The $cosh operator computes the hyperbolic cosine of a number in MongoDB aggregation pipelines. Use it for exponential growth models, catenary curves, and advanced math transformations on numeric data.
Exponential-style math.
One expression inside $cosh.
Always at least 1.
cosh(-x) = cosh(x).
Growth, physics, stats.
Hyperbolic vs circular.
In MongoDB’s aggregation framework, the $cosh operator returns the hyperbolic cosine of a numeric expression. The formula is cosh(x) = (ex + e-x) / 2. For example, cosh(0) = 1 and cosh(1) ≈ 1.543. Unlike circular cosine, the result is always greater than or equal to 1.
Think of $cosh as MongoDB’s version of JavaScript’s Math.cosh(). Use it inside aggregation expression stages like $project or $addFields, not as a query filter.
The $cosh operator takes one numeric expression:
{ $cosh: <expression> }$cosh — returns the hyperbolic cosine of the expression.<expression> — a field reference, literal, or nested numeric expression.≥ 1 (minimum value is 1 at input 0).$cosh is an even function: cosh(-x) = cosh(x).$project, $addFields, or $set.null, the result is null.$cos, hyperbolic cosine never goes below 1| Question | Answer |
|---|---|
| Operator type | Aggregation expression operator (hyperbolic) |
| Syntax | { $cosh: <expression> } |
| Input | Any real number |
| Output range | ≥ 1 (unbounded above) |
| Common stages | $project, $addFields, $set |
{
$cosh: 0
}Returns 1
{
$cosh: "$x"
}From document field
{
$cosh: 1
}≈ 1.543
{
$cosh: null
}Returns null
Compute hyperbolic cosines from stored values, verify the even-function property, and explore growth patterns with $cosh.
Use a values collection and compute $cosh for each numeric field with $project.
Suppose you have a values collection with a numeric field x:
[
{ "_id": ObjectId("609c26812e9274a86871bc6a"), "x": 0 },
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "x": 1 },
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "x": 2 }
]Compute the hyperbolic cosine of each stored value:
db.values.aggregate([
{
$project: {
x: 1,
hyperbolicCosine: { $cosh: "$x" }
}
}
])x: 0 → cosh(0) = 1 (minimum value).x: 1 → cosh(1) ≈ 1.543.x: 2 → cosh(2) ≈ 3.762 (grows faster than linear).Verify the even-function property, model growth, and test boundary values.
Hyperbolic cosine returns the same result for positive and negative inputs:
db.values.aggregate([
{
$project: {
x: 1,
coshPositive: { $cosh: "$x" },
coshNegative: { $cosh: { $multiply: [ "$x", -1 ] } }
}
}
])
// x: 1 → coshPositive ≈ 1.543, coshNegative ≈ 1.543
// x: -2 → both fields return ≈ 3.762This symmetry is useful when your data may contain signed values but the hyperbolic result should be the same magnitude regardless of sign.
Hyperbolic cosine appears in compound growth and catenary (hanging cable) formulas:
db.metrics.aggregate([
{
$project: {
time: 1,
growthFactor: { $cosh: "$time" },
scaledGrowth: {
$multiply: [
{ $cosh: "$time" },
"$baseRate"
]
}
}
}
])As time increases, $cosh(time) grows exponentially. Pair with other operators to build physics, finance, or statistics models inside the pipeline.
Common values every beginner should know:
db.samples.aggregate([
{
$project: {
coshZero: { $cosh: 0 }, // 1
coshOne: { $cosh: 1 }, // ≈ 1.543
coshTwo: { $cosh: 2 }, // ≈ 3.762
coshNegOne:{ $cosh: -1 } // ≈ 1.543 (same as cosh(1))
}
}
])$cosh(0) = 1 is the minimum. $cosh(-1) equals $cosh(1), confirming the even-function property.
$cosh WorksThe pipeline evaluates the expression — a field like "$x" or a numeric literal.
MongoDB computes (ex + e-x) / 2 and returns a value ≥ 1.
The hyperbolic cosine is written to the field you define in $project or $addFields.
Feed into $acosh for the inverse, or combine with $sinh for full hyperbolic identities.
The $cosh operator brings hyperbolic cosine math into MongoDB aggregation pipelines. Remember that output is always at least 1, values grow exponentially for large inputs, and the function is symmetric around zero.
Do not confuse $cosh with $cos (circular, bounded) or $acosh (inverse, requires input ≥ 1). Pick the operator that matches your mathematical model.
≥ 1$acosh when you need the inverse operationcosh(0) = 1 to validate pipelines$sinh for hyperbolic identity calculations$cosh with $cos (different math entirely)$acosh on $cosh output without checking the domainnull input returns null$coshUse these points when working with hyperbolic cosine in MongoDB.
Exponential growth.
PurposeOne expression.
SyntaxMin at cosh(0).
Rangecosh(-x) = cosh(x).
PropertyHyperbolic vs circular.
ImportantMove on to $dateAdd for date arithmetic, or review $cos for circular trigonometry.
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