COSH in Excel: Calculate Symmetric Hyperbolic Curves

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

=COSH(number)

Microsoft describes the required input as a real number. The mathematical relationship is (EXP(x)+EXP(-x))/2. It uses addition of two positive exponential terms, unlike SINH’s difference.

This is not circular cosine and does not automatically interpret a value as a degree angle. Use the dimensionless input defined by the model. English function names, comma separators and decimal-point notation are used in these examples.

Enter −2, −1, 0, 1, 2 in A2:A6. In B2 enter =COSH(A2) and fill down. Expected results, approximately, are 3.762195691, 1.543080635, 1, 1.543080635, 3.762195691.

The real mathematical minimum is one at zero. An input of −1 does not produce a negative result, and a positive result does not reveal the original sign. Preserve source values rather than attempting to infer direction from COSH alone.

=(EXP(1)+EXP(-1))/2
=COSH(1)

Both expected outputs are approximately 1.543080635. EXP is the natural exponential, so replacing it with a base-ten power would change the function.

For another control, =COSH(LN(2)) is approximately 1.25: half the sum of 2 and its reciprocal 0.5. The matching SINH value is 0.75, giving a useful pair for checking a longer expression.

An illustrative curve is specified as y=4*(COSH(x/2)-1). Enter −2, −1, 0, 1, 2 in D2:D6. In E2 enter and fill down:

=4*(COSH(D2/2)-1)

Expected outputs are approximately 2.172322539, 0.510503861, 0, 0.510503861, 2.172322539. Subtracting one makes the response zero at x=0, then multiplication applies the chosen output scale.

Without the subtraction, =4*COSH(D2/2) gives a baseline of four at zero. Parentheses therefore encode a substantive model choice, not merely visual grouping. Label the scale and offset in a reusable workbook so they are not confused.

This is a constructed numerical curve. A real physical interpretation would require an appropriate model, units and assumptions beyond the spreadsheet function itself.

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

Expected result: approximately 1. SINH supplies the related odd function. Replacing subtraction with addition would not be the same identity; at x=1 the sum is approximately 3.762195691 instead.

This check uses modest arguments. For very large values, separately squaring two large nearly equal numbers and subtracting them can lose accuracy or exceed representational limits, even though the symbolic identity remains true.

COSH(−2) and COSH(2) are equal, so the output alone cannot recover the input sign. If a later inverse uses a nonnegative principal branch, retain the original sign separately whenever it matters. Do not assume every forward/inverse pair preserves information that the forward operation discarded.

Check whether an unexpectedly high value is explained by input scaling and exponential growth. Values formatted with few decimals can conceal a meaningful input change. Native extreme-value benchmarks, text coercion and client-specific error displays remain outside this guide’s independently calculated examples.

• Microsoft COSH 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.