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# Distance between latitude/longitude coordinate pairs

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• mslovich • Looker Staff

##Howdy Good Lookers!

###Lucky for you Looker now has a built-in distance dimension that supports this use case!

###So, if you LOVE Trigonometry like me, please read on and enjoy! If not, you can use the built in Looker functionality in the link above!

##Latitude/Longitude Pairs and Great Circle Distance in SQL

There are ways of using basic trigonometric functions to calculate the great circle distance between two pairs of latitude-longitude coordinates on a sphere. Many SQL dialects (including but not limited to: Redshift, Postgres, MySQL) support these trigonometric functions.

The Spherical Law of Cosines accurately calculates the distance between pairs of lat/lon coordinate as long as the two points are greater than ~1.5 meters apart. If you need better accuracy than that, consider implementing the Vincenty’s formulae.

##The Spherical Law of Cosines

ACOS( SIN(lat_a) * SIN(lat_b) + COS(lat_a) * COS(lat_b) * COS(lon_b - lon_a) ) * e_radius = dist_ab

Where:

lat_a, lon_a = latitude and longitude of point ‘a’ (in radians)

dist_ab = distance between point ‘a’ and point ‘b’

Conventions:

Signs:

NORTH latitudes are POSITIVE

SOUTH latitudes are NEGATIVE

EAST longitudes are POSITIVE

WEST longitudes are NEGATIVE

Units of Measure:

Most SQL dialects take arguments for trigonometric functions in radians.

If your raw lat/lon values are in degrees, convert them via:   ( degree_value * π/180 = radian_value )

Define the lat and lon values as double precision elements for the most accurate results

##Potential Use Cases

There are many valuable use cases for this formula. A simple example is calculating the distance of customers from a central distribution center (cdc):

`````` - dimension: distance_from_cdc_in_kilometers
type: number
sql: |
ACOS( SIN(\${cdc_location.lat}) * SIN(\${customer_facts.lat}) +  COS(\${cdc_location.lat}) * COS(\${customer_facts.lat}) * COS(\${customer_facts.lon}-\${cdc_location.lon})  ) * 6371
``````

Another use case is joining tables based on proximity. Maybe you want to join rows in your ‘customers’ table to your ‘storefronts’ table whenever a customer is within 5 kilometers of a storefront. That might look something like this

``````- explore: storefronts
joins:
- join: customers
sql_on : |
ACOS( SIN(\${storefronts.lat}) * SIN(\${customers.lat}) + COS(\${storefronts.lat}) * COS(\${customers.lat}) * COS(\${customers.lon}-\${storefronts.lon})  ) * 6371 <= 5
type: inner
relationship: many_to_many
``````

##Reminders

1. SQL trig functions normally expect arguments in radians so convert degree lat/lon values to radians if necessary. ( degree_value * π/180 = radian_value )

2. Make sure the values you use for earth’s radius and the distance between the lat/lon points are measured in the same units (e.g. kilometers, miles, etc.).

• Brett_Sauve As of 3.44, Looker released a `type: distance` dimension which makes this a whole bunch easier!