SECH Function (LibreOffice Calc)
Use LibreOffice Calc SECH for hyperbolic secant. Check nonzero and negative inputs, build a normalized pulse profile and understand numerical limits at large magnitudes.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: SECH returns hyperbolic secant, mathematically 1/COSH(x) or 2/(EXP(x)+EXP(-x)). For a finite real input, its mathematical value is positive and at most 1. It is a different function from ordinary trigonometric secant.
Syntax and input meaning
=SECH(number)
The one required argument is a real numeric value, cell reference or numeric expression. There is no optional scale or degree-mode argument. Although hyperbolic functions are sometimes described in terms of a hyperbolic angle, do not automatically apply a degrees-to-radians conversion to a dimensionless model input.
Worked example: inspect symmetry and decay
Put the values -2, -1, 0, 1, 2 in A2:A6. Enter =SECH(A2) in B2 and copy down to B6.
| Input | Independently expected SECH value |
|---|---|
| -2 | 0.2658022288 |
| -1 | 0.6480542737 |
| 0 | 1 |
| 1 | 0.6480542737 |
| 2 | 0.2658022288 |
The value at zero follows from COSH(0)=1 and agrees with LibreOffice Help. Equal outputs for -1 and 1, and for -2 and 2, demonstrate even symmetry. The value decreases as the absolute magnitude of the input grows.
Second example: a reciprocal control
For an input of 1, compare =SECH(1) with =1/COSH(1). Both are expected to be approximately 0.6480542737. A further check is =SECH(1)*COSH(1), expected to be approximately 1, allowing for floating-point rounding.
For moderate inputs, =2/(EXP(1)+EXP(-1)) supplies an independent mathematical identity. It is useful for understanding the result, but manually replacing SECH with an exponential expression is not a promise of better numerical behavior for very large inputs.
Advanced application: construct a normalized pulse profile
A simple mathematical profile can be defined as amplitude × sech((position−centre)/scale). Put amplitude 10 in D1, centre 0 in E1 and positive scale 2 in F1. Use positions -2, 0, 2 in D3:D5.
In E3 enter =$D$1*SECH((D3-$E$1)/$F$1) and copy down. Expected values are approximately 6.480542737, 10, 6.480542737. At the centre the normalized argument is zero, so the profile reaches its amplitude. Symmetric offsets have equal heights.
This is a reproducible numerical model, not a claim that every measured signal follows a hyperbolic-secant shape. A zero scale would introduce division by zero before SECH receives an input. Choose units consistently so the normalized argument is dimensionless.
Troubleshooting and large-input limits
Ordinary SEC can grow without bound near its real singularities. Real-valued SECH has no such finite-input singularity; mathematically it tends toward zero for large positive or negative inputs. Spreadsheet implementation still has finite numeric range and precision.
Very large absolute inputs may encounter overflow in an intermediate operation or underflow toward zero. The exact transition and displayed error behavior have not been tested here, so no universal numeric cutoff is asserted. A calculated zero at extreme magnitude should not be interpreted as proof that the mathematical value is exactly zero.
Use numeric inputs and check unit normalization. If a result exceeds 1 for an ordinary finite real input, inspect the formula and data because that conflicts with the mathematical range. Preserve more displayed decimals when comparing small positive results; number formatting can hide them without changing the stored value.
Availability and verification
LibreOffice Help identifies introduction in LibreOffice 3.5. The current desktop Calc reference was checked October 17, 2026; a last functioning version or retirement is not established.
New expected results are independently calculated and checked against the documented contract, not tested in LibreOffice Calc. No screenshot or fresh application execution is claimed.