In an [Event Segmentation](/docs/analytics/charts/event-segmentation/event-segmentation-build) or [Data Table](/docs/analytics/charts/data-tables/data-tables-multi-dimensional-analysis) chart, the **Formula** option in the Measured As module's Advanced drop-down offers more flexibility when performing analyses. Custom formulas also help compare analyses on the same chart.

Choose from more than 20 custom formulas to plot the metrics you need. You can plot up to ten formulas on the same chart, separated by semicolons.

This article explains the mechanics of custom formulas, with examples of formulas you can use right now.

{% callout type="note" heading="" %}
To combine event and session inputs in one expression, (for example, Revenue per Session or Add to Carts per Session), use a [Hybrid Formula](/docs/analytics/charts/metric-explorer/hybrid-formulas) in a Data Table or Metric Explorer chart. The Event Segmentation chart continues to use the standard event-only formula path described on this page.

The Experiment Results chart also uses formula metrics, but in a different way than the Event Segmentation or Data Table charts. For more about those differences, refer to [this Help Center article on using formula metrics in Amplitude's Experiment Results chart](/docs/analytics/charts/experiment-results/experiment-results-use-formula-metrics).
{% /callout %}

## Formula syntax

In your formulas, refer to events selected in the Events Module by their corresponding letter. Functions and parameters aren't case sensitive. You can also perform the following arithmetic operations:

- Parenthesis ().
- Addition (+).
- Subtraction (-).
- Multiplication (\*).
- Division (/).

For example, the letter A in the formula `UNIQUES(A)` refers to the event `View Item Details`, while the letter B in the formula `UNIQUES(B)` refers to the event `Add Item to Cart`. This setup displays the ratio of users that viewed an item's details to users that placed an item in their cart.

You can write a formula that consists of events, grouping each event by a property or properties. For the formula to be valid, the properties must have matching values across all events you segment.

For example, if you have an event called `Page Name`, the following property values don't match:

- `Tutorial` and `TUTORIAL` (matching is case sensitive).
- `1` and `1.0` (non-matching characters).

The order in which you group properties also matters. Both events must have the _grouped by_ values in the same order; otherwise, Amplitude shows a warning that events have no matching group-by values.

{% callout type="note" heading="Ranking with multi-term formulas" %}
When you use multi-term formula metrics with group-bys, Amplitude ranks groups by the sum of unique users across all metrics in the formula, not by the final calculated values. This ranking can affect which groups appear in high-cardinality results. For more details, refer to [Column ranking behavior in Data Tables](/docs/analytics/charts/data-tables/data-tables-results-and-sorting-logic#column-ranking-behavior).
{% /callout %}

Use custom formulas to uncover how many more times users in one cohort trigger a particular event than users in another cohort do.

To compare a metric between two different cohorts or user segments, add the segment number to the letter that designates the event: `UNIQUES(A1)/UNIQUES(A2)`. This setup displays a ratio of your cohorts' performance on the same event as a single plotted line on your graph.

You can also view your metrics in percentages or dollars by adding the following prefixes to your formula:

- Percentage (%:).
- Dollars ($:).

## List of available formulas

This section lists available formulas by type: Metric, Aggregation, and Function. Click a formula name to review its syntax.

### Metrics formulas

With metrics formulas, you can query a metric for a particular event that interests you. These formulas use green color-coding. Each metrics formula requires a letter that corresponds to the event you're interested in as a parameter.

|                               |                                 |                                   |                                   |
| ----------------------------- | ------------------------------- | --------------------------------- | --------------------------------- |
| [ACTIVE](#active)             | [ARPAU](#arpau)                 | [AVG](#avg)                       | [FREQPERCENTILE](#freqpercentile) |
| [HIST](#hist)                 | [PERCENTILE](#percentile)       | [PROPAVG](#propavg)               | [PROPCOUNT](#propcount)           |
| [PROPCOUNTAVG](#propcountavg) | [PROPHIST](#prophist)           | [PROPMAX](#propmax)               | [PROPMIN](#propmin)               |
| [PROPSUM](#propsum)           | [REVENUETOTAL](#revenuetotal)   | [TOTALS](#totals)                 | [UNIQUES](#uniques)               |
| [EVENTTOTALS](#eventtotals)   | [SESSIONTOTALS](#sessiontotals) | [SEMANTICTOTALS](#semantictotals) |                                   |

### Aggregation formulas

Aggregation formulas let you query a rolling average or rolling window for the metric and event that interests you. These formulas use purple color-coding. Each aggregation formula requires three components: the metric to aggregate, the event that interests you, and the interval to aggregate by.

|                   |                     |                     |                                 |
| ----------------- | ------------------- | ------------------- | ------------------------------- |
| [CUMSUM](#cumsum) | [ROLLAVG](#rollavg) | [ROLLWIN](#rollwin) | [ROLLWINBEFORE](#rollwinbefore) |

### Function formulas

Function formulas let you query a mathematical function for a particular event and metric you're interested in. These formulas use blue color-coding. Each function formula requires a value that's either a constant or another formula that contains an event.

|                 |               |                         |                 |
| --------------- | ------------- | ----------------------- | --------------- |
| [EXP](#exp)     | [LN](#ln)     | [LOG](#log)             | [LOG10](#log10) |
| [POWER](#power) | [SQRT](#sqrt) | [TRENDLINE](#trendline) |                 |

## Metrics formulas

### ACTIVE

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`ACTIVE(event)`

**Parameters**

| Parameter | Description                                               |
| --------- | --------------------------------------------------------- |
| `event`   | A letter that corresponds to an event in the Events card. |

**Returns**

The percentage of active users that triggered the event, in decimal fraction form.
{% /card %}

Returns the percentage of active users that triggered the event.

This is the same as the `Active %` [metric](/docs/analytics/charts/data-tables/data-tables-create-metric) in the Measured card, but here it displays in decimal fraction form.

{% callout type="example" heading="Example" %}
`ACTIVE(A)` displays the percentage of active users that have triggered the `View Item Details` event.
{% /callout %}
{% /formula-definition %}

### ARPAU

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`$:ARPAU(event)`

**Parameters**

| Parameter | Description                                                      |
| --------- | ---------------------------------------------------------------- |
| `event`   | A letter that corresponds to a revenue event in the Events card. |

**Returns**

The aggregate sum of the revenue event property formatted as a currency, divided by the number of unique active users in that same time period. Equivalent to `PROPSUM(event) / UNIQUES(any active event)`.
{% /card %}

Returns the aggregate revenue per active user, formatted as a currency.

`ARPAU` works only when you group by a numerical property on the event. The `$:` prefix is optional; its presence ensures the output format is a currency.

{% callout type="example" heading="Example" %}
Use `ARPAU` to calculate the average revenue per active user of a generic e-commerce company.
{% /callout %}

{% callout type="note" %}
You can't use `ARPAU` in conjunction with [aggregation formulas](/docs/analytics/charts/event-segmentation/event-segmentation-custom-formulas).
{% /callout %}
{% /formula-definition %}

### AVG

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`AVG(event)`

**Parameters**

| Parameter | Description                                                                          |
| --------- | ------------------------------------------------------------------------------------ |
| `event`   | A letter that corresponds to an event in the left module of the chart control panel. |

**Returns**

The average number of times users triggered the event. Equivalent to `TOTALS(event)/UNIQUES(event)`.
{% /card %}

Returns the average number of times users triggered the event.

{% callout type="example" heading="Example" %}
`AVG(A); AVG(B)` displays the average number of times users triggered `View Item Details` (event A) and the average number of times users triggered `Add Item to Cart` (event B) on the same chart.
{% /callout %}
{% /formula-definition %}

### FREQPERCENTILE

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`FREQPERCENTILE(event, percentage)`

**Parameters**

| Parameter    | Description                                                         |
| ------------ | ------------------------------------------------------------------- |
| `event`      | A letter that corresponds to an event in the Events card.           |
| `percentage` | The percentile that interests you. Must be less than or equal to 1. |

**Returns**

The event frequency at the specified percentile across all users.
{% /card %}

Returns the inputted [percentile](https://en.wikipedia.org/wiki/Percentile) event frequency across all users.

A percentile is a measure that indicates the value below which a given percentage of values fall. Use the result to create a [behavioral cohort](/docs/analytics/behavioral-cohorts) of your power users and analyze what distinguishes them from users that aren't in the cohort.

{% callout type="example" heading="Example" %}
`FREQPERCENTILE(A, 0.9)` shows the 90th percentile of users that triggered the `View Item Details` event.
{% /callout %}
{% /formula-definition %}

### HIST

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`HIST(event)`

**Parameters**

| Parameter | Description                                               |
| --------- | --------------------------------------------------------- |
| `event`   | A letter that corresponds to an event in the Events card. |

**Returns**

The distribution of the event frequency per unique user over the selected time period.
{% /card %}

Returns the distribution of the event frequency per unique user over the selected time period.
{% /formula-definition %}

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`HIST(session)`

**Parameters**

| Parameter | Description                                                  |
| --------- | ------------------------------------------------------------ |
| `session` | A letter that corresponds to a session in the Sessions card. |

**Returns**

The distribution of session durations, in seconds, over the selected time period.
{% /card %}

The syntax for `HIST` varies slightly for the [User Sessions chart](https://help.amplitude.com/hc/en-us/articles/231275508-The-User-Sessions-chart-Track-engagement-frequency-and-duration) because sessions are the focus of the metrics.

Use this variant when you want to understand how long user sessions last.
{% /formula-definition %}

### PERCENTILE

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`PERCENTILE(event, percentage)`

**Parameters**

| Parameter    | Description                                                         |
| ------------ | ------------------------------------------------------------------- |
| `event`      | A letter that corresponds to an event in the Events card.           |
| `percentage` | The percentile that interests you. Must be less than or equal to 1. |

**Returns**

The value of the grouped-by property at the specified percentile.
{% /card %}

Returns the inputted [percentile](https://en.wikipedia.org/wiki/Percentile) of the property being grouped by.

{% callout type="note" %}
This function works only when you group by a numerical property on the event.
{% /callout %}

{% callout type="example" heading="Example" %}
`PERCENTILE(A, 0.9)` returns the 90th percentile for revenue of all `Complete Purchase` events. `PERCENTILE` is also useful when tracking load times to ensure that a particular percentage of load times stays below a certain threshold.
{% /callout %}
{% /formula-definition %}

### PROPAVG

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`PROPAVG(event)`

**Parameters**

| Parameter | Description                                               |
| --------- | --------------------------------------------------------- |
| `event`   | A letter that corresponds to an event in the Events card. |

**Returns**

The average of the grouped-by property values. Equivalent to `PROPSUM(event)/TOTALS(event)`.
{% /card %}

Returns the average of the property values you are grouping by.

`PROPAVG` works only when you group by a numerical property on the event. If you group by multiple properties, the formula runs the calculation with the first group-by clause.

{% callout type="note" %}
The `PROPAVG` formula ignores events where the selected property value is `(none)`.
{% /callout %}

{% callout type="example" heading="Example" %}
Use `PROPAVG` to calculate the average revenue generated by completed purchases on a given day.
{% /callout %}
{% /formula-definition %}

### PROPCOUNT

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`PROPCOUNT(event)`

**Parameters**

| Parameter | Description                                                                                                                                                     |
| --------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `event`   | A letter that corresponds to an event in the Events card. If you group by multiple properties, the formula runs the calculation with the first group-by clause. |

**Returns**

The number of distinct property values for the property the event is grouped by.
{% /card %}

Returns the number of distinct property values for the property the event is grouped by.

`PROPCOUNT` is an estimate of distinct property values. The estimate comes from a [HyperLogLog algorithm](https://en.wikipedia.org/wiki/HyperLogLog), and its accuracy depends on the amount of data it has to work with. Expect a relative error in the range of 0.1% for fewer than 12,000 unique values, and up to 0.5% for more than 12,000 unique property values, depending on the cardinality of the property.

{% callout type="example" heading="Example" %}
In a DAU chart, `PROPCOUNT(A)` retrieves the number of different countries that had an active user during the given period.
{% /callout %}
{% /formula-definition %}

### PROPCOUNTAVG

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`PROPCOUNTAVG(event)`

**Parameters**

| Parameter | Description                                                                                                                                                     |
| --------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `event`   | A letter that corresponds to an event in the Events card. If you group by multiple properties, the formula runs the calculation with the first group-by clause. |

**Returns**

The average number of distinct values each user has for the grouped-by property.
{% /card %}

Returns the average number of distinct values each user has for a specified property.

{% callout type="example" heading="Example" %}
A music app captures a `Genre_Type` property on each `Play Song or Video` event. Running `PROPCOUNTAVG` on `Play Song or Video` grouped by `Genre_Type` returns the average number of unique `Genre_Type` values per user that fires `Play Song or Video`.
{% /callout %}
{% /formula-definition %}

### PROPHIST

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`PROPHIST(event)`

**Parameters**

| Parameter | Description                                               |
| --------- | --------------------------------------------------------- |
| `event`   | A letter that corresponds to an event in the Events card. |

**Returns**

The distribution of the grouped-by property values over the selected time period.
{% /card %}

Returns the distribution of the property values you are grouping by over the selected time period.

`PROPHIST` works with numeric group-by properties on the event. If you group by multiple properties, the formula runs the calculation with the first group-by clause.

{% callout type="example" heading="Example" %}
`PROPHIST(A)` displays a histogram of cart values of users that completed a purchase during the selected window.
{% /callout %}
{% /formula-definition %}

### PROPMAX

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`PROPMAX(event)`

**Parameters**

| Parameter | Description                                                                                                                                                                             |
| --------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `event`   | A letter that corresponds to an event in the Events card. The grouped-by property must be numeric. If you group by multiple properties, the calculation uses the first group-by clause. |

**Returns**

The maximum value of the grouped-by property for the specified event.
{% /card %}

Returns the maximum value of the property you are grouping the event by.
{% /formula-definition %}

### PROPMIN

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`PROPMIN(event)`

**Parameters**

| Parameter | Description                                                                                                                                                                             |
| --------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `event`   | A letter that corresponds to an event in the Events card. The grouped-by property must be numeric. If you group by multiple properties, the calculation uses the first group-by clause. |

**Returns**

The minimum value of the grouped-by property for the specified event.
{% /card %}

Returns the minimum value of the property you are grouping the event by.
{% /formula-definition %}

### PROPSUM

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`PROPSUM(event)`

**Parameters**

| Parameter | Description                                                                                                            |
| --------- | ---------------------------------------------------------------------------------------------------------------------- |
| `event`   | A letter that corresponds to an event in the Events card. The event must be grouped by the property you'd like to sum. |

**Returns**

The sum of the grouped-by property values for the specified event.
{% /card %}

Returns the sum of the property values you are grouping the event by.

`PROPSUM` works only when you group by a numerical property on the event. If you group by multiple properties, the formula runs the calculation with the first group-by clause.

{% callout type="example" heading="Example" %}
`PROPSUM(A)` shows the total revenue generated by the `Complete Purchase` event.
{% /callout %}
{% /formula-definition %}

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`PROPSUM(session)`

**Parameters**

| Parameter | Description                                                  |
| --------- | ------------------------------------------------------------ |
| `session` | A letter that corresponds to a session in the Sessions card. |

**Returns**

The total time, in seconds, summed across all matching sessions.
{% /card %}

The syntax for `PROPSUM` varies slightly for the [User Sessions chart](https://help.amplitude.com/hc/en-us/articles/231275508-The-User-Sessions-chart-Track-engagement-frequency-and-duration) because sessions are the focus of the metrics.

The chart below shows the total time, in seconds, summed across all sessions.
{% /formula-definition %}

![userSessionsPROPSUM.png](/images/event-segmentation/usersessionspropsum-png.png)

### REVENUETOTAL

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`$:REVENUETOTAL(event)`

**Parameters**

| Parameter | Description                                                      |
| --------- | ---------------------------------------------------------------- |
| `event`   | A letter that corresponds to a revenue event in the Events card. |

**Returns**

The aggregate sum of the property, formatted as a currency. Equivalent to `PROPSUM(event)`.
{% /card %}

Returns the aggregate sum of a revenue property, formatted as a currency.

`REVENUETOTAL` works only when you group by a numerical property on the event. The `$:` prefix is optional; its presence ensures the output format is a currency.

{% callout type="example" heading="Example" %}
`$:REVENUETOTAL(A)` shows the total revenue by day generated by purchases.
{% /callout %}
{% /formula-definition %}

### TOTALS

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`TOTALS(event)`

**Parameters**

| Parameter | Description                                                                          |
| --------- | ------------------------------------------------------------------------------------ |
| `event`   | A letter that corresponds to an event in the left module of the chart control panel. |

**Returns**

The total number of times users triggered the event.
{% /card %}

Returns the total number of times users triggered the event.

{% callout type="example" heading="Example" %}
`TOTALS(A); TOTALS(B)` shows the total number of times users viewed an item's details (event A) plus the total number of times users added an item to a cart (event B).
{% /callout %}
{% /formula-definition %}

### UNIQUES

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`UNIQUES(event)`

**Parameters**

| Parameter | Description                                               |
| --------- | --------------------------------------------------------- |
| `event`   | A letter that corresponds to an event in the Events card. |

**Returns**

The number of unique users that triggered the event.
{% /card %}

Returns the number of unique users that triggered the event.
{% /formula-definition %}

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`UNIQUES(session)`

**Parameters**

| Parameter | Description                                                  |
| --------- | ------------------------------------------------------------ |
| `session` | A letter that corresponds to a session in the Sessions card. |

**Returns**

The number of unique users that engaged in the specified session.
{% /card %}

The syntax for `UNIQUES` varies slightly for the [User Sessions chart](https://help.amplitude.com/hc/en-us/articles/231275508-The-User-Sessions-chart-Track-engagement-frequency-and-duration) because sessions are the focus of the metrics.

{% callout type="example" heading="Example" %}
`UNIQUES(A)/UNIQUES(B)` shows the ratio of users that engaged in sessions longer than one minute to the users that engaged in sessions that contained at least one `Search Items` event.
{% /callout %}
{% /formula-definition %}

![userSessionsUNIQUES.png](/images/event-segmentation/usersessionsuniques-png.png)

### EVENTTOTALS

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`EVENTTOTALS(session)`

**Parameters**

| Parameter | Description                                                  |
| --------- | ------------------------------------------------------------ |
| `session` | A letter that corresponds to a session in the Sessions card. |

**Returns**

The total number of events triggered during each session.
{% /card %}

Returns the total number of events triggered during each session.

This formula metric is **only** available in the [User Sessions chart](https://help.amplitude.com/hc/en-us/articles/231275508-The-User-Sessions-chart-Track-engagement-frequency-and-duration).

{% callout type="example" heading="Example" %}
`EVENTTOTALS(A)` returns the number of `Page Viewed` events across all sessions.
{% /callout %}
{% /formula-definition %}

### SESSIONTOTALS

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

- User Sessions chart: `SESSIONTOTALS(session)`
- Event Segmentation chart: `SESSIONTOTALS(event)`

**Parameters**

| Parameter | Description                                                  |
| --------- | ------------------------------------------------------------ |
| `session` | A letter that corresponds to a session in the Sessions card. |
| `event`   | A letter that corresponds to an event in the Events card.    |

**Returns**

- For `SESSIONTOTALS(session)`: the number of sessions that match the specified session label.
- For `SESSIONTOTALS(event)`: the number of sessions that contain the specified event at least once.

{% /card %}

Returns the number of sessions. Available in both the [User Sessions](/docs/analytics/charts/user-sessions/user-sessions-track-engagement-frequency) and [Event Segmentation](/docs/analytics/charts/event-segmentation/event-segmentation-build) charts.

The value you pass to `SESSIONTOTALS` depends on the chart you're using.

{% callout type="example" heading="Example" %}
The setup below shows the total number of sessions by day over the last 30 days for all users in the United Kingdom who completed at least one `Add to Cart` event during each session.
{% /callout %}
{% /formula-definition %}

![sessionTotalsChart.png](/images/event-segmentation/sessiontotalschart-png.png)

### SEMANTICTOTALS

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`SEMANTICTOTALS(event, semantic)`

**Parameters**

| Parameter  | Description                                                                                                                                                                                                                                                                                            |
| ---------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| `event`    | A letter that corresponds to an event in the Events card.                                                                                                                                                                                                                                              |
| `semantic` | How totals are calculated when grouped by cart properties (array properties). Supported values: `UNIQUE_ARRAY_VALUES` performs "Counting Events" by deduplicating array property values. `ALL_VALUES` performs "Counting Items" by counting each item within the array property without deduplication. |

**Returns**

The total number of times the event occurred, counted according to the chosen `semantic`.
{% /card %}

Returns the total number of times an event occurred, with explicit control over how array properties are counted.

This gives you formula-based access to the same counting options available in the Event Totals and Average measurement controls when grouping by cart properties.

{% callout type="example" heading="Example" %}
A `Checkout` event has the cart property `item_list.product_category`. If a single `Checkout` event contains two tacos (one Crunchy Taco and one Soft Taco) under the same product category "tacos":

- `SEMANTICTOTALS(A, UNIQUE_ARRAY_VALUES)` counts 1 Checkout event.
- `SEMANTICTOTALS(A, ALL_VALUES)` counts 2 Checkout items.

{% /callout %}

{% callout type="note" %}
The default behavior for `TOTALS` remains unchanged (equivalent to "Counting Items"). Use `SEMANTICTOTALS` when you need to explicitly choose between counting events and counting items.
{% /callout %}
{% /formula-definition %}

## Aggregation formulas

### CUMSUM

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`CUMSUM(metric, event)`

**Parameters**

| Parameter | Description                                               |
| --------- | --------------------------------------------------------- |
| `metric`  | One of the metrics formulas listed above.                 |
| `event`   | A letter that corresponds to an event in the Events card. |

**Returns**

The metric for the selected event with a running total of days, weeks, or months over the chart's time frame.
{% /card %}

Returns a metric for the selected event with a running total over the chart's time frame.

`CUMSUM(UNIQUES, A)` returns a deduplicated count of unique users for each data point.

{% callout type="example" heading="Example" %}
A daily [cumulative sum](/docs/analytics/charts/event-segmentation/event-segmentation-interpret-2#cumulative-sum) of revenue from `Complete Purchase` events in the last 30 days. The data point for February 22 is the sum of revenue generated on February 20, 21, and 22.
{% /callout %}
{% /formula-definition %}

### ROLLAVG

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`ROLLAVG(metric, event, intervals)`

**Parameters**

| Parameter   | Description                                                                                                                                                                                                     |
| ----------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `metric`    | One of the metrics formulas listed above.                                                                                                                                                                       |
| `event`     | A letter that corresponds to an event in the Events card.                                                                                                                                                       |
| `intervals` | The number of five-minute intervals, hours, days, weeks, or months to include in the rolling average. The maximum ranges are 36 five-minute intervals (three hours), 72 hours, 90 days, 12 weeks, or 12 months. |

**Returns**

The rolling average of the metric for the event over the specified number of intervals.
{% /card %}

Returns the metric for the event selected with a [rolling average](https://help.amplitude.com/hc/en-us/articles/14056975720091) over the interval selected.

A daily chart allows rolling averages over daily intervals only.

{% callout type="example" heading="Example" %}
A weekly rolling average superimposed on top of daily active users. The blue line shows daily active users and the green line shows the weekly rolling average. Use this comparison to see if your daily active user count is higher or lower than the rolling average.
{% /callout %}
{% /formula-definition %}

### ROLLWIN

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`ROLLWIN(metric, event, intervals)`

**Parameters**

| Parameter   | Description                                                                                                                                                                                                    |
| ----------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `metric`    | One of the metrics formulas listed above.                                                                                                                                                                      |
| `event`     | A letter that corresponds to an event in the Events card.                                                                                                                                                      |
| `intervals` | The number of five-minute intervals, hours, days, weeks, or months to include in the rolling window. The maximum ranges are 36 five-minute intervals (three hours), 72 hours, 90 days, 12 weeks, or 12 months. |

**Returns**

The metric for the event over the rolling window. The rolling window aggregation applies _after_ a cohort filter, if one is in use.
{% /card %}

Returns the metric for the event selected with a [rolling window](/docs/analytics/charts/event-segmentation/event-segmentation-interpret-2#rolling-windows) of the number of days, weeks, or months you specify.

The day, week, or month the chart displays is the last day of the window.

{% callout type="example" heading="Example" %}
This chart first calculates the new users for each time interval, then performs the rolling window aggregation on top of that.
{% /callout %}
{% /formula-definition %}

### ROLLWINBEFORE

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`ROLLWINBEFORE(metric, event, intervals)`

**Parameters**

| Parameter   | Description                                                                                                                                                                                                    |
| ----------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `metric`    | One of the metrics formulas listed above.                                                                                                                                                                      |
| `event`     | A letter that corresponds to an event in the Events card.                                                                                                                                                      |
| `intervals` | The number of five-minute intervals, hours, days, weeks, or months to include in the rolling window. The maximum ranges are 36 five-minute intervals (three hours), 72 hours, 90 days, 12 weeks, or 12 months. |

**Returns**

The metric for the event over the rolling window. The rolling window aggregation applies _before_ a cohort filter, if one is in use.
{% /card %}

Returns the metric for the event selected with a [rolling window](/docs/analytics/charts/event-segmentation/event-segmentation-interpret-2#rolling-windows) over a number of intervals you specify, applied _before_ a cohort filter.

{% callout type="example" heading="Example" %}
This chart first calculates the rolling active users for each time interval, then applies the new user cohort filter on top of that.
{% /callout %}
{% /formula-definition %}

## Function formulas

### EXP

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`EXP(value)`

**Parameters**

| Parameter | Description                                                                                             |
| --------- | ------------------------------------------------------------------------------------------------------- |
| `value`   | A constant or another function (for example, `UNIQUES` of an event). The maximum value accepted is 700. |

**Returns**

_e_ raised to the power of `value`.
{% /card %}

Returns [_e_](<https://en.wikipedia.org/wiki/E_(mathematical_constant)>) to the power of the specified value.

{% callout type="example" heading="Example" %}
`EXP(AVG(A))` computes _e_ to the power of the average number of times users purchase tickets.
{% /callout %}
{% /formula-definition %}

### LN

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`LN(value)`

**Parameters**

| Parameter | Description                                                          |
| --------- | -------------------------------------------------------------------- |
| `value`   | A constant or another function (for example, `UNIQUES` of an event). |

**Returns**

The natural logarithm of `value`.
{% /card %}

Returns the [natural logarithm](https://en.wikipedia.org/wiki/Natural_logarithm) of the value — the logarithm to the base of [_e_](<https://en.wikipedia.org/wiki/E_(mathematical_constant)>).

{% callout type="example" heading="Example" %}
`LN(UNIQUES(A))` calculates the natural logarithm of the number of unique users that triggered event A.
{% /callout %}
{% /formula-definition %}

### LOG

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`LOG(value, base)`

**Parameters**

| Parameter | Description                                                                 |
| --------- | --------------------------------------------------------------------------- |
| `value`   | A constant or another function (for example, `TOTALS` of an event).         |
| `base`    | A constant. The base must be a constant and can't contain another function. |

**Returns**

The logarithm of `value` to the specified `base`.
{% /card %}

Returns the [logarithm](https://en.wikipedia.org/wiki/Logarithm) of the value to the specified base.

{% callout type="example" heading="Example" %}
`LOG(UNIQUES(A), 3)` returns the logarithm of the count of unique active users to base 3.
{% /callout %}
{% /formula-definition %}

### LOG10

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`LOG10(value)`

**Parameters**

| Parameter | Description                                                      |
| --------- | ---------------------------------------------------------------- |
| `value`   | A constant or another function (for example, `AVG` of an event). |

**Returns**

The base-10 logarithm of `value`.
{% /card %}

Returns the [logarithm](https://en.wikipedia.org/wiki/Common_logarithm) of the value to base 10.

{% callout type="example" heading="Example" %}
`LOG10(AVG(A))` returns the base-10 logarithm of the average number of times users triggered `Complete Purchase`.
{% /callout %}
{% /formula-definition %}

### POWER

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`POWER(value, exponent)`

**Parameters**

| Parameter  | Description                                                                     |
| ---------- | ------------------------------------------------------------------------------- |
| `value`    | A constant or another function (for example, `TOTALS` of an event).             |
| `exponent` | A constant. The exponent must be a constant and can't contain another function. |

**Returns**

`value` raised to the power of `exponent`.
{% /card %}

Returns the value raised to the specified exponent.

{% callout type="example" heading="Example" %}
`POWER(UNIQUES(A), 2)` returns the squared number of unique users that triggered event A.
{% /callout %}
{% /formula-definition %}

### SQRT

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`SQRT(value)`

**Parameters**

| Parameter | Description                                                      |
| --------- | ---------------------------------------------------------------- |
| `value`   | A constant or another function (for example, `AVG` of an event). |

**Returns**

The square root of `value`.
{% /card %}

Returns the [square root](https://en.wikipedia.org/wiki/Square_root) of the value.

{% callout type="example" heading="Example" %}
`SQRT(TOTALS(A))` returns the square root of the total number of times users triggered event A.
{% /callout %}
{% /formula-definition %}

### TRENDLINE

{% formula-definition %}
{% card variant="filled" %}
**Syntax**

`TRENDLINE(value)`

**Parameters**

| Parameter | Description                                                          |
| --------- | -------------------------------------------------------------------- |
| `value`   | A constant or another function (for example, `UNIQUES` of an event). |

**Returns**

The ordinary least-squares linear regression trend line of `value`.
{% /card %}

Returns the [ordinary least-squares linear regression](https://en.wikipedia.org/wiki/Ordinary_least_squares) trend line of the value.

Strongly consider plotting another custom formula alongside this one for comparison. Otherwise, the `TRENDLINE` function gives you a straight line with no context on a chart.

{% callout type="example" heading="Example" %}
Use `TRENDLINE` to understand the trend line of the number of users that purchase a song or video and compare it to the unique number of users.
{% /callout %}
{% /formula-definition %}