$sqrt (expression operator)

Definition

$sqrt

Calculates the square root of a positive number and returns the result as a double.

$sqrt has the following syntax:

{ $sqrt: <number> }

The argument can be any valid expression as long as it resolves to a non-negative number. For more information on expressions, see Expressions.

Behavior

The default return type is a double. If at least one operand is a decimal, then the return type is a decimal.

If the argument resolves to a value of null or refers to a field that is missing, $sqrt returns null. If the argument resolves to NaN, $sqrt returns NaN.

$sqrt errors on negative numbers.

Example

A collection points contains the following documents:

db.points.insertMany( [
   { _id: 1, p1: { x: 5, y: 8 }, p2: { x: 0, y: 5} },
   { _id: 2, p1: { x: -2, y: 1 }, p2: { x: 1, y: 5} },
   { _id: 3, p1: { x: 4, y: 4 }, p2: { x: 4, y: 0} }
] )

The following example uses $sqrt to calculate the distance between p1 and p2:

db.points.aggregate([
   {
     $project: {
        distance: {
           $sqrt: {
               $add: [
                  { $pow: [ { $subtract: [ "$p2.y", "$p1.y" ] }, 2 ] },
                  { $pow: [ { $subtract: [ "$p2.x", "$p1.x" ] }, 2 ] }
               ]
           }
        }
     }
   }
])

The operation returns the following results:

{ _id: 1, distance: 5.830951894845301 }
{ _id: 2, distance: 5 }
{ _id: 3, distance: 4 }