ATANH in WPS Spreadsheet: Invert Hyperbolic Tangent Inside Its Strict Domain
Use WPS ATANH for interior inputs, reconstruct a bounded model and inspect endpoint sensitivity without inventing native error codes.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: ATANH(number) is the inverse hyperbolic tangent for real inputs strictly between −1 and 1. =ATANH(0.5) has independently expected result approximately 0.549306144. The endpoints −1 and 1 are excluded by the WPS lesson.
Availability and version history
- Introduced: documented by 2019-06-24 in the official WPS lesson; original introduction is not established.
- Availability: WPS Office for Windows Personal; no numeric release is stated in the edition metadata.
- Scope: exact current supported builds remain unverified. The Windows lesson does not establish equivalent availability in other WPS clients.
- Checked: October 14, 2026 against function-specific documentation. Examples were independently calculated; no native WPS test was performed.
Syntax and open-domain rule
=ATANH(number)
The formal definition and walkthrough agree on the strict input restriction. Do not turn it into an inclusive comparison. For an already numeric input in A2, =AND(A2>-1,A2<1) checks the two mathematical bounds, but is not by itself a complete test of spreadsheet data types.
Examples use English function names and comma separators. Hyperbolic inverse values are not degree angles; do not append a radians-to-degrees conversion unless a separately defined model requires one.
Example 1: calculate signed interior controls
Enter −0.9, −0.5, 0, 0.5 and 0.9 in A2:A6 and fill =ATANH(A2) down:
| Input | Independent expected result |
|---|---|
| -0.9 | -1.472219490 |
| -0.5 | -0.549306144 |
| 0 | 0 |
| 0.5 | 0.549306144 |
| 0.9 | 1.472219490 |
The function is odd: opposite inputs give opposite outputs. All controls are strictly inside the documented interval, including the valid central input zero.
Example 2: verify a logarithmic identity
For the modest input 0.5:
=ATANH(0.5)
=0.5*LN((1+0.5)/(1-0.5))
Both expected results are approximately 0.549306144, half the natural logarithm of three. The numerator and denominator are positive for this selected input.
The formula illustrates the real inverse definition using LN. It is not promoted as an unrestricted numerically stable substitute for every input near an endpoint.
Advanced example: recover a scaled response input
Suppose a fictional response follows y=50+30*tanh(x/2), and the target response is 65. Reverse the offset and scale before applying ATANH:
=2*ATANH((65-50)/30)
Expected x: approximately 1.098612289. Substituting that unrounded value into 50+30*TANH(x/2) gives 65 mathematically. A target of 35 gives the negative value approximately −1.098612289.
The intermediate normalized target is 0.5 or −0.5, respectively. Target 80 would produce 1 and target 20 would produce −1, both excluded. A formula cannot supply a finite real solution at those limiting responses.
Advanced example: inspect sensitivity near one
Use inputs 0.9, 0.99 and 0.999:
=ATANH(0.9)
=ATANH(0.99)
=ATANH(0.999)
Expected results are approximately 1.472219490, 2.646652412 and 3.800201167. The inputs become closer to one, while the outputs keep increasing. A small difference in an input close to the boundary can matter substantially after inversion.
Rounding 0.999 to two decimal places before calculation produces one, which leaves the domain. A cell’s rounded display alone does not change its stored value, whereas explicitly replacing the value with the rounded number does.
Advanced check: reconstruct both directions carefully
=TANH(ATANH(0.5))
=ATANH(TANH(1))
Expected mathematical results are 0.5 and 1. The first begins with a documented interior input; the second begins with a modest real forward input whose mathematical TANH remains interior.
The WPS source states the inverse relationship, but finite precision can matter if a much larger forward input rounds its TANH result to an endpoint. No native threshold for that event is established here. Keep full calculated values and use modest controls before testing extreme cases.
Errors and validation scope
Exactly −1 and 1, as well as values outside that interval, violate the documented domain. The lesson does not give a complete endpoint-error table. It mentions #VALUE! for a non-real argument without defining every blank, Boolean or numeric-text conversion, so no broad native coercion claim is made.
Retain invalid inputs for inspection rather than coercing them into the interval silently. If a modeling process clips data, document that as a separate decision because it changes the value being inverted. See TANH for the forward bounded response.
References and verification
- WPS Academy: ATANH lesson, 2019-06-24 (Chinese; Windows Personal scope).
- Editorial testing standards.
The direct WPS product lesson supports the stated function scope. Worked outputs are independent expectations, not captured native results or proof of support across all current WPS clients.