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The asinh() function returns the inverse hyperbolic sine of a number in radians.
It accepts any real number as input — positive, negative, or zero.
This function is used in advanced math, engineering, and physics calculations.
Internally, it uses the formula: asinh(x) = log(x + sqrt(x² + 1)).
Commonly used to reverse the effect of the sinh() (hyperbolic sine) function.

Syntax

asinh(float $number): float

• Parameter:
  number — any real number (positive, negative, or zero)
• Returns:
  The inverse hyperbolic sine of the number, in radians

File Name: asinh-example.php

<?php
echo asinh(0);     // ➤ 0
echo "\n";
echo asinh(1);     // ➤ 0.88137358701954
echo "\n";
echo asinh(-1);    // ➤ -0.88137358701954
?>

Formula (How it works internally)

asinh(x) = log(x + sqrt(x² + 1))

Use Cases