SECH in ONLYOFFICE: Hyperbolic Secant of a Numeric Argument

Math and Trigonometry Intermediate ONLYOFFICE Spreadsheet Editor

How to use the ONLYOFFICE SECH function: documented radians/numeric input, worksheet examples, reciprocal formulas, limitations and platform notes.

Verification status: Official documentation referenced; example outcomes independently reasoned or arithmetically checked where stated. Not executed in ONLYOFFICE Spreadsheet Editor. How formula examples are checked

Quick answer. SECH(number) returns the hyperbolic secant. In mathematics, it is the reciprocal of hyperbolic cosine: sech(x)=1/cosh(x). See ONLYOFFICE’s current SECH reference for the vendor’s one-argument signature. The examples are independently calculated mathematical expectations; native ONLYOFFICE execution was not performed.

What SECH does—and what its number means

SECH makes a symmetric, nonnegative bell-shaped weight: it equals 1 at zero and decreases toward zero as the absolute input grows. The mathematical definition is:

SECH(x)=1/COSH(x) for every finite real x, mathematically. This identity is a mathematical derivation, not an execution claim for ONLYOFFICE.

Exact official syntax, arguments, and defaults

=SECH(number)

Argument	Position	Required?	Input type and unit described by ONLYOFFICE	Default
`number`	1	Yes; the only documented argument	Numeric angle in radians; its absolute value must be strictly less than 2^27 (134,217,728)	No optional argument/default documented

The official page explicitly states the strict bound abs(number)<2^27; an argument equal to the boundary is outside the documented input range. It does not establish a particular returned error code for violating that limit, nor specify how blank cells, quoted numerals or Boolean inputs are coerced. This guide uses ordinary numeric cells. Official evidence.

Hyperbolic input note: The ONLYOFFICE page describes this as an angle in radians, but for a hyperbolic model the underlying real number can instead be a dimensionless score. Here column A contains the numeric argument directly and RADIANS is not applied.

Reproduce the worksheet from a blank file

Open an editable spreadsheet in ONLYOFFICE Spreadsheet Editor. Its current function-entry guide shows Formula → Function or manually entering a formula beginning with =.
Put numeric input x in A1 and SECH result in B1. Type the following numeric values, one per row, into A2:A9: -3, -2, -1, 0, 0.5, 1, 2, 3.
Enter =SECH(A2) in B2 and fill down through B9. The row references should change automatically. Use English formula language for these exact names.
Compare B2:B9 to the independent mathematical expectations, not to claimed screenshots or observed runtime outputs:

Cell / row	Value in column A	Enter in column B (or fill down)	Independently calculated expectation
A2	-3	`=SECH(A2)`	≈ 0.099327927419
A3	-2	`=SECH(A3)`	≈ 0.26580222883
A4	-1	`=SECH(A4)`	≈ 0.64805427366
A5	0	`=SECH(A5)`	≈ 1
A6	0.5	`=SECH(A6)`	≈ 0.88681888397
A7	1	`=SECH(A7)`	≈ 0.64805427366
A8	2	`=SECH(A8)`	≈ 0.26580222883
A9	3	`=SECH(A9)`	≈ 0.099327927419

For extra verification, open Formula → Function and search for SECH as described in the vendor’s insertion instructions. This checks that the feature is exposed in your installation; it is not proof that every historical release supports it.

Additional reproducible formulas and independently calculated results

These are directly pasteable English-language examples in separate empty cells. They are expected results from independent mathematical calculations, not native ONLYOFFICE observations. Answers marked ≈ are rounded for display; compare a few decimals.

English-locale formula	Mathematical expected result	Why it matters
`=SECH(0)`	≈ 1	peak at zero
`=SECH(1)`	≈ 0.64805427366	positive input
`=SECH(-1)`	≈ 0.64805427366	even symmetry
`=SECH(2)`	≈ 0.26580222883	decay as magnitude increases
`=SECH(0.5)`	≈ 0.88681888397	half-unit input
`=SECH(3)`	≈ 0.099327927419	larger magnitude
`=1/COSH(2)`	≈ 0.26580222883	reciprocal definition
`=SECH(2)^2`	≈ 0.070650824853	square of hyperbolic secant
`=SECH(2)^2+TANH(2)^2`	≈ 1	hyperbolic identity near 1
`=SECH((60-50)/10)`	≈ 0.64805427366	scale 10 around target 50
`=SECH((50-50)/10)`	≈ 1	target equals center
`=SECH((40-50)/10)`	≈ 0.64805427366	symmetry around center
`=2EXP(-ABS(2))/(1+EXP(-2ABS(2)))`	≈ 0.26580222883	stable algebraic reformulation

Advanced applications and important mathematical limits

1. Build a symmetric, bounded weight

Suppose a value in A2 is compared with a target of 50 using a scale of 10. =SECH((A2-50)/10) creates a smooth nonnegative weight. At A2=50 the expected result is 1; at 40 or 60 it is approximately 0.648054273664; at 30 or 70 it is approximately 0.265802228834. This is an illustrative mathematical weighting function, not automatically a probability distribution or a vendor-supplied statistical model.

2. Verify an identity using a different function

Mathematically SECH(x)=1/COSH(x) and SECH(x)^2+TANH(x)^2=1. With input 2, =1/COSH(2) is expected to be approximately 0.265802228834, and =SECH(2)^2+TANH(2)^2 should be approximately 1. The published ONLYOFFICE references document separate functions; these identity checks are independent mathematics, not observed workbook results.

3. Avoid unnecessary exponential overflow

The identity SECH(x)=2/(EXP(x)+EXP(-x)) is mathematically valid for real x but can be numerically troublesome for very large absolute values. A re-arranged mathematical expression 2*EXP(-ABS(x))/(1+EXP(-2*ABS(x))) avoids the large positive exponent. Whether a particular ONLYOFFICE version evaluates one form more reliably is untested and must not be assumed.

Errors, apparent surprises and safe troubleshooting

Formula or symptom	Explanation and action
`=SECH(0)`	Mathematically defined; expected 1. Unlike SEC, SECH has no real-valued zero denominator for finite real inputs.
Very large finite inputs	The exact mathematical result approaches zero; intermediate calculations may overflow or underflow. The vendor page only documents the `2^27` magnitude restriction, not error codes or precision at extreme values.
Entering degrees without context	The vendor describes its argument as an angle in radians, but hyperbolic functions can be used with dimensionless model inputs. Do not apply `RADIANS` automatically to a non-angle score.
`=SECH(134217728)`	Outside the documented range: the vendor requires absolute argument strictly smaller than `2^27`. The function page does not promise a specific error code; do not assert one.
A quoted numeral (`"1"`), blank reference, logical TRUE or multiple arguments	The one-argument vendor reference does not specify coercion or precise errors for these cases. Enter a genuine numeric value and check the real Desktop/web version instead of assuming behaviour from a different spreadsheet program.
Formula name appears unknown	Check the installed ONLYOFFICE editor version, Formula Language, and actual Function picker. A vendor’s current unversioned help article is not a guarantee about an old or custom-hosted installation.
Last decimal digits differ	Formatting, finite-precision π/radian conversion, argument reduction or transcendental evaluation can affect displayed digits. Use a tolerance rather than exact floating-point equality.

A safer check for boundary-sensitive formulas

If your model will ever evaluate a mathematically singular point, test the domain before evaluation rather than relying on a specific error message or last-digit numerical coincidence. Avoid building critical logic around comparing COS(RADIANS(90)) or SIN(PI()) to exactly zero; floating-point values near the mathematical singularity need a numeric tolerance. This is mathematical design advice, not a verified ONLYOFFICE evaluation rule.

COSH — official ONLYOFFICE documentation (checked 2026-10-13 UTC).
TANH — official ONLYOFFICE documentation (checked 2026-10-13 UTC).
EXP — official ONLYOFFICE documentation (checked 2026-10-13 UTC).

Documentation and evidence classification (checked 2026-10-13 UTC)

ONLYOFFICE function-page evidence: SECH documents the displayed formula name, the one-argument signature, an input described as an angle in radians, and the magnitude restriction. It does not document native results for this article’s custom worksheet.
Function entry workflow: ONLYOFFICE Docs: Inserting functions describes selecting Formula → Function, searching by name, and entering formulas with an equals sign. It gives English formula examples using commas as argument separators.
Regional settings: Spreadsheet Editor Advanced Settings describes Formula Language, region, and decimal/thousands separators. Examples here use the English function name and decimal dot. Verify formula translation and separators in your installation rather than asserting a tested locale matrix.
Product editions and versions: The ONLYOFFICE Docs changelog lists Docs 10.0.0, released 10 October 2026, whereas the Desktop Editors changelog separately lists Desktop Editors 9.4.0, released 19 May 2026. The official Desktop GitHub releases also lists 10.0.0 released 13 October 2026. These release references do not establish the first version supporting this function, nor prove Desktop/web runtime parity.
Runtime confidence: Custom numerical expectations were independently recalculated at high precision. Native ONLYOFFICE Desktop/web execution and locale-specific parsing were not tested.

Native compatibility checks

For compatibility checks, record the named Docs web version and Desktop build, cell results, function availability, extreme-input behavior and relevant singular boundaries. Repeat with the formula language and regional settings actually used.

What SECH does—and what its number means▾

Exact official syntax, arguments, and defaults▾

Reproduce the worksheet from a blank file▾

Additional reproducible formulas and independently calculated results▾

Advanced applications and important mathematical limits▾