The $acosh operator returns the inverse hyperbolic cosine of a number in MongoDB aggregation pipelines. It is the reverse of $cosh and is useful when analyzing exponential growth, decay, or other hyperbolic relationships in your data.
Reverse of hyperbolic cosine.
One expression inside $acosh.
Values must be ≥ 1.
Add computed fields easily.
Growth, finance, statistics.
acosh(1) = 0
In MongoDB’s aggregation framework, the $acosh operator computes the inverse hyperbolic cosine of a numeric expression. If cosh(y) = x, then acosh(x) = y. For example, $acosh(1) returns 0, and $acosh(2) returns approximately 1.317.
Think of $acosh as MongoDB’s version of JavaScript’s Math.acosh(). Use it inside aggregation expression stages, not as a standalone query filter operator.
The $acosh operator takes one numeric expression:
{ $acosh: <expression> }$acosh — returns the inverse hyperbolic cosine of the expression.<expression> — must evaluate to a number greater than or equal to 1.$project, $addFields, or $set.null, the result is null.1 return NaN.$acosh is only defined for values greater than or equal to 1. Values below 1 return NaN.
| Question | Answer |
|---|---|
| Operator type | Aggregation expression operator (hyperbolic) |
| Syntax | { $acosh: <expression> } |
| Input range | ≥ 1 |
| Inverse of | $cosh |
| Common stages | $project, $addFields, $set |
{
$acosh: 1
}Returns 0
{
$acosh: "$x"
}From document field
{
$acosh: 2
}≈ 1.317
{
$acosh: null
}Returns null
Walk through sample data, run an aggregation pipeline, and inspect the inverse hyperbolic cosine results.
Use a values collection and compute $acosh for each numeric field with $project.
Suppose you have a values collection with a numeric field x:
[
{ "_id": ObjectId("609c26812e9274a86871bc6a"), "x": 1 },
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "x": 2 },
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "x": 3 }
]Compute the inverse hyperbolic cosine for each value:
db.values.aggregate([
{
$project: {
acoshValue: { $acosh: "$x" }
}
}
])x is 1 → acosh(1) = 0.x is 2 → acosh(2) ≈ 1.317.x is 3 → acosh(3) ≈ 1.763.Apply $acosh in growth modeling and validate results with rounding.
When a field stores a hyperbolic cosine result, recover the original scale factor:
db.growth.aggregate([
{
$project: {
label: 1,
coshResult: 1,
scaleFactor: { $acosh: "$coshResult" },
scaleFactorRounded: {
$round: [ { $acosh: "$coshResult" }, 3 ]
}
}
}
])If a prior pipeline stage computed $cosh(t), applying $acosh on that result recovers t (when the value is ≥ 1). Use $round for cleaner display values.
Only compute $acosh when the value is at least 1; otherwise return null:
db.values.aggregate([
{
$project: {
x: 1,
acoshValue: {
$cond: [
{ $gte: [ "$x", 1 ] },
{ $acosh: "$x" },
null
]
}
}
}
])Wrapping $acosh in $cond prevents NaN results when your data may contain values below 1.
Common boundary values every beginner should know:
db.samples.aggregate([
{
$project: {
acoshOne: { $acosh: 1 }, // 0
acoshTwo: { $acosh: 2 }, // ≈ 1.317
acoshTen: { $acosh: 10 } // ≈ 2.993
}
}
])$acosh(1) = 0 is the most important edge case. Larger inputs produce progressively larger results, growing slowly compared to exponential functions.
$acosh WorksThe pipeline evaluates the input — a field like "$x" or a numeric expression.
If the value is below 1, MongoDB returns NaN. Valid inputs proceed to the calculation.
MongoDB applies the inverse hyperbolic cosine and stores the result in your projected field.
You get a numeric result ready for further math, grouping, or reporting.
The $acosh operator is a specialized but powerful math tool in MongoDB aggregation pipelines. It reverses hyperbolic cosine values and supports growth modeling, financial analysis, and statistical transformations.
For beginners, remember three things: input must be ≥ 1, acosh(1) = 0, and values below 1 return NaN. Use $cond to guard against invalid inputs in real-world data.
$acoshacosh(1) = 0 when checking results$round for readable output values$cosh to verify round-trip calculations$ifNull when neededNaN$acosh with $acos (different functions)$acosh as a query filter operator outside expressionsNaN)$acoshUse these points when working with hyperbolic math in MongoDB.
Reverse of $cosh.
{ $acosh: expr }
Must be ≥ 1.
Domainacosh(1) = 0
Returns NaN.
Edge caseMove on to $add or review $acos for arc cosine calculations.
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