> For the complete documentation index, see [llms.txt](https://docs.carto.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.carto.com/data-and-analysis/analytics-toolbox-for-bigquery/sql-reference/measurements.md).
# measurements
This module contains functions that compute measurements of distance, area and angles. There are also functions to compute geometry values determined by measurements.
## ST\_ANGLE
```sql
ST_ANGLE(startPoint, midPoint, endPoint, mercator)
```
**Description**
Finds the angle formed by two adjacent segments defined by 3 points. The result will be the (positive clockwise) angle with origin on the startPoint-midPoint segment, or its explementary angle if required.
**Input parameters**
* `startPoint`: `GEOGRAPHY` start Point Coordinates.
* `midPoint`: `GEOGRAPHY` mid Point Coordinates.
* `endPoint`: `GEOGRAPHY` end Point Coordinates.
* `mercator`: `BOOL`|`NULL` if calculations should be performed over Mercator or WGS84 projection. If `NULL` the default value `false` is used.
**Return type**
`FLOAT64`
**Example**
{% tabs %}
{% tab title="carto-un" %}
```sql
SELECT `carto-un`.carto.ST_ANGLE(ST_GEOGPOINT(-3.70325 ,40.4167), ST_GEOGPOINT(-4.70325 ,10.4167), ST_GEOGPOINT(-5.70325 ,40.4167), FALSE);
-- 3.933094586038578
```
{% endtab %}
{% tab title="carto-un-eu" %}
```sql
SELECT `carto-un-eu`.carto.ST_ANGLE(ST_GEOGPOINT(-3.70325 ,40.4167), ST_GEOGPOINT(-4.70325 ,10.4167), ST_GEOGPOINT(-5.70325 ,40.4167), FALSE);
-- 3.933094586038578
```
{% endtab %}
{% tab title="manual" %}
```sql
SELECT carto.ST_ANGLE(ST_GEOGPOINT(-3.70325 ,40.4167), ST_GEOGPOINT(-4.70325 ,10.4167), ST_GEOGPOINT(-5.70325 ,40.4167), FALSE);
-- 3.933094586038578
```
{% endtab %}
{% endtabs %}
## ST\_MINKOWSKIDISTANCE
```sql
ST_MINKOWSKIDISTANCE(geog, p)
```
**Description**
Calculate the Minkowski p-norm distance between two features.
**Input parameters**
* `geog`: `ARRAY` featureCollection.
* `p`: `FLOAT64` minkowski p-norm distance parameter. 1: Manhattan distance. 2: Euclidean distance. 1 =< p <= infinity. If `NULL` the default value `2` is used.
**Return type**
`ARRAY`
**Example**
{% tabs %}
{% tab title="carto-un" %}
```sql
SELECT `carto-un`.carto.ST_MINKOWSKIDISTANCE([ST_GEOGPOINT(10,10),ST_GEOGPOINT(13,10)],2);
-- ["0,0.3333333333333333","0.3333333333333333,0"]
```
{% endtab %}
{% tab title="carto-un-eu" %}
```sql
SELECT `carto-un-eu`.carto.ST_MINKOWSKIDISTANCE([ST_GEOGPOINT(10,10),ST_GEOGPOINT(13,10)],2);
-- ["0,0.3333333333333333","0.3333333333333333,0"]
```
{% endtab %}
{% tab title="manual" %}
```sql
SELECT carto.ST_MINKOWSKIDISTANCE([ST_GEOGPOINT(10,10),ST_GEOGPOINT(13,10)],2);
-- ["0,0.3333333333333333","0.3333333333333333,0"]
```
{% endtab %}
{% endtabs %}
This project has received funding from the [European Union’s Horizon 2020](https://ec.europa.eu/programmes/horizon2020/en) research and innovation programme under grant agreement No 960401.
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