Great-circle mathematics helper library for platforms using Swift -

What's New

Minor release for Swift 5



Carthage compatible GitHub version

Supports Swift 5.0

Euclid is a cross-platform (iOS, macOS, tvOS, watchOS) utility class written in Swift that provides convenience methods allowing the user to perform Great-Circle mathematics with ease.


  • Calculates the distance between two given coordinates
  • Calculates the initial bearing when given source and destination coordinates
  • Includes toRadians() and toDegrees() helper methods as extensions on CLLocationDegrees
  • When given a start coordinate, bearing and distance to travel a destination coordinate is calculated
  • Supports bearings in the range -180 to 180 degrees and bearings in a compass range of 0 to 360 degrees
  • 100% unit test coverage
System requirements
  • Deployment target of iOS 9.0+ / macOS 10.11+ / tvOS 10.1+ / watchOS 3.1+
  • Xcode 10.0+
  • Swift 5.0+



The key Great-Circle method provided by the library is destination and this is accessible as a static func on the Euclid class.

public static func destination(start: CLLocationCoordinate2D, distance: CLLocationDistance, bearing: Bearing) -> CLLocationCoordinate2D { } // Destination coordinate given start, distance and bearing
let calculatedDestination = Euclid.destination(start: source, distance: 100000, bearing: bearing)

Extensions on CLLocationCoordinate2D

public func distance(from coordinate: CLLocationCoordinate2D) -> CLLocationDistance { }
source.distance(from: destination) // Distance in metres

public func bearing(to coordinate: CLLocationCoordinate2D) -> CLLocationDirection { }
source.bearing(to: destination) // Bearing in range -180 - 180

public func bearing(to coordinate: CLLocationCoordinate2D) -> Bearing { }
source.compassBearing(to: destination) // Bearing in range 0 - 360

Useful constants and types

Euclid.kEarthRadiusMetres // Radius of the earth in metres used by all calculations (6371e3)

public typealias Bearing = Double // Representing a bearing in the range -180 - 180

In addition to Euclid there is an additional type of BoundingBox that can be used to represent rectangular areas on a sphere.

public struct BoundingBox : CustomStringConvertible, CustomDebugStringConvertible {
    public let lowerLeft: CLLocationCoordinate2D
    public let upperRight: CLLocationCoordinate2D
    public let diagonal: CLLocationDistance
    public let midpoint: CLLocationCoordinate2D



To integrate Euclid into your Xcode project using Carthage, specify it in your Cartfile:

github "timsearle/Euclid"

Run carthage update to build the framework and drag the built Euclid.framework into your Xcode project and update your run scripts as appropriate. For additional support, please visit the Carthage documentation.

Apps using Euclid

We'd love to hear what you have used Euclid for, if you would like your app displayed here, please send a pull request!


Currently Euclid has all the features that it was originally developed for, but the world of Euclidean geometry is far larger. If you wish to contribute to Euclid please fork the repository and send a pull request. Contributions and feature requests are always welcome, please do not hesistate to raise an issue with the appropriate label so that any contributors can see.


Euclid is released under the MIT license. See LICENSE for details.


  • Swift Tools 5.1.0
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Last updated: Fri Mar 17 2023 15:21:35 GMT-0500 (GMT-05:00)