How to calculate the distance between two GPS coordinates without using Google Maps API?

Distance between two coordinates on earth is usually calculated using Haversine formula. This formula takes into consideration earth shape and radius. This is the code I use to calculate distance in meters.

def distance(loc1, loc2)
  rad_per_deg = Math::PI/180  # PI / 180
  rkm = 6371                  # Earth radius in kilometers
  rm = rkm * 1000             # Radius in meters

  dlat_rad = (loc2[0]-loc1[0]) * rad_per_deg  # Delta, converted to rad
  dlon_rad = (loc2[1]-loc1[1]) * rad_per_deg

  lat1_rad, lon1_rad = loc1.map {|i| i * rad_per_deg }
  lat2_rad, lon2_rad = loc2.map {|i| i * rad_per_deg }

  a = Math.sin(dlat_rad/2)**2 + Math.cos(lat1_rad) * Math.cos(lat2_rad) * Math.sin(dlon_rad/2)**2
  c = 2 * Math::atan2(Math::sqrt(a), Math::sqrt(1-a))

  rm * c # Delta in meters
end

puts distance([46.3625, 15.114444],[46.055556, 14.508333])
# => 57794.35510874037

You can use the geokit ruby gem. It does these calculations internally, but also supports resolving addresses via google and other services if you need it to.

require 'geokit'

current_location = Geokit::LatLng.new(37.79363,-122.396116)
destination = "37.786217,-122.41619"
current_location.distance_to(destination) 

# Returns distance in miles: 1.211200074136264

You can also find out the bearing_to (direction expressed as a float in degrees between 0-360) and midpoint_to (returns an object you can run .latitude and .longitude methods on).

Just a little shorter & separated parameter version of @Lunivore's answer

RAD_PER_DEG = Math::PI / 180
RM = 6371000 # Earth radius in meters

def distance_between(lat1, lon1, lat2, lon2)
  lat1_rad, lat2_rad = lat1 * RAD_PER_DEG, lat2 * RAD_PER_DEG
  lon1_rad, lon2_rad = lon1 * RAD_PER_DEG, lon2 * RAD_PER_DEG

  a = Math.sin((lat2_rad - lat1_rad) / 2) ** 2 + Math.cos(lat1_rad) * Math.cos(lat2_rad) * Math.sin((lon2_rad - lon1_rad) / 2) ** 2
  c = 2 * Math::atan2(Math::sqrt(a), Math::sqrt(1 - a))

  RM * c # Delta in meters
end