MongoDB $sinh Operator

What Is $sinh?

$sinh is a MongoDB aggregation expression that returns the hyperbolic sine of a number: (ex − e−x) / 2. Inputs are treated as radians. Unlike $sin, the result is not limited to −1…1 and is not periodic.

$sinh = Math.sinh for aggregation

{ $sinh: <expression> }

sinh(x) = (e^x − e^(-x)) / 2

$sinh(0)  → 0
$sinh(1)  → ≈ 1.175
$sinh(-1) → ≈ -1.175   // odd: sinh(-x) = -sinh(x)

null / missing → null
degrees → convert with $degreesToRadians first

How to Use $sinh in MongoDB

Pass a numeric expression in radians (convert degrees if needed).

1. Choose an expression stage ($addFields or $project).
2. Provide a number, field, or nested math as the argument.
3. If the value is in degrees, wrap with $degreesToRadians first.
4. Pass that expression to $sinh.

Pseudocode

for each document:
    x = evaluate(expression)
    if x is null or missing:
        result = null
    else if x is NaN:
        result = NaN
    else if x is ±Infinity:
        result = ±Infinity
    else:
        result = (e^x - e^(-x)) / 2
    emit { ..., field: result }

Cheat Sheet

Keep these facts handy while writing hyperbolic-sine expressions.

Live Preview

Watch $sinh compute hyperbolic sine. Try common radian inputs.

x = 1
$sinh(x) → 1.175201

{ result: 1.175201 }

Worked Walkthrough — sinh(1)

Compute hyperbolic sine of 1 using the definition with e.

x = 1

e^1  ≈ 2.71828
e^-1 ≈ 0.36788

sinh(1) = (e^1 − e^-1) / 2
        ≈ (2.71828 − 0.36788) / 2
        ≈ 2.35040 / 2
        ≈ 1.17520

$sinh(1) → ≈ 1.175201

Check: sinh(-1) ≈ -1.175201 (odd function) ✓

MongoDB Examples

We use a small hyperbola collection of radian values, then show a degrees conversion. Run these in mongosh after inserting the sample data once.

db.hyperbola.insertMany([
  { _id: 1, x: 0 },
  { _id: 2, x: 1 },
  { _id: 3, x: -1 }
]);

db.hyperbola.find()

[
  { _id: 1, x: 0 },
  { _id: 2, x: 1 },
  { _id: 3, x: -1 }
]

db.hyperbola.aggregate([
  {
    $addFields: {
      sinh_x: { $sinh: "$x" }
    }
  }
]);

{
  _id: 1,
  x: 0,
  sinh_x: 0
}
{
  _id: 2,
  x: 1,
  sinh_x: 1.1752011936438014
}
{
  _id: 3,
  x: -1,
  sinh_x: -1.1752011936438014
}

db.trigonometry.insertOne({
  _id: 1,
  angle: 53.13010235415598
});

db.trigonometry.aggregate([
  {
    $addFields: {
      sinh_output: {
        $sinh: { $degreesToRadians: "$angle" }
      }
    }
  }
]);

{
  _id: 1,
  angle: 53.13010235415598,
  sinh_output: 1.0660204044057324
}

Performance Notes

Hyperbolic math is cheap compared with large sorts or joins. Filter early with $match when only some documents need $sinh.

Key Takeaways