The $exp operator computes ex (Euler’s number raised to a power) in MongoDB aggregation pipelines. It is the natural exponential function, widely used for compound growth, decay curves, and probability modeling.
Compute ex in pipelines.
One expression inside $exp.
Add computed growth fields.
Apply to document fields.
Growth, decay, finance.
Pairs with natural log.
In MongoDB’s aggregation framework, the $exp operator raises Euler’s number e (approximately 2.718) to the power of a numeric expression. For example, { $exp: 0 } returns 1, and { $exp: 1 } returns approximately 2.718. This is the same as JavaScript’s Math.exp() and is essential for continuous growth and decay formulas.
Think of $exp as computing ex. Use it inside expression stages like $project or $addFields. For general base-to-power math (like 210), use $pow instead.
The $exp operator takes one numeric expression (the exponent):
{ $exp: <expression> }$exp — returns e raised to the power of the expression (ex).<expression> — can be a field path ("$rate"), a literal number, or another numeric expression.$project, $addFields, or $set.null, the result is null.These reference values help validate pipeline output:
| Question | Answer |
|---|---|
| Operator type | Aggregation expression operator (math) |
| Syntax | { $exp: <expression> } |
| Formula | ex where e ≈ 2.718 |
| Output | Positive number (or null) |
| Common stages | $project, $addFields, $set |
{
$exp: 2
}≈ 7.389 (e²)
{
$exp: "$rate"
}e raised to rate
{
$exp: 0
}Returns 1
{
$exp: null
}Returns null
Walk through sample growth data, compute exponential values with $project, and see how ex applies to real-world formulas.
Start with a metrics collection and compute ex for stored rate values using $project.
Suppose you have a metrics collection with a rate field representing an exponent:
[
{ "_id": ObjectId("609c26812e9274a86871bc6a"), "label": "Baseline", "rate": 0 },
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "label": "Unit growth", "rate": 1 },
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "label": "Double growth", "rate": 2 }
]Compute erate for each document:
db.metrics.aggregate([
{
$project: {
label: 1,
rate: 1,
expValue: { $exp: "$rate" }
}
}
])e&sup0; = 1e¹ ≈ 2.718e² ≈ 7.389Apply $exp to growth formulas, decay curves, and combined math in pipelines.
Calculate a growth multiplier using the formula P × ert, where r is the rate and t is time:
db.investments.aggregate([
{
$project: {
principal: 1,
rate: 1,
years: 1,
growthFactor: {
$exp: {
$multiply: [ "$rate", "$years" ]
}
},
futureValue: {
$multiply: [
"$principal",
{ $exp: { $multiply: [ "$rate", "$years" ] } }
]
}
}
}
])Multiply rate by time first with $multiply, then pass the result to $exp. Multiply by principal to get the future value.
Model decay with a negative exponent: e-λt:
db.sensors.aggregate([
{
$addFields: {
decayFactor: {
$exp: {
$multiply: [ -1, "$decayRate", "$elapsedTime" ]
}
}
}
}
])Negative exponents produce values between 0 and 1, modeling how a signal or substance decreases over time.
Common reference values every beginner should know:
db.samples.aggregate([
{
$project: {
expZero: { $exp: 0 }, // 1
expOne: { $exp: 1 }, // ≈ 2.718
expNeg: { $exp: -1 } // ≈ 0.368
}
}
])$exp(0) = 1, $exp(1) ≈ 2.718, and $exp(-1) ≈ 0.368. Use these to validate pipeline logic or as constants in formulas.
$exp WorksThe pipeline evaluates the input — a field like "$rate" or a numeric expression such as { $multiply: [ "$rate", "$years" ] }.
MongoDB raises e (approximately 2.718) to the power of the exponent and returns the result.
The computed value is written to the field you define in $project or $addFields.
You get growth factors, decay rates, or transformed values for charts, forecasts, and scientific calculations.
The $exp operator brings the natural exponential function into MongoDB aggregation pipelines. It is essential for continuous growth and decay formulas, financial projections, and any calculation that requires raising e to a power.
For beginners, the key idea is simple: wrap any numeric exponent in { $exp: ... } inside a stage like $project, and MongoDB returns ex. Remember that $exp(0) = 1 and $exp(1) ≈ 2.718.
$exp for ex (natural exponential) calculations$multiply for formulas like ert$round when displaying results to users$ln for log/exp round-trip transforms$exp when you need $pow with base 2 or 10$exp as a query filter outside expressionsnull input returns null$expUse these points when working with exponential math in MongoDB.
Computes ex.
Purpose{ $exp: expr }
$project, $addFields, $set.
UsageFinance and science.
Use caseexp(0)=1, exp(1)≈2.718.
Edge caseMove on to $expr for aggregation expressions in queries, or review $exists for field presence checks.
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