The Great Circle Arc Distance calculator computes the distance between two points on a spherical body along a great circle arc using the Haversine formula based on the latitude and longitude of two points and the mean spherical radius of the sphere.   

INSTRUCTIONS: Enter the following:

• (Lat1) Latitude of point 1
• (Lon1) Longitude of point 1
• (Lat2) Latitude of point 2
• (Lon2) Longitude of point 2
• (r) Mean Radius of the sphere.  Note, the default is the mean spherical radius of the Earth

Great Circle Arc Distance (D): The calculator returns the distance between the two points in kilometers.  However, this can be automatically converted to other distance units (e.g. miles or nautical miles) via the pull-down menu.

The Math / Science

The Haversine equation is used to determine the distance between two points (x and y) on the Earth based on a mean spherical earth radius.  The Haversine - Distance equation is important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes. It is a special case of a more general formula in spherical trigonometry, the law of haversines, relating the sides and angles of spherical triangles. The first table of haversines in English was published by James Andrew in 1805. Florian Cajori credits an earlier use by Jose de Mendoza y Ríos in 1801. The term haversine was coined in 1835 by Prof. James Inman.

The haversine formula is:

    `D = 2 *sin^-1(sqrt(sin((lat2 - lat1)/2)^2 + sin((lon2 - lon1)/2)^2 * cos(lat1) * cos(lat2))) * r`
where

• D = the distance between the two points (along a great circle of the sphere; see spherical distance),
• r = Mean Radius
• lat₁ , lon₁ = First point on the sphere
• lat₂ , lon₂ = Second point on the sphere

Great Circle Calculators

• Compute decimal degree angles from degrees, minutes and seconds,CLICK HERE.
• Compute the time to travel between two latitudes and longitudes
• Compute the Distance Between two Points on a Sphere (Great Circle Arc)
• Compute the Great Circle Arc Central Angle
• Great Circle Arc Angle (Vincenty's)

Sphere Calculators

• Sphere Surface Area based radius (r)
• Sphere Surface Area from Volume
• Sphere Volume from Radius
• Sphere Volume from Circumference
• Sphere Volume from Surface Area
• Sphere Volume from Mass and Density
• Sphere Radius from Volume
• Sphere Radius from Surface Area
• Sphere Weight (Mass) from volume and density
• Sphere Density
• Area of Triangle on a Sphere
• Distance between Two Points on a Sphere
• Sphere Cap Surface Area
• Sphere Cap Volume
• Sphere Cap Weight (Mass) 
• Sphere Segment Volume
• Sphere Segment Weight (Mass)
• Sphere Segment Wall Surface Area (without the circular top and bottom ends)
• Sphere Segment Full Surface Area  (with the top and bottom circles, aka ends)
• Volume of Spherical Shell
• Mass of Spherical Shell

See Also

• Haversine Travel Time- equation to compute time of travel over a great circle arc at constant velocity.
• Sphere Calculator - calculator with formulas related to spherical objects
• Correction Angle -  navigation equation that compensates for air or water currents.

References

• wikipedia - http://en.wikipedia.org/wiki/Haversine_formula