalize the code according to your dataset:

  • Change all the occurrences of the cell C2 to the first cell in your dataset where you’d start the sine inverse calculation.
  • Modify the code element A2/B2 to an appropriate syntax that represents height by hypotenuse.
  • The code copies the formula from C2 to C3:C4. If you performed the same in another cell, like D2, then C3:C4 should be D3:D4 or according to the length of column D.

If you only have the sine values in your worksheet, then use the following Office Scripts code:

function main(workbook: ExcelScript.Workbook) {
	let selectedSheet = workbook.getActiveWorksheet();
	// Set range B2 on selectedSheet
	selectedSheet.getRange("B2").setFormulaLocal("=DEGREES(ASIN(A2))");
	// Paste to range B3:B4 on selectedSheet from range B2 on selectedSheet
	selectedSheet.getRange("B3:B4").copyFrom(selectedSheet.getRange("B2"), ExcelScript.RangeCopyType.all, false, false);
}

In this script, "B2" is the destination cell for the calculation and A2 is the source cell for sine values.

Considering you’ll calculate the sine inverse right next to the column of the source data, "B3:B4" is the cell range where the above code will copy and paste the formula from B2.

📝 Note: Office Scripts is only available when you get Microsoft 365 Business Standard or better subscriptions. Most Microsoft 365 plans offered by businesses come with Office Scripts. If you don’t see the Automate tab in your Excel for the web or Excel for Microsoft 365 desktop app, you can’t use the feature.

Conclusions

Calculating inverse sine in Excel is a value-adding skill for you if you’re likely to work on Excel projects that’ll deal with mathematics, trigonometry, engineering, sound waves, etc.

Try the methods mentioned above using your own datasets and you’ll see how easy it’s to implement the skill in real-life scenarios.

Don’t forget to write a comment in the comment box below about your experience in implementing the above methods.

About the Author

Bipasha Nath

Bipasha Nath

Bipasha is a technical content writer with 10+ years of experience in the technology industry. She previously worked in a SaaS software development company focused on SharePoint, OneDrive, Word, Excel, Word solutions.

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John MacDougall

I’m John, and my goal is to help you Excel!

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