How this calculator works
An antipode is the point diametrically opposite another point on a sphere. Take the latitude, flip its sign, and add 180 degrees to the longitude. A point at 45 degrees north, 75 degrees west therefore has its antipode at 45 degrees south, 105 degrees east. The two points are separated by half the Earth circumference in every direction, so the great-circle distance is always the same, about 20,015 kilometres on the mean spherical Earth. Real terrain does not change the answer: the antipode is defined geometrically, even if one end is deep ocean and the other is a mountain range.
Formula
antipode latitude = -latitude. antipode longitude = longitude + 180 degrees, wrapped to the range -180 to 180 degrees. Distance = pi x R, where R = 6,371.0088 km is the IUGG mean Earth radius. Angular separation = 180 degrees.
Worked example
Ottawa is close to 45.42 degrees north, 75.70 degrees west. Flip the latitude to 45.42 degrees south. Add 180 degrees to the longitude: -75.70 + 180 = 104.30 degrees east. The antipode lies in the Indian Ocean west of Australia. The distance is pi x 6,371.0088 = 20,015.1 km, or about 12,437 miles.
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Frequently asked questions
Why does the longitude change by 180 degrees?
A line through the Earth centre exits the other side on the opposite meridian. Every meridian is a half-circle, so the opposite half-circle lies 180 degrees away. If the result is outside -180 to 180 degrees, subtract or add 360 to bring it back into range.
Does every point have an antipode?
Yes, on any sphere. On the real, slightly flattened Earth the geometric opposite point still exists, but the distance varies a little with latitude, from about 20,004 km along a meridian to about 20,038 km along the equator.
Is the antipode always on land or always at sea?
Neither. Because most of the surface is ocean, most antipodes are in water, but some pairs link land to land. The antipode of a point in Argentina can fall in China, for example.
Can I enter latitudes in radians?
Yes. Switch the unit selector beside the field. The calculator converts the value before working, and the result can be shown in degrees, radians or gradians.