# $exp (aggregation)¶

On this page

## Definition¶

`$exp`

¶*New in version 3.2*.Raises Euler's number (i.e.

*e*) to the specified exponent and returns the result.`$exp`

has the following syntax:{ $exp: <exponent> } The

`<exponent>`

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

## Behavior¶

If the argument resolves to a value of `null`

or refers to a field that is
missing, `$exp`

returns `null`

. If the argument resolves to
`NaN`

, `$exp`

returns `NaN`

.

Example | Results |
---|---|

`{ $exp: 0 }` | `1` |

`{ $exp: 2 }` | `7.38905609893065` |

`{ $exp: -2 }` | `0.1353352832366127` |

## Example¶

A collection named `accounts`

contains the following documents:

{ _id: 1, rate: .08, pv: 10000 } { _id: 2, rate: .0825, pv: 250000 } { _id: 3, rate: .0425, pv: 1000 }

The following example calculates the effective interest rate for continuous compounding:

db.accounts.aggregate( [ { $project: { effectiveRate: { $subtract: [ { $exp: "$rate"}, 1 ] } } } ] )

The operation returns the following results:

{ "_id" : 1, "effectiveRate" : 0.08328706767495864 } { "_id" : 2, "effectiveRate" : 0.08599867343905654 } { "_id" : 3, "effectiveRate" : 0.04341605637367807 }

Give Feedback