Introduction to MongoDB $acosh Operator

The $acosh operator is a mathematical operator in MongoDB used to calculate the inverse hyperbolic cosine value of a given numeric value. Hyperbolic cosine is a trigonometric function whose value represents the hyperbolic cosine value of an angle in a right-angled triangle. The inverse hyperbolic cosine is the inverse function of hyperbolic cosine, which can convert hyperbolic cosine values back to their original angle. The $acosh operator can be used in aggregation pipelines to perform calculations and transformations on numeric fields.


The syntax of the $acosh operator is as follows:

{ $acosh: <expression> }

Here, <expression> represents the numeric expression for which the inverse hyperbolic cosine value is to be calculated. It can be any valid numeric field or expression.

Use Cases

The $acosh operator is typically used in aggregation operations that involve calculations and transformations of numeric fields. For example, when analyzing website traffic data, the $acosh operator can be used to calculate the time users spend on the website to determine the busiest time periods.


Suppose we have a collection named sales containing the following documents:

{ "_id" : 1, "product" : "apple", "price" : 1.5 }
{ "_id" : 2, "product" : "banana", "price" : 2.0 }
{ "_id" : 3, "product" : "orange", "price" : 1.0 }

Now, we want to calculate the inverse hyperbolic cosine value of each product’s price. This can be done using the following aggregation pipeline:

    $project: {
      product: 1,
      acosh_price: { $acosh: "$price" }

The above pipeline uses the $project stage to project the product field from the original document and the acosh_price field from the computed result. In the $acosh operator, we take the price field from the document as input and calculate the inverse hyperbolic cosine value of each product’s price. Running the above aggregation pipeline produces the following result:

{ "_id" : 1, "product" : "apple", "acosh_price" : 0.9624236501192069 }
{ "_id" : 2, "product" : "banana", "acosh_price" : 1.3169578969248166 }
{ "_id" : 3, "product" : "orange", "acosh_price" : 0 }

As can be seen, we have successfully calculated the inverse hyperbolic cosine value of each product’s price and saved the result in the acosh_price field. Note that since the domain of the acosh function is positive real numbers, the $acosh operator can only be used to calculate values greater than 1. Otherwise, an error will occur. Therefore, when using the $acosh operator, it is necessary to properly process and filter the data to ensure that only the data that meets the conditions is calculated.

In addition to using the $acosh operator to calculate the inverse hyperbolic cosine value of prices as shown in the example above, there are other use cases, such as calculating the rate of change of angles, velocities, etc. in mathematical and physical fields, and compressing and normalizing relatively large numerical values in data processing.


In summary, the MongoDB $acosh operator is a very useful mathematical function operator that can conveniently calculate the inverse hyperbolic cosine value of the input value and save the result as a new field in the output document. It is suitable for various scenarios that require processing and calculating numerical values.