﻿---
title: Derivative aggregation
description: A parent pipeline aggregation which calculates the derivative of a specified metric in a parent histogram (or date_histogram) aggregation. The specified...
url: https://www.elastic.co/elastic/docs-builder/docs/2545/reference/aggregations/search-aggregations-pipeline-derivative-aggregation
products:
  - Elasticsearch
---

# Derivative aggregation
A parent pipeline aggregation which calculates the derivative of a specified metric in a parent histogram (or date_histogram) aggregation. The specified metric must be numeric and the enclosing histogram must have `min_doc_count` set to `0` (default for `histogram` aggregations).

## Syntax

A `derivative` aggregation looks like this in isolation:
```js
"derivative": {
  "buckets_path": "the_sum"
}
```



| Parameter Name | Description                                                                                                                                                                                                                          | Required | Default Value |
|----------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------|---------------|
| `buckets_path` | The path to the buckets we wish to find the derivative for (see [`buckets_path` Syntax](/elastic/docs-builder/docs/2545/reference/aggregations/pipeline#buckets-path-syntax) for more details)                                       | Required |               |
| `gap_policy`   | The policy to apply when gaps are found in the data (see [Dealing with gaps in the data](/elastic/docs-builder/docs/2545/reference/aggregations/pipeline#gap-policy) for more details)                                               | Optional | `skip`        |
| `format`       | [DecimalFormat pattern](https://docs.oracle.com/en/java/javase/11/docs/api/java.base/java/text/DecimalFormat.html) for theoutput value. If specified, the formatted value is returned in the aggregation’s`value_as_string` property | Optional | `null`        |


## First Order Derivative

The following snippet calculates the derivative of the total monthly `sales`:
```json

{
  "size": 0,
  "aggs": {
    "sales_per_month": {
      "date_histogram": {
        "field": "date",
        "calendar_interval": "month"
      },
      "aggs": {
        "sales": {
          "sum": {
            "field": "price"
          }
        },
        "sales_deriv": {
          "derivative": {
            "buckets_path": "sales" <1>
          }
        }
      }
    }
  }
}
```

And the following may be the response:
```json
{
   "took": 11,
   "timed_out": false,
   "_shards": ...,
   "hits": ...,
   "aggregations": {
      "sales_per_month": {
         "buckets": [
            {
               "key_as_string": "2015/01/01 00:00:00",
               "key": 1420070400000,
               "doc_count": 3,
               "sales": {
                  "value": 550.0
               } 
            },
            {
               "key_as_string": "2015/02/01 00:00:00",
               "key": 1422748800000,
               "doc_count": 2,
               "sales": {
                  "value": 60.0
               },
               "sales_deriv": {
                  "value": -490.0 
               }
            },
            {
               "key_as_string": "2015/03/01 00:00:00",
               "key": 1425168000000,
               "doc_count": 2, 
               "sales": {
                  "value": 375.0
               },
               "sales_deriv": {
                  "value": 315.0
               }
            }
         ]
      }
   }
}
```


## Second Order Derivative

A second order derivative can be calculated by chaining the derivative pipeline aggregation onto the result of another derivative pipeline aggregation as in the following example which will calculate both the first and the second order derivative of the total monthly sales:
```json

{
  "size": 0,
  "aggs": {
    "sales_per_month": {
      "date_histogram": {
        "field": "date",
        "calendar_interval": "month"
      },
      "aggs": {
        "sales": {
          "sum": {
            "field": "price"
          }
        },
        "sales_deriv": {
          "derivative": {
            "buckets_path": "sales"
          }
        },
        "sales_2nd_deriv": {
          "derivative": {
            "buckets_path": "sales_deriv" <1>
          }
        }
      }
    }
  }
}
```

And the following may be the response:
```json
{
   "took": 50,
   "timed_out": false,
   "_shards": ...,
   "hits": ...,
   "aggregations": {
      "sales_per_month": {
         "buckets": [
            {
               "key_as_string": "2015/01/01 00:00:00",
               "key": 1420070400000,
               "doc_count": 3,
               "sales": {
                  "value": 550.0
               } 
            },
            {
               "key_as_string": "2015/02/01 00:00:00",
               "key": 1422748800000,
               "doc_count": 2,
               "sales": {
                  "value": 60.0
               },
               "sales_deriv": {
                  "value": -490.0
               } 
            },
            {
               "key_as_string": "2015/03/01 00:00:00",
               "key": 1425168000000,
               "doc_count": 2,
               "sales": {
                  "value": 375.0
               },
               "sales_deriv": {
                  "value": 315.0
               },
               "sales_2nd_deriv": {
                  "value": 805.0
               }
            }
         ]
      }
   }
}
```


## Units

The derivative aggregation allows the units of the derivative values to be specified. This returns an extra field in the response `normalized_value` which reports the derivative value in the desired x-axis units. In the below example we calculate the derivative of the total sales per month but ask for the derivative of the sales as in the units of sales per day:
```json

{
  "size": 0,
  "aggs": {
    "sales_per_month": {
      "date_histogram": {
        "field": "date",
        "calendar_interval": "month"
      },
      "aggs": {
        "sales": {
          "sum": {
            "field": "price"
          }
        },
        "sales_deriv": {
          "derivative": {
            "buckets_path": "sales",
            "unit": "day" <1>
          }
        }
      }
    }
  }
}
```

And the following may be the response:
```json
{
   "took": 50,
   "timed_out": false,
   "_shards": ...,
   "hits": ...,
   "aggregations": {
      "sales_per_month": {
         "buckets": [
            {
               "key_as_string": "2015/01/01 00:00:00",
               "key": 1420070400000,
               "doc_count": 3,
               "sales": {
                  "value": 550.0
               } 
            },
            {
               "key_as_string": "2015/02/01 00:00:00",
               "key": 1422748800000,
               "doc_count": 2,
               "sales": {
                  "value": 60.0
               },
               "sales_deriv": {
                  "value": -490.0, 
                  "normalized_value": -15.806451612903226 
               }
            },
            {
               "key_as_string": "2015/03/01 00:00:00",
               "key": 1425168000000,
               "doc_count": 2,
               "sales": {
                  "value": 375.0
               },
               "sales_deriv": {
                  "value": 315.0,
                  "normalized_value": 11.25
               }
            }
         ]
      }
   }
}
```