SINH in Excel: Model Signed Hyperbolic Growth with Explicit Scaling

• Introduced: original introduction release and first numeric build are not established by the official history reviewed.
• Availability: the official SINH 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.

=SINH(number)

The required argument is a real number. The mathematical definition is (EXP(x)-EXP(-x))/2. EXP supplies the natural exponential. The subtraction makes SINH an odd function: reversing the input sign reverses the result sign.

Do not apply a degrees-to-radians conversion merely because the name contains SIN. The input should be the dimensionless quantity required by the particular hyperbolic model. Examples use English function names, decimal points and comma separators where needed.

Enter −2, −1, 0, 1, 2 in A2:A6 and =SINH(A2) in B2, filled down. Expected outputs, approximately:

Unlike circular sine, these results are not bounded between −1 and 1. A value above one is consistent with the function’s definition and is not itself a spreadsheet error.

=(EXP(1)-EXP(-1))/2
=SINH(1)

Both expected outputs are approximately 1.175201194. The formula is a mathematical cross-check, not a recommendation to replace the dedicated function for every input. Subtracting nearly equal exponentials near zero can lose relative precision, and extreme exponentials can exceed a finite representation.

Another useful exact mathematical control is =SINH(LN(2)), expected to be approximately 0.75. EXP(LN(2)) corresponds to 2 and its reciprocal is 0.5; their half-difference is 0.75. Keep unrounded intermediate values for this check.

Suppose a constructed response is defined as y=6*SINH(x/2). Enter x values −2, −1, 0, 1, 2 in D2:D6 and use:

=6*SINH(D2/2)

Expected outputs are approximately −7.051207162, −3.126571833, 0, 3.126571833, 7.051207162. Dividing by two changes the argument scale; multiplying by six changes the response scale. Those two roles are not interchangeable.

A source x of 2 gives argument 1. If x has units, the divisor must provide a compatible reference scale so the function receives the intended dimensionless input. This formula illustrates an explicitly assumed model; it does not establish a physical law or fit observed data.

For input 1:

=COSH(1)^2-SINH(1)^2

The expected result is approximately 1. COSH is the corresponding hyperbolic cosine. The minus sign matters: the familiar circular identity uses a different combination.

You can also recover SINH(1) as TANH(1)*COSH(1) for ordinary finite values. Such identities help detect a mistaken use of SIN or COS in a hyperbolic expression but do not guarantee identical last-bit rounding in all formulations.

Check the sign, input scaling and whether the task actually specifies a hyperbolic relationship. A negative input should have a negative mathematical SINH, while zero gives zero. An unexpectedly enormous value may come from an oversized exponent rather than a simple sign error.

The cited definition accepts real inputs, but this guide does not certify native overflow thresholds, tiny-input relative accuracy or arbitrary text coercion. Keep small signed controls and original untransformed inputs beside any larger model.

• Microsoft SINH 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.