Distance between two sets of geographic coordinates (latitude, longitude) in Ruby, JS, SQL, and Python using the Haversine Formula.
In this article I’ve put together some code samples of the Haversine formula in JS, Ruby, and SQL.
First, let me provide an explanation for the formula known as the Haversine Formula.
Haversine allows you to calculate the distance between two sets of coordinates on a sphere — which is considerably different than calculating distances on a flat plane: Flat Earth folks will be working with the Pythagorean Theorem directly so they can Click Here.
The best explanation I’ve seen personally is taken directly from an ESRI community post by regular contributor SimonKettle¹:
The Haversine formula is perhaps the first equation to consider when understanding how to calculate distances on a sphere. The word "Haversine" comes from the function:haversine(θ) = sin²(θ/2)The following equation where φ is latitude, λ is longitude, R is earth’s radius (mean radius = 6,371km) is how we translate the above formula to include latitude and longitude coordinates. Note that angles need to be in radians to pass to trig functions:a = sin²(φB — φA/2) + cos φA * cos φB * sin²(λB — λA/2)
c = 2 * atan2( √a, √(1−a) )
d = R ⋅ c
The haversine formula is a re-formulation of the spherical law of cosines, but the formulation in terms of haversines is more useful for small angles and distances. — SimonKettle
The author goes on to provide an example in Python as well which I will detail at the base of this
Javascript — Haversine Formula
Example Usage: https://replit.com/@AbeFlansburg/haversine#index.js
Ruby — Haversine Formula
Example Usage: https://replit.com/@AbeFlansburg/haversine-1#main.rb
SQL — Haversine Formula
Keeping in mind that I am not a Master of the SQL and that I was working with a sample data set while using an example seen on StackOverflow²:
SELECT carrier.code, carrier.description, airport.lat, airport.long, ( 3959 * acos( cos( radians(airport.lat) ) * cos( radians( 61.2181 ) ) * cos( radians(149.9003) - radians(airport.long) ) + sin( radians(airport.lat) ) * sin( radians(61.2181)))) as distance_to_anchorageFROM carrierINNER JOIN airport ON airport.code=carrier.codeWHERE airport.city LIKE '%AK' AND LOWER(carrier.description) LIKE '%inc%'
where this is the relevant line of code:
( 3959 * acos( cos( radians(latitude1) ) * cos( radians( latitude2 ) ) * cos( radians(longitude2) - radians(longitude1) ) + sin( radians(latitude1) ) * sin( radians(latitude2))))Python — Haversine
Taken directly from https://community.esri.com/t5/coordinate-reference-systems/distance-on-a-sphere-the-haversine-formula/ba-p/902128¹
'''
Calculate distance using the Haversine Formula
'''
def haversine(coord1: object, coord2: object):
import math
# Coordinates in decimal degrees (e.g. 2.89078, 12.79797)
lon1, lat1 = coord1
lon2, lat2 = coord2
R = 6371000 # radius of Earth in meters
phi_1 = math.radians(lat1)
phi_2 = math.radians(lat2)
delta_phi = math.radians(lat2 - lat1)
delta_lambda = math.radians(lon2 - lon1)
a = math.sin(delta_phi / 2.0) ** 2 + math.cos(phi_1) * math.cos(phi_2) * math.sin(delta_lambda / 2.0) ** 2
c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a))
meters = R * c # output distance in meters
km = meters / 1000.0 # output distance in kilometers
meters = round(meters, 3)
km = round(km, 3)
print(f"Distance: {meters} m")
print(f"Distance: {km} km")I hope this can be helpful to someone looking to calculate straight line distances given two sets of latitude and longitude on a sphere.
Sources
[1] Kettle, Simon (Oct-5–2017). Distance on a sphere: The Haversine Formula.
https://community.esri.com/t5/coordinate-reference-systems/distance-on-a-sphere-the-haversine-formula/ba-p/902128
[2] Saadb (Sep-5–2016). SQL query of Haversine formula in SQL server
https://stackoverflow.com/questions/39338167/sql-query-of-haversine-formula-in-sql-server
