Google Sheets TANH Function: Syntax, Examples & Tips

What Is TANH?

TANH returns the hyperbolic tangent of a number. It is defined as

TANH(x) = SINH(x) / COSH(x) = (e^x − e^−x) / (e^x + e^−x)

Despite the similar name, TANH is not a trigonometric function of an angle — it belongs to the hyperbolic family (SINH, COSH, TANH), which is built from the exponential function. There is no need to convert to radians.

Key Properties

• Output range: the result is always strictly between −1 and 1.
• Zero in, zero out: TANH(0) is 0.
• Odd function: TANH(-x) = -TANH(x).
• Saturation: as x gets large, TANH approaches 1; as x gets very negative, it approaches −1. Around |x| > 20 the result rounds to exactly ±1 in Sheets.
• Near zero it is almost linear: for small x, TANH(x) ≈ x.

This S-shaped curve is what makes TANH useful — it squashes any input into a bounded range while preserving the sign and ordering.

Basic Examples

Hyperbolic tangent of a number

=TANH(1)

Returns approximately 0.7616.

Large values saturate

=TANH(5)

Returns approximately 0.9999.

Negative input

=TANH(-0.5)

Returns approximately −0.4621.

Apply to a column

=ARRAYFORMULA(TANH(B2:B100))

Practical Uses

Squashing scores into a bounded range

If you have unbounded scores (for example, net sentiment or z-scores) and want them between −1 and 1 without hard clipping, TANH gives a smooth result:

=TANH(B2 / 10)

Dividing by a scale factor controls how quickly values saturate.

Neural network activations

TANH is a classic activation function. If you are prototyping a tiny model or teaching how one works in a spreadsheet, you can compute a neuron's output with:

=TANH(SUMPRODUCT(B2:D2, $B$10:$D$10) + $E$10)

Inverse: ATANH

To reverse the operation, use ATANH, which accepts values strictly between −1 and 1:

=ATANH(TANH(0.8))

returns 0.8. ATANH is also the Fisher transformation used to normalise correlation coefficients: =ATANH(CORREL(A2:A50, B2:B50)).

Converting to a 0–1 scale

The logistic (sigmoid) function is closely related: (TANH(x/2) + 1) / 2 equals 1 / (1 + EXP(-x)).

Common Use Cases

• Data science and ML teaching: Activation functions.
• Statistics: Back-transforming Fisher z values (=TANH(z) returns a correlation).
• Physics: Velocity of falling objects with drag, magnetisation models.
• Score normalisation: Soft-capping outliers.

Common Errors

• Confusing TANH with TAN: TAN works on angles in radians and has asymptotes; TANH works on any number and is bounded. They give very different results.
• #VALUE!: The input is text that isn't numeric.
• ATANH of ±1: When reversing, ATANH(1) and ATANH(−1) return #NUM! because the result would be infinite.

Tips and Best Practices

• Scale your input before applying TANH so the useful range of your data falls roughly between −3 and 3, where the curve is most responsive.
• Round results for presentation; the raw output has many decimal places.
• Use FISHERINV as an alternative name when back-transforming Fisher z values — it computes the same thing as TANH.

Related Functions

SINH, COSH, ATANH, TAN, EXP, FISHER, and FISHERINV.