ASINH in Excel: Invert Hyperbolic Sine and Preserve Signed Inputs

• Introduced: First introduction version is not established by the official history reviewed.
• Availability: official help 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; official ASINH reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=ASINH(number)

The one argument is required. Microsoft permits any real number and defines the function by its inverse relationship with SINH. It is different from ASIN, which inverts a circular sine ratio and has the narrower −1-to-1 input domain.

Examples use English function names, comma argument separators and decimal points. The input is a numeric model value, not automatically a degree angle. Do not apply a degree conversion merely because the function name contains sine.

Enter −3, −1, 0, 1, 3 in A2:A6. In B2 enter =ASINH(A2) and fill down.

Opposite inputs yield opposite outputs. The result is not restricted to an angle interval such as −90 to 90 degrees. Keep the function family and input interpretation explicit.

For the value 3, compare:

=SINH(ASINH(3))
=ASINH(SINH(-1))

Expected results are approximately 3 and −1. SINH is monotonic on the real numbers, so its real inverse preserves sign rather than selecting one of several circular phases.

Use unrounded intermediate results for reconstruction. Retyping only the nine displayed decimal places changes the input to the second calculation and can create an avoidable discrepancy.

Suppose a fictional measure is transformed as ASINH(x/4). Enter source values −12, −4, 0, 4, 12 in D2:D6, and use:

=ASINH(D2/4)

Expected transformed values are −1.818446459, −0.881373587, 0, 0.881373587, 1.818446459. The scale of four is an explicit modeling choice. It changes how source magnitudes map to the transformed scale; it is not a formatting option.

If E2 contains the unrounded transformed result, reconstruct the source in F2 with =4*SINH(E2). Filled down, the expected recovered values are approximately −12, −4, 0, 4, 12. Store the scale beside the data so a later reader can reverse the same transformation.

For a moderate positive input such as 3, =LN(3+SQRT(3^2+1)) gives the same expected value 1.818446459. LN and SQRT expose the mathematical construction.

For large negative inputs, the expanded expression can subtract nearly equal magnitudes inside the logarithm. Squaring a very large input can also create an overflowing intermediate. The identity does not justify replacing the dedicated ASINH function in every precision-sensitive workbook.

Check whether the intended operation is ASIN or ASINH and whether a scale was applied exactly once. Zero is valid here, so rejecting all nonpositive inputs would impose an unrelated logarithm rule. Conversely, mathematical permission for any real number does not certify every text coercion or extreme floating-point value.

• Microsoft ASINH reference.
• Editorial testing standards.

Worked inputs are fictional. Decimal answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.