The $asin operator returns the arc sine (inverse sine) of a number in MongoDB aggregation pipelines. If you know a sine value, $asin tells you the angle in radians.
Sine value → angle.
One expression inside $asin.
Output is always in radians.
Values must be -1 to 1.
Geometry, robotics, signals.
Convert with $multiply/$divide.
In MongoDB’s aggregation framework, the $asin operator computes the arc sine of a numeric expression. For example, if sin(30°) = 0.5, then $asin(0.5) returns approximately 0.524 radians (which is 30°). The input is a sine ratio, not an angle — and the output is the angle in radians.
Think of $asin as the reverse of $sin. Use it inside aggregation expression stages like $project or $addFields, not as a standalone query filter.
The $asin operator takes one numeric expression:
{ $asin: <expression> }$asin — returns the arc sine of the expression in radians.<expression> — must evaluate to a number between -1 and 1 (inclusive).$project, $addFields, or $set.null, the result is null.[-1, 1] return null or NaN.$asin only accepts sine values in the range -1 to 1. Anything outside that range returns null or NaN.
| Question | Answer |
|---|---|
| Operator type | Aggregation expression operator (trigonometry) |
| Syntax | { $asin: <expression> } |
| Input range | -1 to 1 (inclusive) |
| Output unit | Radians (range -π/2 to π/2) |
| Common stages | $project, $addFields, $set |
{
$asin: 0.5
}≈ 0.524 rad (30°)
{
$asin: "$sine"
}Angle from sine field
{
$asin: 0
}Returns 0 radians
{
$asin: null
}Returns null
Start with sine values, run an aggregation pipeline, and see the resulting angles in radians.
Use an angles collection with stored sine values and recover the angle in radians with $project.
Suppose you have an angles collection where each document stores a sine value (not an angle):
[
{ "_id": ObjectId("609c26812e9274a86871bc6a"), "sine": 0.5 },
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "sine": 0.8 },
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "sine": 1.2 }
]Compute the angle in radians for each sine value:
db.angles.aggregate([
{
$project: {
sine: 1,
angleRadians: { $asin: "$sine" }
}
}
])sine is 0.5 → asin(0.5) ≈ 0.524 rad (30°).sine is 0.8 → asin(0.8) ≈ 0.927 rad.sine is 1.2 → out of range, returns null.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: {
sine: 1,
angleRadians: { $asin: "$sine" },
angleDegrees: {
$multiply: [
{ $asin: "$sine" },
{ $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 y-axis using the sine value:
db.vectors.aggregate([
{
$project: {
label: 1,
x: 1,
y: 1,
angleFromYAxis: { $asin: "$y" }
}
}
])For a unit vector, the y-component equals sin(θ). Applying $asin on $y recovers the angle from the horizontal axis in radians.
Common boundary values every beginner should know:
db.samples.aggregate([
{
$project: {
asinZero: { $asin: 0 }, // 0 rad (0°)
asinHalf: { $asin: 0.5 }, // ≈ 0.524 rad (30°)
asinOne: { $asin: 1 }, // ≈ 1.571 rad (90°)
asinNeg: { $asin: -1 } // ≈ -1.571 rad (-90°)
}
}
])$asin(0) = 0, $asin(1) = π/2, and $asin(-1) = -π/2. These edge cases help validate pipeline logic.
$asin WorksThe pipeline evaluates the input — a field like "$sine" or a numeric expression between -1 and 1.
MongoDB applies the arc sine function and returns the angle in radians ( -π/2 to π/2 ).
The angle is written to the field you define in $project or $addFields.
Use the radians directly or convert to degrees for reports and dashboards.
The $asin operator is a practical trigonometry tool in MongoDB aggregation pipelines. It converts sine values back into angles, which is essential for geometry, engineering, robotics, and any dataset that stores trig ratios instead of raw angles.
For beginners, remember three things: input must be between -1 and 1, output is in radians, and values outside the valid range return null.
$round when displaying angle results$sin to verify round-trip calculations$ifNull when needed$asin — it expects a sine ratio$asin (inverse sine) with $sin (sine)$asin as a query filter outside expressions$asinUse these points when working with trigonometric data in MongoDB.
Sine ratio → angle in radians.
Purpose{ $asin: expr }
-1 to 1 only.
DomainConvert to degrees if needed.
UnitsValues > 1 return null.
Edge caseMove on to $asinh or review $acos for arc cosine calculations.
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