---
title: exponentialMovingAverage() function
description: >
  `exponentialMovingAverage()` calculates the exponential moving average of `n`
  number of values in the `_value` column giving more weight to more recent data.
menu:
  flux_v0_ref:
    name: exponentialMovingAverage
    parent: universe
    identifier: universe/exponentialMovingAverage
weight: 101
flux/v0/tags: [transformations]
introduced: 0.37.0
---

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`exponentialMovingAverage()` calculates the exponential moving average of `n`
number of values in the `_value` column giving more weight to more recent data.

### Exponential moving average rules

- The first value of an exponential moving average over `n` values is the algebraic mean of `n` values.
- Subsequent values are calculated as `y(t) = x(t) * k + y(t-1) * (1 - k)`, where:
    - `y(t)` is the exponential moving average at time `t`.
    - `x(t)` is the value at time `t`.
    - `k = 2 / (1 + n)`.
- The average over a period populated by only `null` values is `null`.
- Exponential moving averages skip `null` values.

##### Function type signature

```js
(<-tables: stream[{A with _value: B}], n: int) => stream[{A with _value: B}] where B: Numeric
```

{{% caption %}}
For more information, see [Function type signatures](/flux/v0/function-type-signatures/).
{{% /caption %}}

## Parameters

### n
({{< req >}})
Number of values to average.



### tables

Input data. Default is piped-forward data (`<-`).




## Examples

- [Calculate a three point exponential moving average](#calculate-a-three-point-exponential-moving-average)
- [Calculate a three point exponential moving average with null values](#calculate-a-three-point-exponential-moving-average-with-null-values)

### Calculate a three point exponential moving average

```js
import "sampledata"

sampledata.int()
    |> exponentialMovingAverage(n: 3)

```

{{< expand-wrapper >}}
{{% expand "View example input and output" %}}

#### Input data

| _time                | _value  | *tag |
| -------------------- | ------- | ---- |
| 2021-01-01T00:00:00Z | -2      | t1   |
| 2021-01-01T00:00:10Z | 10      | t1   |
| 2021-01-01T00:00:20Z | 7       | t1   |
| 2021-01-01T00:00:30Z | 17      | t1   |
| 2021-01-01T00:00:40Z | 15      | t1   |
| 2021-01-01T00:00:50Z | 4       | t1   |

| _time                | _value  | *tag |
| -------------------- | ------- | ---- |
| 2021-01-01T00:00:00Z | 19      | t2   |
| 2021-01-01T00:00:10Z | 4       | t2   |
| 2021-01-01T00:00:20Z | -3      | t2   |
| 2021-01-01T00:00:30Z | 19      | t2   |
| 2021-01-01T00:00:40Z | 13      | t2   |
| 2021-01-01T00:00:50Z | 1       | t2   |


#### Output data

| _time                | _value  | *tag |
| -------------------- | ------- | ---- |
| 2021-01-01T00:00:20Z | 5       | t1   |
| 2021-01-01T00:00:30Z | 11      | t1   |
| 2021-01-01T00:00:40Z | 13      | t1   |
| 2021-01-01T00:00:50Z | 8.5     | t1   |

| _time                | _value             | *tag |
| -------------------- | ------------------ | ---- |
| 2021-01-01T00:00:20Z | 6.666666666666667  | t2   |
| 2021-01-01T00:00:30Z | 12.833333333333334 | t2   |
| 2021-01-01T00:00:40Z | 12.916666666666668 | t2   |
| 2021-01-01T00:00:50Z | 6.958333333333334  | t2   |

{{% /expand %}}
{{< /expand-wrapper >}}

### Calculate a three point exponential moving average with null values

```js
import "sampledata"

sampledata.int(includeNull: true)
    |> exponentialMovingAverage(n: 3)

```

{{< expand-wrapper >}}
{{% expand "View example input and output" %}}

#### Input data

| _time                | _value  | *tag |
| -------------------- | ------- | ---- |
| 2021-01-01T00:00:00Z | -2      | t1   |
| 2021-01-01T00:00:10Z |         | t1   |
| 2021-01-01T00:00:20Z | 7       | t1   |
| 2021-01-01T00:00:30Z |         | t1   |
| 2021-01-01T00:00:40Z |         | t1   |
| 2021-01-01T00:00:50Z | 4       | t1   |

| _time                | _value  | *tag |
| -------------------- | ------- | ---- |
| 2021-01-01T00:00:00Z |         | t2   |
| 2021-01-01T00:00:10Z | 4       | t2   |
| 2021-01-01T00:00:20Z | -3      | t2   |
| 2021-01-01T00:00:30Z | 19      | t2   |
| 2021-01-01T00:00:40Z |         | t2   |
| 2021-01-01T00:00:50Z | 1       | t2   |


#### Output data

| _time                | _value  | *tag |
| -------------------- | ------- | ---- |
| 2021-01-01T00:00:20Z | 2.5     | t1   |
| 2021-01-01T00:00:30Z | 2.5     | t1   |
| 2021-01-01T00:00:40Z | 2.5     | t1   |
| 2021-01-01T00:00:50Z | 3.25    | t1   |

| _time                | _value  | *tag |
| -------------------- | ------- | ---- |
| 2021-01-01T00:00:20Z | 0.5     | t2   |
| 2021-01-01T00:00:30Z | 9.75    | t2   |
| 2021-01-01T00:00:40Z | 9.75    | t2   |
| 2021-01-01T00:00:50Z | 5.375   | t2   |

{{% /expand %}}
{{< /expand-wrapper >}}