Antipodes, Explained
After reading this you can compute the antipode of any point by hand, understand why almost every land antipode lands in ocean, and read the tool's two maps without being fooled by longitude wrap-around.
An antipode is the point on Earth exactly opposite another, straight through the center. Stand at the North Pole and your antipode is the South Pole. Stand in Madrid and your antipode is a patch of the South Pacific east of New Zealand. The word comes from Greek for "feet opposite": someone standing at your antipode has the soles of their feet pointed at the soles of yours.
The hook most people find surprising: if you dig straight down from where you are, you almost certainly hit ocean. Only about 4% of land has land on the other side. The tool marks your point and its antipode on two maps so you can see this for yourself.
What the antipode actually is
Take a point on the surface. Draw a line from it through the geometric center of the Earth. It exits the surface on the far side. That exit point is the antipode. Because the line passes through the center, the two points are the two ends of a diameter, and they are the farthest apart any two points on the sphere can be: half the circumference, roughly 20037 km apart.
Every point has exactly one antipode, and the relationship is symmetric. If B is the antipode of A, then A is the antipode of B. The poles are antipodes of each other. Any point on the equator has its antipode also on the equator, 180^\circ of longitude away.
When to use it, and when not
Use the antipode when you want the single most distant point from a location, or when you are curious what lies on the opposite side of the planet. It answers trivia ("what is directly under Beijing?") and it is a sanity check for anyone reasoning about long-distance geometry.
Do not confuse the antipode with the farthest point you can travel to, or with the point on the opposite side of an ocean. Those are different questions. The antipode is a pure geometric fact about the sphere. It ignores travel, ignores the shape of coastlines, and ignores the fact that the real Earth is a slightly flattened ellipsoid.
On the WGS84 ellipsoid the Earth is about 21.4 km wider across the equator than pole to pole. The antipode formula below treats Earth as a perfect sphere, so the true diametric opposite of a point can sit a few kilometers off the computed antipode. For finding what continent or ocean is on the far side, that error never matters.
The formula and why it works
Given a point at latitude \varphi and longitude \lambda in decimal degrees, the antipode is:
The latitude flips sign. North becomes south by the same amount. A point at 40^\circ N maps to 40^\circ S. This is because the diameter passes through the center, so it rises as far above the equatorial plane on one side as it drops below on the other.
The longitude shifts by half a turn. Adding 180^\circ puts you on the opposite meridian. The wrap keeps the result in the standard range. If \lambda + 180^\circ \gt 180^\circ, subtract 360^\circ. If it drops below -180^\circ, add 360^\circ. So +150° becomes +150 + 180 = 330, then 330 - 360 = -30°.
That is the whole calculation. No trigonometry is needed because the antipode is defined by symmetry through the center, not by distance along the surface.
Worked example: the antipode of Madrid
The tool's defaults put you near Madrid, Spain, at roughly 40.4168° N, 3.7038° W. In signed decimal degrees that is \varphi = 40.4168, \lambda = -3.7038.
- Flip the latitude: \varphi' = -40.4168, so
40.4168° S. - Add 180 to the longitude:
-3.7038 + 180 = 176.2962. - Check the range:
176.2962is between-180and180, so no wrap is needed. The antipode longitude is176.2962° E.
The antipode of Madrid is about 40.42° S, 176.30° E, which sits in the South Pacific just off the east coast of New Zealand's North Island, near Hawke's Bay. That is why Spain and New Zealand are a famous near-miss pair: much of Spain lands in the sea just short of New Zealand's coast.
Reading the two maps
The tool shows your point and its antipode marker on one map, and keeps a second map centered on the antipode so you can pan around and see the surroundings. Read the coordinates, not just the dots. A marker near the edge of a world map can be visually misleading because the map is a projection: the left and right edges are the same meridian at ±180°.
The distance between a point and its antipode is always the same. Half the mean circumference is \pi \times 6371 \approx 20015 km along the surface. Any straight tunnel between them is one Earth diameter, about 12742 km. The idealized frictionless fall through that tunnel takes about 42 minutes, and the same 42 minutes holds for a straight tunnel between any two surface points, not only antipodes.
Why so little land matches
Land covers about 29% of Earth's surface. If land were scattered randomly, the chance that a random land point had land at its antipode would be about 29%, and roughly 29% × 29% ≈ 8.4% of the surface would be land-over-land. The measured figure is smaller, near 4% of land, because land is not scattered randomly. Most continents sit opposite ocean by the geometry of how the landmasses are arranged. The Atlantic and Pacific basins line up with continents on the far side more often than not.
The chart uses 0.29 × 0.29 = 0.0841 for the random case, expressed as a share of the whole surface. As a share of land alone the random case is 29%, and the observed share of land alone is roughly 4%. Either way, land antipodes are rare.
Common mistakes
The most frequent error is forgetting the sign convention. West longitude and south latitude are negative. If you enter Madrid's longitude as +3.7038 instead of -3.7038, your antipode comes out near 40° S, 176° W in the open ocean far from New Zealand, and you miss the near-miss pairing entirely.
Do not add 180 to the longitude and stop. You must wrap. A longitude of +150° plus 180° is 330°, which is not a valid longitude. Subtract 360° to get -30°. Skipping the wrap places the marker off the map or on the wrong side.
A second mistake is negating the longitude instead of adding 180. Negating gives the mirror image across the prime meridian, not the antipode. For latitude you negate; for longitude you add 180 and wrap. They are different operations.
A third is expecting the antipode of a coastal city to be another coastal city. Antipodes rarely respect coastlines. Beijing's antipode is in Argentina near Bahía Blanca, Shanghai's is in Argentina too, and Chile's coast sits opposite eastern China. These pairs are close but almost never exact.
Related tools
If you have coordinates in an unfamiliar format, the Coordinate Converter turns DMS, UTM, MGRS, geohash and Plus Codes into the decimal degrees this tool expects. To plot your own points from a file, use the GeoJSON & CSV Map Viewer. For the shortest surface path between a point and any other, including its antipode, see Great Circle vs Rhumb Line. To see which side of the planet is in daylight while you explore antipodes, open the Day & Night World Map, and to compare clock time with sun time at either point try Solar Time vs Clock Time.
Frequently asked questions
Would I really pop out at the antipode if I dug straight down?
Only if you dug perpendicular to the surface, straight toward the center. That line exits at the antipode. A tunnel dug in any other direction comes out somewhere else, and the idealized frictionless fall through any straight tunnel takes about 42 minutes regardless.
Why is the antipode of the United States mostly in the Indian Ocean?
The contiguous US spans roughly 25° to 49° N and -125° to -67° W. Flipping latitude gives the southern hemisphere, and adding 180 to those longitudes lands you around 55° to 113° E, which is the southern Indian Ocean. Almost no US land has land at its antipode.
Does the tool use a sphere or the real ellipsoid?
The antipode is computed on a sphere: negate latitude, add 180 to longitude, wrap. On the WGS84 ellipsoid the true diametric opposite can differ by a few kilometers, which never changes which ocean or continent you land in.
What are the antipode "near-miss" pairs?
Places where a landmass almost lines up with land on the far side. Spain and New Zealand, Chile and China, Ireland and a point near New Zealand's South Island, and parts of Argentina opposite eastern China are the best known. The tool lists these because exact land-over-land pairs are rare.
How far apart are a point and its antipode?
Along the surface, half the circumference, about 20015 km using a mean radius of 6371 km. Straight through, one diameter, about 12742 km. Both are the maximum possible for their kind of path.
Related tools
Coordinate Converter
Convert between decimal degrees, DMS, UTM, MGRS, geohash and Plus Codes — with a map.
Great Circle vs Rhumb Line
Why flights look curved on the map: shortest path vs constant bearing between any two points.
Planetarium & Star Chart
The whole sky over any place and time: stars, constellations, planets, the Moon and satellite passes.
Star Photo Identifier
Drop a photo of the night sky and every star, constellation and nebula in it is found and named, along with where the camera was pointing.
Day & Night World Map
Live sunlight terminator on a world map, with date and time sliders.
GeoJSON & CSV Map Viewer
Drop a GeoJSON file or a CSV with coordinates and see it on a map.