The $acos operator returns the arc cosine (inverse cosine) of a number in MongoDB aggregation pipelines. If you know a cosine value, $acos tells you the angle in radians.
Cosine value → angle.
One expression inside $acos.
Output is always in radians.
Values must be -1 to 1.
Geometry, robotics, signals.
Convert with $multiply/$divide.
In MongoDB’s aggregation framework, the $acos operator computes the arccosine of a numeric expression. For example, if cos(60°) = 0.5, then $acos(0.5) returns approximately 1.047 radians (which is 60°). This is useful when your data stores cosine values and you need to recover the original angle.
Think of $acos as the reverse of $cos. Use it inside aggregation expression stages like $project or $addFields, not as a standalone query filter.
The $acos operator takes one numeric expression:
{ $acos: <expression> }$acos — returns the arc cosine of the expression in radians.<expression> — must evaluate to a number between -1 and 1 (inclusive).$project, $addFields, or $set.null, the result is null.[-1, 1] return NaN.$acos only accepts cosine values in the range -1 to 1. Anything outside that range returns NaN.
| Question | Answer |
|---|---|
| Operator type | Aggregation expression operator (trigonometry) |
| Syntax | { $acos: <expression> } |
| Input range | -1 to 1 (inclusive) |
| Output unit | Radians (range 0 to π) |
| Common stages | $project, $addFields, $set |
{
$acos: 0.5
}≈ 1.047 rad (60°)
{
$acos: "$cosine"
}Angle from cosine field
{
$acos: 1
}Returns 0 radians
{
$acos: null
}Returns null
Start with cosine values, run an aggregation pipeline, and see the resulting angles in radians.
Use an angles collection with stored cosine values and recover the angle in radians with $project.
Suppose you have an angles collection where each document stores a cosine value:
[
{ "_id": ObjectId("609c26812e9274a86871bc6a"), "cosine": 0.5 },
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "cosine": 0.866 },
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "cosine": 0.707 }
]Compute the angle in radians for each cosine value:
db.angles.aggregate([
{
$project: {
angleRadians: { $acos: "$cosine" }
}
}
])cosine is 0.5 → acos(0.5) ≈ 1.047 rad (60°).cosine is 0.866 → acos(0.866) ≈ 0.524 rad (30°).cosine is 0.707 → acos(0.707) ≈ 0.785 rad (45°).Convert radians to degrees and handle common trigonometric edge cases in pipelines.
MongoDB returns radians by default. Multiply by 180 / π to get degrees:
db.angles.aggregate([
{
$project: {
cosine: 1,
angleRadians: { $acos: "$cosine" },
angleDegrees: {
$multiply: [
{ $acos: "$cosine" },
{ $divide: [ 180, 3.141592653589793 ] }
]
}
}
}
])The formula is degrees = radians × (180 / π). Use $multiply and $divide to apply it inside the pipeline.
When you have x/y components of a unit vector, compute the angle from the x-axis:
db.vectors.aggregate([
{
$project: {
label: 1,
x: 1,
y: 1,
angleFromXAxis: { $acos: "$x" }
}
}
])For a unit vector, the x-component equals cos(θ). Applying $acos on $x recovers the angle from the positive x-axis.
Common boundary values every beginner should know:
db.samples.aggregate([
{
$project: {
acosOne: { $acos: 1 }, // 0 rad (0°)
acosZero: { $acos: 0 }, // π/2 rad (90°)
acosNeg: { $acos: -1 } // π rad (180°)
}
}
])$acos(1) = 0, $acos(0) = π/2, and $acos(-1) = π. These edge cases are useful for validating pipeline logic.
$acos WorksThe pipeline evaluates the input — a field like "$cosine" or a numeric expression between -1 and 1.
MongoDB applies the arccosine function and returns the angle in radians (0 to π).
The angle is written to the field you define in $project or $addFields.
You can use the radians directly or convert to degrees for reports and dashboards.
The $acos operator is a practical trigonometry tool in MongoDB aggregation pipelines. It converts cosine values back into angles, which is essential for geometry, engineering, robotics, and any dataset that stores trig components instead of raw angles.
For beginners, remember three things: input must be between -1 and 1, output is in radians, and you can convert to degrees with a simple multiply/divide step.
$round when displaying angle results$cos to verify round-trip calculations$ifNull when needed$acos as a query filter outside expressionsNaN$acos (inverse cosine) with $cos (cosine)$acosUse these points when working with trigonometric data in MongoDB.
Cosine → angle in radians.
Purpose{ $acos: expr }
-1 to 1 only.
DomainConvert to degrees if needed.
UnitsValues > 1 return NaN.
Edge caseMove on to $acosh or review $abs for absolute value calculations.
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