CSCH in Excel: Calculate Hyperbolic Cosecant and Check Zero

• Introduced: Microsoft marks the function as introduced in Excel 2013. Version-marker reference.
• Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2019 for Mac, Excel 2016.
• Checked: October 14, 2026; official CSCH reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=CSCH(number)

The single argument is required. Microsoft documents a magnitude below 2^27, #NUM! outside that restriction and #VALUE! for nonnumeric input. Its current Applies To list differs slightly from neighboring function pages; the availability section reproduces this function’s own list rather than filling gaps by assumption.

The help describes a hyperbolic angle in radians. In the explicitly defined response models below, the numeric argument is a dimensionless ratio. Apply an angle conversion only when the source model actually supplies an angle in degrees.

Enter −2, −0.5, 0.5, 1, 2 in A2:A6 and fill =CSCH(A2) down. Expected values are approximately −0.275720565, −1.919034751, 1.919034751, 0.850918128, 0.275720565.

The output can be either smaller or larger than one in magnitude. It approaches zero as the input magnitude increases, while its magnitude grows near zero. Do not import the output bounds of circular CSC into this hyperbolic function.

=1/SINH(1)
=CSCH(1)

Both expected results are approximately 0.850918128. SINH preserves sign, so reciprocal values do too. At −1, the expected result is approximately −0.850918128.

For an additional logarithm-based control, =CSCH(LN(2)) is expected to give 1.333333333, because SINH(LN(2)) equals 0.75. Keep the exact formula instead of retyping a rounded logarithm.

Define a fictional response y=6*CSCH(x/2) for positive x. Enter 1, 2, 4 in D2:D4 and use:

=6*CSCH(D2/2)

Expected results are approximately 11.514208508, 5.105508769, 1.654323389. The input divisor and output multiplier have distinct effects. Moving the six inside CSCH would change the model rather than merely its display.

The selected positive domain avoids the singularity and produces positive responses. A fitted use would need its own reasons for this form and parameter scale; the function name alone does not validate a physical interpretation.

For nonzero ordinary real x, the mathematical identity ASINH(1/CSCH(x)) reconstructs x. Using x=1 gives approximately 1, and x=−1 gives approximately −1. ASINH allows both signs.

A rounded CSCH value of zero at an extreme input would make that reciprocal fail, so the inverse identity is not a universal finite-precision recovery guarantee. Retain the original value when exact provenance matters.

At zero, the mathematical reciprocal of SINH is undefined. The reviewed page does not explicitly establish the exact native zero-input error code; the guide does not copy one from COT or another product.

Near zero, small input changes can have a large effect. At large magnitudes, an independently expanded exponential formula can overflow while its reciprocal target is small. Test the actual workbook for extreme-value behavior instead of treating these moderate examples as a numerical-limit benchmark.

• Microsoft CSCH reference.
• Editorial testing standards.

Worked inputs are fictional. Decimal answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.