SINH Function in Apple Numbers: Formula, Examples, and Signs

=SINH(0) has an expected result of 0; =SINH(1) has an expected result of about 1.175201. SINH calculates hyperbolic sine for a numeric argument. It is not the same function as SIN, and its input is not an angle in degrees.

Use SINH when a model calls for the hyperbolic sine of a real input, such as the exponential solutions of some differential equations. In ordinary business spreadsheets it is less common than SUM or SIN; do not apply it simply because a cell contains an angle. The figures in this guide are expected results independently calculated from mathematics and cross-checked with Apple’s examples. They are not observations from Numbers running on a device.

Apple’s English Formulas and Functions Help 15.4, checked 2026-10-11 UTC, documents the following exact expression:

=SINH(num)

• num — required: a number value, as Apple labels the argument. It is the input to the hyperbolic sine function. No optional second argument, fallback, or default is documented.
• Argument order: the sole argument goes inside the parentheses; for a cell use =SINH(B2). Enter an initial equals sign in a Numbers formula cell. Formula names are not case-sensitive according to Apple’s overview.
• Regional notation: these examples assume an English-style decimal point (0.5, -0.5). In decimal-comma regions enter numbers using the locale-compatible numeric syntax. Apple’s semicolon rule applies when separating multiple arguments, not to this one-argument function. In another function such as IF, commas in English may become semicolons when the locale uses decimal commas.
• Platform/version qualification: 15.4 is the documentation edition, not a verified first-supported Numbers release. This single-function reference does not establish parity across every Mac, iPhone, iPad, iCloud, or earlier Numbers edition; none of those applications was run during preparation.

Official claims: Apple SINH — syntax, numeric parameter, and examples; Apple functions overview — formula entry and locale separators.

1. Create a blank Numbers document and insert a regular table named InputData (or rename a blank table to InputData). Keep row 1 as headers.
2. Enter Label in A1, Input in B1, and Result in C1. Type the numeric B-column values below; do not copy the descriptions into B.
3. Format column B as Number and column C as Number with at least six decimal places. Cell formatting changes the display, not the underlying stored precision.
4. Type =SINH(B2) in C2. Fill the formula down to C10. Check that copied formulas use B3, B4, and so on, rather than B2 repeatedly.
5. Compare the expected six-decimal figures with your cells. The table below was calculated independently using Python math.sinh and is not a record of Numbers execution. If a displayed value disagrees, confirm whether it is a real numeric input and that the correct function was selected.

Row: 2

A: Label
negative five

B: Numeric input
-5

C: Formula
=SINH(B2)

C: Expected six-decimal output
-74.203211

Row: 3

A: Label
negative two

B: Numeric input
-2

C: Formula
=SINH(B3)

C: Expected six-decimal output
-3.626860

Row: 4

A: Label
negative one

B: Numeric input
-1

C: Formula
=SINH(B4)

C: Expected six-decimal output
-1.175201

Row: 5

A: Label
negative half

B: Numeric input
-0.5

C: Formula
=SINH(B5)

C: Expected six-decimal output
-0.521095

Row: 6

A: Label
zero

B: Numeric input
0

C: Formula
=SINH(B6)

C: Expected six-decimal output
0.000000

Row: 7

A: Label
positive half

B: Numeric input
0.5

C: Formula
=SINH(B7)

C: Expected six-decimal output
0.521095

Row: 8

A: Label
one

B: Numeric input
1

C: Formula
=SINH(B8)

C: Expected six-decimal output
1.175201

Row: 9

A: Label
two

B: Numeric input
2

C: Formula
=SINH(B9)

C: Expected six-decimal output
3.626860

Row: 10

A: Label
five

B: Numeric input
5

C: Formula
=SINH(B10)

C: Expected six-decimal output
74.203211

Refer to another table or sheet

If C2 belongs to a different Numbers table from the inputs, an explicit table reference can help: =SINH(InputData::B2). Apple’s documentation also describes sheet-qualified references in the form Sheet Name::Table Name::B2 when needed. Use the formula editor and click the intended cell instead of manually guessing tokenization for names with spaces. A same-table B2 reference generally needs no table qualifier. Apple’s cell-reference guide provides the syntax and copy/paste rules.

Odd symmetry: a fast sign check

Hyperbolic sine is odd: mathematically, sinh(-x) = -sinh(x). For a worksheet containing -2 in B2 and 2 in B3, the expected values are the same size with opposite signs. A simple validation formula is =SINH(-B2)+SINH(B2), whose mathematically expected value is 0 for ordinary finite inputs. Floating-point implementations may produce a tiny numerical remainder instead of exact equality.

Understand the exponential definition

For a moderate real number x, sinh(x) = (e^x − e^(−x))/2. In Numbers, =(EXP(B2)-EXP(-B2))/2 expresses the identity, so B2=1 gives approximately 1.175201. This is a derivation illustration, not a recommendation to replace SINH: separate exponentials can overflow or lose precision where the built-in function may be preferable. No comparative Apple Numbers precision test was performed.

How SINH relates to its inverse

For a moderate numeric x, =ASINH(SINH(B2)) is mathematically equal to B2; this makes an instructive cross-check because ASINH is the inverse hyperbolic sine. Large magnitudes and machine precision may prevent exact equality in a real spreadsheet. The independently predicted round trip with B2=-1 is approximately −1, not a measured Numbers result.

Compare a similarly named function

With B2=1, =SINH(B2) is about 1.175201, while =SIN(B2) is about 0.841471. The latter treats its numeric argument as a radian angle; SINH is the exponential hyperbolic function, not a degree/radian conversion. Only use RADIANS when the intended function needs an angle in radians.

Decide whether the input is a number before diagnosing a math error

The Apple function reference specifies a numeric argument. Imported CSV values may look numeric while being stored as text; a custom-format display can also obscure precision. Test with a freshly typed number such as 1 first, then inspect the imported input. This guide does not claim any undocumented implicit conversion of text, empty cells, logical values, or dates into a number.

Numerical and version limitations: The mathematical real-valued function accepts all finite real inputs, but its magnitude grows roughly exponentially. Practical floating-point overflow/underflow thresholds, exact spreadsheet errors, and handling of infinities or nonnumbers are not verified in Numbers. Do not claim a universal Numbers maximum x. Specific Apple Numbers error text, implicit coercion, exact large-value limits, behavior of non-finite inputs, and platform-specific differences have not been tested. Small last-digit differences are possible with floating-point calculation and display rounding; do not require exact string equality for approximate examples.

Excel and Google Sheets also document a function called SINH. In ordinary real-number mathematics the function definition is the same, so the example figures are suitable comparison expectations. This does not establish identical application behavior for imported text, rounding, errors, extreme floating-point values, cross-table syntax, or release support. Check these when transferring a spreadsheet.

• Apple Numbers: uses tables as formula-reference units, so another table can be referenced as InputData::B2.
• Excel / Google Sheets: frequently use sheet-centric references such as Sheet1!B2; those are not a Numbers table-qualified reference.
• Google Sheets: consult Google’s official function list for its function signature. For Excel, Microsoft’s official SINH reference documents a one-number argument, but confirm the intended Excel edition separately.
• Regional settings: test the file’s actual decimal and argument separators in the target spreadsheet. The one-argument SINH formula itself has no separator to translate.

• Apple: SINH function — official syntax, argument type and Apple examples. Formulas and Functions Help 15.4, consulted 2026-10-11 UTC.
• Apple: Functions overview — case conventions, formulas, and locale argument separators; consulted 2026-10-11 UTC.
• Apple: Refer to cells in formulas — same-table and cross-table reference forms; consulted 2026-10-11 UTC.
• Apple: Functions Help welcome — general function browser/platform context, not a first-release guarantee; consulted 2026-10-11 UTC.
• Google Sheets function list — cross-application signature existence; consulted 2026-10-11 UTC.
• Microsoft Excel SINH documentation — documented Excel function name and signature, consulted 2026-10-11 UTC. Exact release/locale parity was not tested.

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

For a software-specific comparison: LibreOffice Calc SINH, Apache OpenOffice Calc SINH, Gnumeric SINH. 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.