SINH in Google Sheets: Calculate a Signed Hyperbolic Response

• Introduced: original service launch date is not established by the official history reviewed; Sheets has no corresponding numbered desktop release in this guide.
• Availability: documented in the rolling Google Sheets service; examples use an ordinary web spreadsheet and numeric cells.
• Checked: October 14, 2026; official SINH reference. Documentation and independent calculations, without native Sheets execution or broader client certification.

=SINH(value)

Google identifies the input as a real value. Mathematically, SINH(x) equals (EXP(x)-EXP(-x))/2. The two exponentials make this a different operation from SIN’s periodic angle ratio.

Do not add a degree conversion automatically. A hyperbolic model should specify its argument, often as a dimensionless ratio of a quantity to a reference scale. The examples use ordinary finite real numbers, English function names and decimal-point notation.

The help page’s broad wording about complex numbers is not used here to claim that Sheets lacks separate complex-number functions. The scope is this real-valued SINH operation.

Enter −1.5, −0.5, 0, 0.5, 1.5 in A2:A6. In B2 enter =SINH(A2) and fill down. Expected values are approximately −2.129279455, −0.521095305, 0, 0.521095305, 2.129279455.

The signs reverse symmetrically. A magnitude above one is valid and shows why interpreting SINH as a bounded circular sine would be incorrect. Keep the original numeric argument beside the response when comparing these results.

=(EXP(0.5)-EXP(-0.5))/2
=SINH(0.5)

Both expected outputs are approximately 0.521095305. EXP uses Euler’s base e, not base ten.

For another control, =SINH(LN(3)) is approximately 1.333333333: half the difference between 3 and 1/3. The identity is mathematical reasoning, not a benchmark claiming identical native rounding for every formulation.

Define an illustrative model y=4*SINH(x/3). Enter x values −3, −1.5, 0, 1.5, 3 in D2:D6. In E2 enter:

=4*SINH(D2/3)

Fill down. Expected outputs are approximately −4.700804775, −2.084381222, 0, 2.084381222, 4.700804775. Division by three changes the argument; multiplication by four changes the response amplitude. These operations cannot be moved across SINH as though it were a linear function.

If x has units, the reference scale must carry compatible units so the argument has the intended meaning. This is a constructed response, not a claim that any observed process must follow hyperbolic growth. Preserve the source and parameter definitions when adapting it.

At input 0.5:

=COSH(0.5)^2-SINH(0.5)^2

Expected result: approximately 1. COSH is the corresponding hyperbolic cosine. The subtraction distinguishes this identity from the circular sine/cosine identity.

TANH(0.5)*COSH(0.5) also reconstructs SINH(0.5) for ordinary finite values. Use these controls to catch a mistaken function family, while allowing a sensible numerical tolerance rather than demanding exact stored equality.

A hand-built exponential difference can subtract nearly equal values near zero and can involve extremely large intermediates elsewhere. The dedicated function should not be replaced casually on the assumption that every algebraically equivalent expression is equally stable.

Inspect the sign and scale when a response is unexpectedly large. Native overflow thresholds, relative accuracy near zero and arbitrary text coercion are not established by these small independent examples. Check the actual file for precision-critical applications and keep the input values available for diagnosis.

• Google SINH help.
• Editorial testing standards.

Worked inputs are fictional and outputs independently calculated. Approximate values are rounded mathematical expectations, not captured native results. Imported types, extreme magnitudes and a complete error/coercion matrix remain outside the tests.