ASINH Function in Apple Numbers: Formula, Examples, and Domain Rules

=ASINH(0) returns 0; =ASINH(-2.5) has the expected result about −1.647231. Convert a hyperbolic sine measurement back to its real parameter. Unlike ASIN, ASINH accepts any finite real numeric input, including negative values and magnitudes above 1.

Important: Real-valued domain: any real number. Negative inputs yield negative results; zero yields zero. Text entries that only look numeric should be reviewed rather than assumed valid. These are expected mathematical results, not screenshots or observed outputs from an Apple Numbers installation.

Apple’s current English Formulas and Functions Help 15.4 documents the function below. This guide does not establish the first Numbers release supporting it, or certify exact feature parity on all devices and historical versions. The documentation was accessed 2026-10-11 UTC.

=ASINH(num)

One required numeric argument, num, with no optional parameters or default. The domain is all real numbers; Apple describes the argument as a number value.

Enter an equals sign first. Apple prints uppercase function names but allows lowercase names when typed. No second argument, separator, or optional setting is defined for this function. Decimal notation in the examples uses a period, as in 0.5. Apple’s general documentation says that for formulas with multiple arguments, a decimal-comma locale uses a semicolon separator; this particular one-argument formula has no argument separator. Change example constants to the decimal convention accepted by your configured locale, and confirm the stored B-column values are numeric. ASINH official syntax; Apple function entry rules.

Real-valued domain: any real number. Negative inputs yield negative results; zero yields zero. Text entries that only look numeric should be reviewed rather than assumed valid.

1. Open an editable Numbers sheet and add a regular table (or reuse a blank table). Name it InputData to make references unambiguous.
2. Keep the first row as a header, with Label, Input, and Result in columns A, B and C.
3. Enter the exact sample numbers from the table below into B2 downward. Format B and C as Number and show at least six decimal places in C before comparing.
4. Enter =ASINH(B2) into C2. Confirm it references the input number (not its text label).
5. Copy the C2 formula down through the last valid test row. Use the invalid input only as a controlled domain troubleshooting exercise, not as a successful-output test.
6. Compare each cell with the expected numbers below. Last-digit differences can arise from finite precision; do not compare rounded display text as exact mathematical equality.

Row: 2

A: Label
negative ten

B: Input
-10

C: Formula
=ASINH(B2)

C: Expected output (6 decimals)
-2.998223

Row: 3

A: Label
negative two-and-half

B: Input
-2.5

C: Formula
=ASINH(B3)

C: Expected output (6 decimals)
-1.647231

Row: 4

A: Label
negative one

B: Input
-1

C: Formula
=ASINH(B4)

C: Expected output (6 decimals)
-0.881374

Row: 5

A: Label
zero

B: Input
0

C: Formula
=ASINH(B5)

C: Expected output (6 decimals)
0.000000

Row: 6

A: Label
half

B: Input
0.5

C: Formula
=ASINH(B6)

C: Expected output (6 decimals)
0.481212

Row: 7

A: Label
one

B: Input
1

C: Formula
=ASINH(B7)

C: Expected output (6 decimals)
0.881374

Row: 8

A: Label
ten

B: Input
10

C: Formula
=ASINH(B8)

C: Expected output (6 decimals)
2.998223

The figures above were calculated independently with Python’s math.asinh function for the same real inputs. They are predictions, not observations in Numbers. The body values can be entered as constants without any external connection or data import.

Reading a value from another Numbers table

If InputData is a different table on the same sheet, use =ASINH(InputData::B2) rather than a bare B2 where ambiguity could arise. If it is on a different sheet, Apple documents the pattern SheetName::TableName::Cell, for example =ASINH(Sheet 2::InputData::B2). Use the formula editor’s reference selection to avoid mistakes with spaces and headers. Apple reference syntax.

Use signed measurements without losing the sign

Unlike the inverse hyperbolic cosine, ASINH is an odd function: ASINH(-x) = -ASINH(x). If a calibrated sensor produces signed values, a single =ASINH(B2) formula handles both sides of zero. For example, input −2.5 gives an expected result near −1.647231, while +2.5 gives +1.647231.

Validate a model by applying the forward function

For a finite real input x, =SINH(ASINH(x)) should reproduce x within floating-point rounding. Conversely, =ASINH(SINH(2)) should be approximately 2. Do not interpret tiny discrepancies after extensive formulas as evidence of a different mathematical definition.

Normalize readings that span positive and negative ranges

The transformation is often useful as an explanatory example for data with large magnitude spread: it behaves approximately linearly near zero and logarithmically in magnitude for large abs(x). It does not automatically normalize a statistical distribution or make different measurements comparable. Apply domain knowledge before using it as a preprocessing transform.

Calculate the same relationship from logarithms for a manual check

For real x, asinh(x) = ln(x + sqrt(x²+1)). A Numbers expression with the same mathematical form is =LN(B2+SQRT(B2^2+1)). This expanded expression is unstable for sufficiently large negative numbers because subtractive cancellation can occur; prefer ASINH(B2) in the workbook. This is a mathematical cross-check, not a recommendation to substitute the longer formula in production.

Numbers’ exact displayed error wording, numerical underflow/overflow thresholds, and any implicit conversion of nonnumeric cells have not been tested here. Do not infer those implementation details from Python or from another spreadsheet product. The real-domain restrictions in this guide come from Apple’s official function documentation.

Excel documents ASINH(number) for any real number, and Google Sheets documents ASINH(value). These names refer to the same mathematical operation. Functions may differ in coercion, locale display and specific error presentation; no cross-application execution was performed.

• Numbers: ASINH (Apple Formulas and Functions Help 15.4). One argument called num.
• Excel: ASINH (Microsoft’s function reference). Numeric argument is called number.
• Google Sheets: ASINH (Google Docs Editors Help). Numeric argument is called value.

As a portability check, a numeric constant and one argument will avoid table-reference differences. Numbers uses InputData::B2 to disambiguate cross-table references; Excel or Sheets worksheet/cell references use different conventions. No cross-product application executions have been performed for this article. Excel, Sheets and Numbers have their own locale and calculation settings; compare reasonable numeric tolerances, not formatting alone.

ASIN; SINH. These references explain the related mathematical operations in Apple’s documentation.

For syntax details, see Apple’s functions overview, cell-reference formats and argument value types. All linked Apple function pages above were accessible in the English 15.4 documentation during the documentation check. No native Numbers screenshots are included; the guide does not use mock application images.

What happens when the input is negative? A negative input produces an equal-magnitude negative result relative to the positive counterpart.

Does ASINH require an input between −1 and 1? No. That restriction belongs to ASIN, not ASINH.

Are outputs degrees? No. They are inverse-hyperbolic function values, not circular angle measurements. Do not add DEGREES without a separately justified model.

Official documentation: ASINH; Apple Functions Overview; Apple Cell References; Apple Argument Types.

• ACOSH — continue with a related Apple Numbers calculation.
• ATANH — continue with a related Apple Numbers calculation.
• COSH — continue with a related Apple Numbers calculation.
• SINH — continue with a related Apple Numbers calculation.
• TANH — continue with a related Apple Numbers calculation.

For a software-specific comparison: LibreOffice Calc ASINH, Apache OpenOffice Calc ASINH, Gnumeric ASINH. A shared name does not establish identical argument, error or version behaviour.

The linked official function documentation was reviewed on October 12, 2026. Apple’s Formulas and Functions Help 15.4 identifies the documentation edition, not a minimum Numbers release or a guarantee of historical platform parity. Selected worked examples were checked using independent mathematical or text-processing models; results are expected values, not observations from the spreadsheet application. Native Apple Numbers execution was not performed. Undocumented coercion, exact error messages and platform-specific behaviour remain unverified.

View reproducible example inputs and independent check results. This record is not a native spreadsheet test log.