Antipode Calculator: Find the Opposite Point on Earth

What Is an Antipode Calculator?

An antipode calculator finds the point on Earth's surface that is diametrically opposite a given location. That opposite point is called the antipode. If a straight line were drawn through the center of the Earth starting at any location, it would come out the other side at that location's antipode.

The word "antipode" comes from Greek: anti ("opposite") and pous ("foot"). Ancient Greek philosophers used it to describe people who would stand "feet opposite" to one another on a spherical Earth, long before anyone could travel far enough to check. Pythagoras and later Aristotle argued Earth was round, which raised the question of what lay on the far side. The idea stayed theoretical until European voyages in the 15th and 16th centuries, including the 1519–1522 circumnavigation completed after Ferdinand Magellan's expedition, showed that the far side of the globe was real and reachable.

How to Calculate an Antipode

The tool needs two numbers: latitude and longitude, both in decimal degrees.

1. Enter latitude, a number from -90 to 90. Positive values are north of the equator, negative values are south.
2. Enter longitude, a number from -180 to 180. Positive values are east of the Prime Meridian, negative values are west.
3. Select "Calculate Antipode."

The result shows the antipode's coordinates next to the original point, and a map plots both as markers so the relationship is easy to see. A copy button lets the result be pasted elsewhere. Coordinates can usually be found by right-clicking a location in an online map and copying the numbers that appear.

Antipode Formula

Because Earth is treated as a sphere for this purpose, the antipode formula is simple.

Latitude is flipped in sign:

$\text{lat}_{\text{antipode}} = -\,\text{lat}_{\text{original}}$

A location 40° north of the equator has an antipode 40° south of it, and vice versa.

Longitude is shifted by 180°, then kept inside the -180° to 180° range:

• If the original longitude is greater than 0°: subtract 180°.
• If the original longitude is 0° or less: add 180°.

$$\text{lon}_{\text{antipode}} = \begin{cases} \text{lon}_{\text{original}} - 180° & \text{if } \text{lon}_{\text{original}} > 0° \\ \text{lon}_{\text{original}} + 180° & \text{if } \text{lon}_{\text{original}} \le 0° \end{cases}$$

This works because going 180° east or 180° west from any meridian lands on the same opposite meridian; a full trip around the globe is 360°, so half a trip is 180°.

The calculation only uses angles, so it does not depend on Earth's exact shape. Earth is technically an oblate spheroid, slightly wider at the equator than pole to pole, but that flattening does not change which point is antipodal to another. It only affects distance measurements, not this calculation.

1function antipode(lat, lon) {
2  const antipodeLat = -lat;
3  let antipodeLon = lon + 180;
4  if (antipodeLon > 180) antipodeLon -= 360;
5  return { lat: antipodeLat, lon: antipodeLon };
6}
7

Worked Examples

Take Madrid as an example. Its latitude is 40.4168°, so the antipode's latitude is -40.4168°. Its longitude is -3.7038°, which is 0° or less, so 180° is added: -3.7038° + 180° = 176.2962°. The antipode, near Wellington, New Zealand, sits at (-40.4168°, 176.2962°).

The poles are a special case. Every line of longitude meets at the poles, so longitude has no real meaning there. The calculator still returns a specific value using the same formula: for (90°, 0°), longitude 0° is 0° or less, so 180° is added, giving 180° rather than 0°. The result, (-90°, 180°), and (-90°, 0°) describe the same physical point, the South Pole, since -180° and 180° mark the same line of longitude.

Coordinate Precision

Results are shown to four decimal places, for example 40.4168°. One ten-thousandth of a degree of latitude corresponds to roughly 11 meters on the ground, about the length of a small building. That level of detail is far more precise than antipode calculations normally need, since the interesting fact is usually which country or ocean the antipode falls in, not its exact meter.

Internally, the calculation uses standard 64-bit floating-point numbers, which hold about 15 to 17 significant digits before the result is rounded for display.

Why Most Antipodes Fall in the Ocean

Water covers about 71% of Earth's surface, so most antipodes, of land or sea alike, land in an ocean. Estimates suggest only a small share of land locations, often put around 4%, have land at their antipode. Most of the continental United States, for instance, has an antipode somewhere in the Indian Ocean. One well-known near exception is Madrid and Wellington, New Zealand, two major cities that are almost exactly antipodal.

Real-World Uses

Education. Antipodes give students a concrete way to see that Earth is round rather than flat, since a flat surface has no consistent "opposite point" for every location.

Time and communication. Because longitude is offset by exactly 180° at an antipode, the two points are on opposite sides of the planet relative to the sun: when it is solar midday at one, it is solar midnight at the other.

Seismology. Earthquakes send seismic waves through Earth's interior, and scientists studying how those waves travel pay attention to the antipode of the quake, where waves arriving from many directions converge.

Geography and trivia. Comparing a place to its antipode is a common way to illustrate how far apart two points on Earth can be, since no location on the sphere is farther from another location than its antipode.

Frequently Asked Questions

What is an antipode? An antipode is the point on Earth exactly opposite another point, as if a line were drawn straight through the planet's center from one to the other.

What is the formula for finding an antipode? Flip the sign of the latitude. For longitude, subtract 180° if the original value is positive, or add 180° if it is zero or negative.

How accurate is this calculator? It displays coordinates to four decimal places, about 11 meters of precision, using standard 64-bit floating-point arithmetic internally.

Why are so many antipodes in the ocean? Because oceans cover about 71% of Earth's surface. A location on land is statistically more likely to have its antipode fall on water than on other land.

Are the North and South Poles antipodes of each other? Yes. Every line of longitude meets at the poles, so any point at the North Pole is antipodal to any point at the South Pole regardless of which longitude is entered.

Is an antipode the same as the opposite hemisphere? No. A point in the opposite hemisphere only has the opposite latitude sign, for example 10°N and 10°S at the same longitude. An antipode needs both an opposite latitude sign and a longitude shifted by 180°.