SECH in WPS Spreadsheet: Build a Symmetric Hyperbolic Secant Profile
Build a symmetric hyperbolic secant peak in WPS Spreadsheet, with separate settings for its center, width and height.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: SECH returns hyperbolic secant. =SECH(0) has mathematical expected result 1.
Availability and evidence scope
The official WPS Windows pages, checked October 19, 2026, document this function and advertise ordinary entry and calculation without membership. Their last-updated date is 2026-07-13; that is a documentation date, not its introduction release. They do not name an exact minimum or last supported build. Availability on Mac, Linux, mobile, web or historical builds is not established here.
The examples below are independently calculated mathematical expectations, rounded to nine decimal places where appropriate. They were not executed in WPS, and no native screenshot is claimed. Before relying on an installation, check its function prompt and run a small control example.
Syntax and arguments
=SECH(number)
One required numeric argument, number, supplies the hyperbolic input. For a scaled profile, pass the dimensionless displacement/scale ratio. SECH is reciprocal hyperbolic cosine, not inverse hyperbolic cosine.
The documented Windows workflow supports typing the formula in a cell or choosing the function through Formula → Insert Function. These formulas use English names and comma separators. Inspect the destination formula after filling down so that relative references and fixed settings still point to the intended cells.
Example 1: calculate a symmetric profile
Enter -2, -1, 0, 1 and 2 in A2:A6. Fill =SECH(A2) down B2:B6. Expected values are 0.265802229, 0.648054274, 1, 0.648054274 and 0.265802229. The equal values at opposite inputs and the center value one make useful spreadsheet controls.
This grid can illustrate a localized mathematical profile. Unlike circular secant, hyperbolic secant does not repeatedly oscillate or have real-input poles.
Example 2: shift and scale a peak
Define y=5*sech((x-10)/2). Put x values 6, 8, 10, 12 and 14 in D2:D6. Put center 10 in G1, width scale 2 in H1 and amplitude 5 in I1. Fill =$I$1*SECH((D2-$G$1)/$H$1) down E2:E6.
Expected outputs are 1.329011144, 3.240271368, 5, 3.240271368 and 1.329011144. Subtracting the center shifts the peak to x=10; dividing by the width scale changes its spread; multiplying by amplitude changes its height. This is a defined mathematical profile, not a fitted probability distribution or a validated physical model.
Advanced checks: denominator and maximum
For x=1, compare =SECH(1) with =1/COSH(1) and =2/(EXP(1)+EXP(-1)). All three mathematical expectations are 0.648054274. The denominator’s symmetry explains why the sign of x does not change the answer.
For finite real mathematical inputs, 0<sech(x)≤1, so the positive-amplitude profile above cannot exceed five mathematically. That is a model-level check, not a promise that every floating-point implementation avoids underflow at extreme inputs. Test only modest values when using the exponential identity as an independent check.
Troubleshooting and limits
- Do not substitute SEC or ACOSH. Their mathematical roles differ from reciprocal hyperbolic cosine.
- If the peak moves when filling down, inspect the dollar signs on the center and scale references.
- A value smaller than one away from zero is expected. Displaying too few decimals can make the tails look like zero.
- WPS’s FAQ recommends checking numeric input when
#VALUE!appears. Exact overflow/underflow behavior, supported magnitudes and text/blank coercion remain unverified.