ASIN in Excel: Recover the Principal Angle from a Sine Ratio

• Introduced: original introduction release and first numeric build are not established by the official history reviewed.
• Availability: the official ASIN reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026. Documentation and independently calculated finite-value examples; no native Excel execution or broader platform certification.

=ASIN(number)

Microsoft requires a number from −1 through 1, including both endpoints. The result is in radians between −PI()/2 and PI()/2. Multiply the output by 180/PI() or use DEGREES for degrees.

The permitted input interval and chosen output interval are different concepts. A positive sine ratio does not establish which of all possible angles originally produced it. ASIN selects one representative according to its principal branch.

Enter ratios −1, −0.5, 0, 0.5, 1 in A2:A6. In B2 enter and fill down:

=ASIN(A2)*180/PI()

Expected degree results: −90, −30, 0, 30, 90. In radians, the middle positive result is approximately 0.523598776.

Do not multiply A2 by PI()/180: these inputs are already ratios. Unit conversion belongs to the returned angle. The examples use English function names and comma separators where multiple arguments occur.

Suppose a constructed right triangle has opposite side 5 and hypotenuse 13 in the same unit. Use:

=ASIN(5/13)*180/PI()

Expected angle: approximately 22.619864948 degrees. The ratio is dimensionless and within the domain. SIN of the corresponding radian angle reconstructs approximately 5/13, or 0.384615385.

The denominator is the hypotenuse, not the adjacent side. A zero denominator makes the ratio invalid before ASIN is evaluated. A side longer than the hypotenuse produces a ratio above one and contradicts this right-triangle model.

=ASIN(SIN(150*PI()/180))*180/PI()
=ASIN(SIN(30*PI()/180))*180/PI()

Both expected outputs are 30. The original 150-degree angle cannot be recovered from the sine value alone. Within a 0-to-180-degree context, 30 and 150 are two angles sharing sine 0.5; choosing between them requires additional information.

Do not call the round trip incorrect simply because it fails to reproduce every starting angle. It follows the documented principal range. Preserve source angles or signed coordinates when full direction is part of the task.

Put candidate ratios 0.6, 1, 1.02, −1.02 in D2:D5. In E2 use:

=IF(ABS(D2)<=1,ASIN(D2)*180/PI(),"Review ratio")

Expected outputs for these scalar numeric controls: approximately 36.869897646, 90, Review ratio, Review ratio. The guard marks out-of-domain values instead of quietly changing them to an endpoint. It is not a general promise about lazy evaluation in every array or imported-expression context.

A value displayed as 1.00 can still be stored slightly above one. Inspect the underlying value and the calculation that produced it. Rounding or clipping may be justified by a particular measurement policy, but ASIN does not supply that policy automatically.

The official page states the input domain but does not provide an exhaustive error/coercion table. This guide therefore distinguishes invalid real inputs without assigning unverified native error labels to all of them. Test actual source types and workbook behavior separately when migrating data.

Keep angles and ratios in separately labelled columns. Use tolerances for numerical inverse checks, rather than demanding bit-for-bit equality from every computed fraction and transcendental result.

• Microsoft ASIN reference.
• Editorial testing standards.

Numerical outputs are independent mathematical expectations, rounded where stated. Product-specific syntax and scope come from the cited reference. Native error/coercion matrices and extreme-value precision remain untested.