The $asinh operator returns the inverse hyperbolic sine of a number in MongoDB aggregation pipelines. It is the reverse of $sinh and accepts any real number — positive, negative, or zero.
Reverse of hyperbolic sine.
One expression inside $asinh.
Any number is valid input.
Add computed fields easily.
Stats, signals, transforms.
asinh(0) = 0
In MongoDB’s aggregation framework, the $asinh operator computes the inverse hyperbolic sine of a numeric expression. If sinh(y) = x, then asinh(x) = y. For example, $asinh(1) returns approximately 0.881, and $asinh(0) returns 0.
Unlike $acosh, $asinh works on any real number including negatives. Think of it as MongoDB’s version of JavaScript’s Math.asinh().
The $asinh operator takes one numeric expression:
{ $asinh: <expression> }$asinh — returns the inverse hyperbolic sine of the expression.<expression> — can be any real number (positive, negative, or zero).$project, $addFields, or $set.null, the result is null.$acosh (which requires input ≥ 1).Both are inverse hyperbolic operators, but their input domains differ:
| Question | Answer |
|---|---|
| Operator type | Aggregation expression operator (hyperbolic) |
| Syntax | { $asinh: <expression> } |
| Input range | All real numbers |
| Inverse of | $sinh |
| Common stages | $project, $addFields, $set |
{
$asinh: 1
}≈ 0.881
{
$asinh: -2
}≈ -1.444
{
$asinh: 0
}Returns 0
{
$asinh: null
}Returns null
Compute inverse hyperbolic sine on sample values, including positive, negative, and zero inputs.
Use a data collection and compute $asinh for each numeric field with $project.
Suppose you have a data collection with a numeric value field:
[
{ "_id": ObjectId("609c26812e9274a86871bc6a"), "value": 1 },
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "value": 2 },
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "value": 3 }
]Compute the inverse hyperbolic sine for each value:
db.data.aggregate([
{
$project: {
value: 1,
asinhValue: { $asinh: "$value" }
}
}
])asinh(1) ≈ 0.881.asinh(2) ≈ 1.444.asinh(3) ≈ 1.818.Handle negative values, round results, and apply statistical transformations.
Unlike $acosh, $asinh handles negative inputs:
db.data.aggregate([
{
$project: {
value: 1,
asinhValue: { $asinh: "$value" },
asinhRounded: {
$round: [ { $asinh: "$value" }, 3 ]
}
}
}
])
// Sample values: -2, 0, 1.5
// asinh(-2) ≈ -1.444
// asinh(0) = 0
// asinh(1.5) ≈ 1.195$asinh is an odd function: asinh(-x) = -asinh(x). Negative inputs produce negative outputs.
Apply an inverse hyperbolic sine transform to stabilize skewed numeric distributions:
db.sales.aggregate([
{
$project: {
region: 1,
revenue: 1,
logRevenue: { $asinh: "$revenue" }
}
},
{
$group: {
_id: "$region",
avgLogRevenue: { $avg: "$logRevenue" }
}
}
])The asinh transform compresses large values while preserving sign. It is commonly used in statistics and econometrics to handle skewed revenue or count data before averaging.
Common values for quick validation:
db.samples.aggregate([
{
$project: {
asinhZero: { $asinh: 0 }, // 0
asinhOne: { $asinh: 1 }, // ≈ 0.881
asinhNeg: { $asinh: -1 }, // ≈ -0.881
asinhLarge: { $asinh: 100 } // ≈ 5.298
}
}
])asinh(0) = 0 is the key edge case. For large inputs, asinh grows slowly (like a log), which makes it useful for compressing extreme values.
$asinh WorksThe pipeline evaluates the input — a field like "$value" or a numeric expression.
MongoDB applies the inverse hyperbolic sine function. Any real number is valid input.
The computed value is written to the field you define in $project or $addFields.
Use the result for grouping, averaging, or further pipeline stages.
The $asinh operator is a versatile hyperbolic math tool in MongoDB aggregation pipelines. It accepts any real number, handles negatives naturally, and is especially useful for statistical transforms and compressing skewed data.
For beginners, remember: asinh(0) = 0, negatives are valid, and pair with $round when you need clean display values.
$asinh for skewed data transforms before averagingasinh(0) = 0 when checking results$round for readable output values$sinh to verify round-trip calculations$ifNull when needed$asinh with $asin (different functions)$acosh (asinh has no minimum)$asinh as a query filter outside expressions$asinhUse these points when working with hyperbolic math in MongoDB.
Reverse of $sinh.
{ $asinh: expr }
Any number is valid.
Domainasinh(-x) = -asinh(x).
Propertyasinh(0) = 0.
SpecialMove on to $atan or review $asin for arc sine calculations.
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