ASINH in Google Sheets: Transform Signed Values and Reverse the Scale

• Introduced: first service launch date is not established by the official history reviewed; no numbered desktop introduction is assigned.
• Availability: documented in the rolling Google Sheets service. Examples use ordinary web-spreadsheet numeric cells; other clients and imported files are not separately certified.
• Checked: October 14, 2026; official ASINH reference. Documentation and independent calculations, without native Sheets execution.

=ASINH(value)

Google defines one input value for the inverse hyperbolic sine. It is different from ASIN, the inverse circular sine: a source of 2 is suitable for the real ASINH model but outside ASIN’s −1-to-1 domain.

Use English function names and adapt separators to the spreadsheet locale. No degree conversion is implied by these numeric model inputs. The help’s broad complex-number note is not used to claim that Sheets lacks separate complex-number functions; this article covers the real-valued operation.

Enter −5, −2, 0, 2, 5 in A2:A6. In B2 enter =ASINH(A2) and fill down. Expected outputs are approximately −2.312438341, −1.443635475, 0, 1.443635475, 2.312438341.

The sign survives the transformation. The output is not proportional to the input: moving from 2 to 5 does not multiply the transformed value by 2.5. Preserve the source column rather than treating the transformed number as the same quantity under a different format.

=SINH(ASINH(5))
=ASINH(SINH(-2))

Expected results are approximately 5 and −2. SINH is the forward partner. These moderate values illustrate the real inverse relationship without an ambiguous circular phase choice.

Keep full intermediate precision. Retyping a shortened displayed answer before applying the inverse can introduce an avoidable round-trip difference.

Define a fictional transformed value as ASINH(x/7). Put −35, −14, 0, 14, 35 in D2:D6 and use:

=ASINH(D2/7)

The expected sequence is −2.312438341, −1.443635475, 0, 1.443635475, 2.312438341. Dividing by seven makes the argument relative to an explicit reference scale. If x carries units, the scale should carry compatible units.

With those unrounded results in E2:E6, =7*SINH(E2) filled down reconstructs approximately −35, −14, 0, 14, 35. Omitting the factor seven during reconstruction would recover the normalized values, not the original source.

For positive input 2, =LN(2+SQRT(2^2+1)) is expected to return 1.443635475. The formula exposes the mathematics using LN, but is not a universal replacement for the dedicated function.

For large negative arguments, the expanded sum can involve cancellation, and squaring can create unnecessarily large intermediates. An algebraic identity does not guarantee identical native precision or overflow handling.

Check function family, scale and stored numeric type before changing the transformation. A nonpositive value is not automatically invalid for ASINH as it would be for an ordinary real logarithm. The small controls do not establish the native limits of the service, every text coercion or a suitable statistical model for an unexamined dataset.

• Google ASINH help.
• Editorial testing standards.

Inputs are fictional. Approximate numerical answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Complete coercion, extreme-magnitude and cross-client behavior remain untested.