The $degreesToRadians operator converts an angle from degrees to radians in MongoDB aggregation pipelines. Use it when your data stores angles in degrees but you need radians for trigonometry or geospatial math.
Convert angle units in pipelines.
One expression inside $degreesToRadians.
Prepare angles for $sin, $cos.
degrees × (π / 180).
Geospatial, sensors, robotics.
Convert stored degree fields.
In MongoDB’s aggregation framework, the $degreesToRadians operator converts a numeric degree value into radians. For example, 180 degrees becomes approximately 3.142 radians (π), and 90 degrees becomes approximately 1.571 radians (π/2). This is essential because MongoDB trigonometric operators such as $sin, $cos, and $tan expect radians, not degrees.
Think of $degreesToRadians as MongoDB’s built-in version of converting compass headings or map angles into the format required by math functions. Use it inside expression stages like $project or $addFields.
The $degreesToRadians operator takes one numeric expression (an angle in degrees):
{ $degreesToRadians: <expression> }$degreesToRadians — multiplies the input by π/180 and returns radians.<expression> — can be a field path ("$bearing"), a literal number, or another numeric expression.$project, $addFields, or $set.null, the result is null.MongoDB applies the standard math formula. Full rotations and common angles convert predictably:
| Question | Answer |
|---|---|
| Operator type | Aggregation expression operator (math / unit conversion) |
| Syntax | { $degreesToRadians: <expression> } |
| Input | Angle in degrees (any numeric value) |
| Output unit | Radians |
| Common stages | $project, $addFields, $set |
{
$degreesToRadians: 180
}≈ 3.142 rad (π)
{
$degreesToRadians: "$bearing"
}Convert stored degrees
{
$degreesToRadians: 90
}≈ 1.571 rad (π/2)
{
$degreesToRadians: null
}Returns null
Start with angles stored in degrees, run an aggregation pipeline, and see the converted radian values step by step.
Use a locations collection with bearing angles in degrees and convert them to radians with $project.
Suppose you have a locations collection where each document stores a compass bearing in degrees:
[
{ "_id": ObjectId("609c26812e9274a86871bc6a"), "name": "North Tower", "bearingDeg": 0 },
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "name": "East Gate", "bearingDeg": 90 },
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "name": "South Pier", "bearingDeg": 180 }
]Convert each bearing from degrees to radians:
db.locations.aggregate([
{
$project: {
name: 1,
bearingDeg: 1,
bearingRad: { $degreesToRadians: "$bearingDeg" }
}
}
])0 degrees → 0 radians.90 degrees → ≈ 1.571 radians (π/2).180 degrees → ≈ 3.142 radians (π).Chain $degreesToRadians with trigonometry and handle common angle values in pipelines.
MongoDB trig functions expect radians. Convert degrees first, then compute the sine:
db.locations.aggregate([
{
$project: {
name: 1,
bearingDeg: 1,
bearingRad: { $degreesToRadians: "$bearingDeg" },
sinValue: {
$sin: { $degreesToRadians: "$bearingDeg" }
}
}
}
])Without conversion, passing 90 directly to $sin would not give the expected result. Convert to radians first so sin(90°) correctly returns 1.
Add a radian field for downstream geospatial or robotics calculations without overwriting the original degree value:
db.sensors.aggregate([
{
$addFields: {
headingRad: { $degreesToRadians: "$headingDeg" },
pitchRad: { $degreesToRadians: "$pitchDeg" }
}
}
])Keep human-readable degree fields for dashboards, but add radian fields for math-heavy pipeline stages like distance or vector calculations.
Common angle values every beginner should know:
db.samples.aggregate([
{
$project: {
rad0: { $degreesToRadians: 0 }, // 0 rad
rad90: { $degreesToRadians: 90 }, // π/2 rad
rad180: { $degreesToRadians: 180 }, // π rad
rad360: { $degreesToRadians: 360 } // 2π rad
}
}
])0° → 0, 90° → π/2, 180° → π, and 360° → 2π. Use these to validate pipeline logic or as constants in geospatial formulas.
$sin, $cos, or $tan.$degreesToRadians WorksThe pipeline evaluates the input — a field like "$bearingDeg" or a numeric literal such as 90.
MongoDB multiplies the value by π/180 to produce the equivalent angle in radians.
The radian value is written to the field you define in $project or $addFields.
You can pass the result directly to trig operators or geospatial formulas that require radians.
The $degreesToRadians operator is a small but essential math tool in MongoDB aggregation pipelines. It bridges the gap between human-friendly degree values and the radian format required by trigonometric functions, making it invaluable for geospatial, navigation, and sensor data workflows.
For beginners, the key idea is simple: wrap any degree expression in { $degreesToRadians: ... } inside a stage like $project, and MongoDB returns the radian equivalent using the standard π/180 formula.
$degreesToRadians before $sin, $cos, or $tan$radiansToDegrees for round-trip conversions$ifNull when needed$sin or $cos without converting$degreesToRadians as a query filter outside expressionsnull input returns null$degreesToRadians with $radiansToDegrees$degreesToRadiansUse these points when converting angles in MongoDB pipelines.
Multiply by π/180.
Purpose{ $degreesToRadians: expr }
Required before $sin/$cos.
UsageConvert bearings and headings.
Use casenull in → null out.
Edge caseMove on to $divide for division in pipelines, or review $dayOfYear for date extraction.
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