The $sinh operator computes the hyperbolic sine of a number in MongoDB aggregation pipelines. Use it for exponential growth models, physics simulations, and advanced math transformations on numeric data.
Exponential-style math.
One expression inside $sinh.
Zero at origin.
sinh(-x) = -sinh(x).
Growth, physics, stats.
Hyperbolic vs circular.
In MongoDB’s aggregation framework, the $sinh operator returns the hyperbolic sine of a numeric expression. The formula is sinh(x) = (ex - e-x) / 2. For example, sinh(0) = 0, sinh(1) ≈ 1.175, and sinh(2) ≈ 3.627. Values grow exponentially as the input moves away from zero.
Think of $sinh as MongoDB’s version of JavaScript’s Math.sinh(). Use it inside aggregation expression stages like $project or $addFields, not as a query filter.
The $sinh operator takes one numeric expression:
{ $sinh: <expression> }$sinh — returns the hyperbolic sine of the expression.<expression> — a field reference, literal, or nested numeric expression.sinh(0) = 0 — the function passes through the origin.$sinh is an odd function: sinh(-x) = -sinh(x).$project, $addFields, or $set.null, the result is null.| Question | Answer |
|---|---|
| Operator type | Aggregation expression operator (hyperbolic) |
| Syntax | { $sinh: <expression> } |
| Input | Any real number |
| Output at zero | 0 |
| Common stages | $project, $addFields, $set |
{
$sinh: 0
}Returns 0
{
$sinh: "$x"
}From document field
{
$sinh: 1
}≈ 1.175
{
$sinh: null
}Returns null
Compute hyperbolic sines from stored values, verify the odd-function property, and explore exponential growth with $sinh.
Use an exponentialData collection and compute $sinh for each numeric field with $project.
Suppose you have an exponentialData collection with a numeric field x:
[
{ "_id": ObjectId("609c26812e9274a86871bc6a"), "x": 1 },
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "x": 2 },
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "x": 3 }
]Compute the hyperbolic sine of each stored value:
db.exponentialData.aggregate([
{
$project: {
x: 1,
sinhValue: { $sinh: "$x" }
}
}
])x: 1 → sinh(1) ≈ 1.175.x: 2 → sinh(2) ≈ 3.627.x: 3 → sinh(3) ≈ 10.018 (grows faster than linear).Verify the odd-function property, model growth, and test boundary values.
Hyperbolic sine negates its result for negative inputs:
db.exponentialData.aggregate([
{
$project: {
x: 1,
sinhPositive: { $sinh: "$x" },
sinhNegative: { $sinh: { $multiply: [ "$x", -1 ] } }
}
}
])
// x: 2 → sinhPositive ≈ 3.627, sinhNegative ≈ -3.627
// x: -1 → sinhPositive ≈ -1.175Unlike $cosh (even function), $sinh flips sign for negative inputs. This symmetry is important in physics and signal-processing formulas.
Hyperbolic sine models rapid growth and decay in scientific datasets:
db.metrics.aggregate([
{
$project: {
time: 1,
growthFactor: { $sinh: "$time" },
scaledGrowth: {
$multiply: [
{ $sinh: "$time" },
"$baseRate"
]
}
}
}
])As time increases, $sinh(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: {
sinhZero: { $sinh: 0 }, // 0
sinhOne: { $sinh: 1 }, // ≈ 1.175
sinhTwo: { $sinh: 2 }, // ≈ 3.627
sinhNegOne:{ $sinh: -1 } // ≈ -1.175 (opposite of sinh(1))
}
}
])$sinh(0) = 0. $sinh(-1) equals the negative of $sinh(1), confirming the odd-function property.
$sinh WorksThe pipeline evaluates the expression — a field like "$x" or a numeric literal.
MongoDB computes (ex - e-x) / 2 and returns the result.
The hyperbolic sine value is written to the field you define in $project or $addFields.
Use in further math, pair with $cosh, or feed into $asinh for the inverse.
The $sinh operator brings hyperbolic sine math directly into MongoDB aggregation pipelines. Remember that sinh(0) = 0, the function is odd (sinh(-x) = -sinh(x)), and values grow exponentially for large inputs.
Do not confuse $sinh with circular $sin — they behave very differently. Next in the series: $size.
$sinh for exponential-style growth and hyperbolic transformssinh(0) = 0 when validating pipeline output$cosh when both hyperbolic components are needed$asinh for the inverse when recovering original values$sinh (hyperbolic) with $sin (circular trig)$sin — $sinh grows without limit$sinh is even like $cosh — it is odd$sinhUse these points when computing hyperbolic sines in MongoDB.
Exponential math.
PurposeOne expression.
SyntaxPasses origin.
RuleFlips sign.
PropertyHyperbolic vs circular.
ImportantMove on to $size to count array elements, or review $sin for circular trigonometry.
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