Last updated: July 16, 2026
Antipode Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The Antipode Calculator finds the geographic point diametrically opposite any latitude/longitude coordinate on Earth. It applies the formulas: antipode latitude = −φ, and antipode longitude = λ + 180° (if λ ≤ 0) or λ − 180° (if λ > 0), then formats the result with cardinal directions (N/S/E/W).
To find the antipode of any location, negate its latitude and add or subtract 180 degrees from its longitude, keeping the result between minus 180 and plus 180 degrees. Most antipodal points fall in ocean because about 71 percent of Earth's surface is water.
Key Takeaways
- The antipode of any point (φ, λ) is simply (−φ, λ ± 180°) — negate the latitude and shift longitude by 180°.
- About 96% of Earth's land areas have their antipode in ocean, because 71% of Earth's surface is water.
- The North Pole and South Pole are each other's antipodes — the only point pair where the antipode is a single pole.
- The Auckland–Spain antipodal pair is one of the rare examples where two major cities are each other's antipodes.
- Applying the antipode formula twice always returns you to the original coordinates, confirming its symmetry.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
Lat_antipode = −φ; Lng_antipode = λ + 180° (if λ ≤ 0) or λ − 180° (if λ > 0)
Where:
- φ=Latitude(°)
- λ=Longitude(°)
- φ_antipode=Antipode Latitude(°)
- λ_antipode=Antipode Longitude(°)
Worked Examples
New York City, USA
Find the antipode of New York City at 40.7128°N, 74.006°W.
- 1Antipode latitude = −40.7128 = 40.7128°S
- 2Longitude is negative (−74.006), so antipode longitude = −74.006 + 180 = 105.994
- 3Antipode longitude = 105.9940°E
- 4Result: 40.7128°S, 105.9940°E — located in the southern Indian Ocean
London, United Kingdom
Find the antipode of London at 51.5074°N, 0.1278°W.
- 1Antipode latitude = −51.5074 = 51.5074°S
- 2Longitude is negative (−0.1278), so antipode longitude = −0.1278 + 180 = 179.8722
- 3Antipode longitude = 179.8722°E
- 4Result: 51.5074°S, 179.8722°E — located in the South Pacific Ocean near New Zealand
Sydney, Australia
Find the antipode of Sydney at 33.8688°S, 151.2093°E.
- 1Antipode latitude = −(−33.8688) = 33.8688 = 33.8688°N
- 2Longitude is positive (151.2093), so antipode longitude = 151.2093 − 180 = −28.7907
- 3Antipode longitude = 28.7907°W
- 4Result: 33.8688°N, 28.7907°W — located in the Atlantic Ocean off the Azores
Introduction
An antipode is the geographic point on Earth's surface that is diametrically opposite to a given location — if you could drill a tunnel straight through the center of the Earth, you would emerge at the antipode. The word comes from the Greek *antipodes*, meaning "having the feet opposite." This calculator uses the simple, exact mathematical formulas to find the antipodal coordinates of any latitude/longitude pair: negate the latitude and shift the longitude by 180 degrees.
How the Antipode Formula Works
The antipode calculation is one of the most elegant in spherical geometry. Given a point at latitude φ and longitude λ, its antipode lies at: - Antipode latitude = −φ (simply negate the latitude) - Antipode longitude = λ + 180° if λ ≤ 0, or λ − 180° if λ > 0 The longitude rule ensures the result stays within the conventional [−180°, +180°] range. For example, if you start at −74° (74°W), adding 180° gives 106°E. If you start at 151°E, subtracting 180° gives −29° (29°W). For related direction and bearing calculations, see the Azimuth Calculator and the Latitude-Longitude Distance Calculator, which measure bearing and distance between two coordinate pairs.
Famous Antipodal Pairs
Most places on Earth have their antipode in ocean — this is because roughly 71% of Earth's surface is water. Here are some notable antipodal pairs: | Location | Coordinates | Antipode Coordinates | Antipode Region | |---|---|---|---| | Madrid, Spain | 40.4°N, 3.7°W | 40.4°S, 176.3°E | New Zealand (near Wellington) | | Shanghai, China | 31.2°N, 121.5°E | 31.2°S, 58.5°W | Argentina (near Buenos Aires) | | Auckland, New Zealand | 36.9°S, 174.8°E | 36.9°N, 5.2°W | Málaga, Spain | | Taipei, Taiwan | 25.0°N, 121.5°E | 25.0°S, 58.5°W | Eastern Paraguay | The Auckland–Spain antipodal pair is one of the few city-to-land antipodal relationships. For more information on Earth's geography, see Wikipedia: Antipodal Points.
Special Cases: Poles and the Equator
The geographic poles are unique antipodal cases: - The North Pole (90°N, 0°) has its antipode at the South Pole (90°S, 180°) — the longitude assigned is arbitrary since all meridians converge at the poles. - Any point on the equator (φ = 0°) has its antipode also on the equator but exactly on the opposite side of the globe. - Points on the prime meridian (λ = 0°) have antipodes on the 180th meridian (λ = 180°), which runs through the Pacific Ocean. According to the National Oceanic and Atmospheric Administration (NOAA), only about 4% of Earth's land area has its antipode also on land, making land-to-land antipodal pairs geographically rare.
Practical Applications of Antipodal Coordinates
Antipodal calculations have real-world applications in: - Seismology: Earthquake waves converge and amplify at the antipode of the epicenter, helping geophysicists study Earth's interior composition. Research published in *Geophysical Research Letters* has documented antipodal seismic focusing effects. - Telecommunications: Geostationary satellite coverage zones are sometimes described in relation to antipodal ground tracks. - Astronomy and navigation: Historic celestial navigation methods referenced antipodal relationships, and modern GPS systems use geodetic frameworks built on antipodal symmetry. - Education: Antipodal maps are widely used in school geography to illustrate Earth's spherical nature. See also the Vertical Exaggeration Calculator for related geographic visualization tools, and the Angle of Impact Calculator for related coordinate geometry.
Accuracy and Limitations
The antipode formula gives mathematically exact results on a perfect sphere. In practice, Earth is an oblate spheroid (slightly flattened at the poles), so the true diametrically opposite point differs by at most a few kilometers from the spherical antipode. For most geographic and educational purposes this difference is negligible. Coordinate precision matters: inputs given to four decimal places (≈11 m resolution) produce equally precise antipodal outputs. For professional geodetic applications, refer to the World Geodetic System 1984 (WGS 84) standard used by GPS, documented by the National Geospatial-Intelligence Agency. The formula implemented here is consistent with standard spherical geometry and gives results identical to those expected by WGS 84 spherical approximations.
Understanding Coordinate Conventions
Geographic coordinates follow these conventions: - Latitude: ranges from −90° (South Pole) to +90° (North Pole). Positive values are north of the equator, negative values are south. - Longitude: ranges from −180° to +180°. Positive values are east of the prime meridian (Greenwich), negative values are west. When entering coordinates, use decimal degrees rather than degrees/minutes/seconds. To convert: decimal degrees = degrees + (minutes/60) + (seconds/3600). Most GPS devices and online maps (including Google Maps) display decimal-degree coordinates by default. For a comprehensive overview of the geographic coordinate system, see the USGS educational resource on map projections.
Quick Reference Card
Antipode Quick Reference
Quick reference • Antipode Calculator
Lat_antipode = −φ; Lng_antipode = λ ± 180°Valid range: Latitude: −90° to 90°; Longitude: −180° to 180°
Common Values
⚠ Watch Out
- •Latitude must be between −90° and +90°; values outside this range are invalid.
- •Longitude must be between −180° and +180°; values outside this range are invalid.
- •The poles (±90° latitude) have ambiguous antipodal longitude since all meridians converge there.
- •The antipode formula gives a spherical result; true geodetic antipodes on the WGS 84 ellipsoid differ slightly.
Pro Tips
- →Use decimal degrees for best precision; convert DMS (degrees, minutes, seconds) before entering.
- →Applying the formula twice returns you to the original coordinates — use this to verify your inputs.
- →The sign of longitude flips when you add or subtract 180°; check whether your result is E or W.
- →For city antipodes, expect the result to be in ocean more than 95% of the time.
FAQs
What is an antipode?
An antipode is the geographic point on Earth's surface that is diametrically opposite to a given location. If you drew a straight line from any point on Earth through the exact center of the globe, the point where that line emerges on the other side is the antipode.
Is most of Earth's antipode in the ocean?
Yes. Approximately 71% of Earth's surface is ocean, and about 96% of land areas have their antipode in ocean. Only a few regions — parts of Spain/Portugal opposite New Zealand, and portions of Asia opposite South America — have land-to-land antipodal pairs.
What is the antipode of the North Pole?
The antipode of the North Pole (90°N) is the South Pole (90°S). The longitude is conventionally listed as 0° or 180°, but since all meridians converge at the poles, the longitude is not meaningful there.
How accurate is this antipode calculator?
The calculator applies the exact spherical formula and is accurate to the precision of your input coordinates. On a perfect sphere, the result is exact. Earth's real oblateness (1/298.257 flattening) causes the true diametrically opposite point to differ by at most a few kilometers, which is negligible for most geographic purposes.
Can two locations be each other's antipode?
Yes — antipodal pairs are symmetric. If location A is the antipode of location B, then B is also the antipode of A. Applying the antipode formula twice returns you to the original coordinates.
What happens at the 180th meridian (the International Date Line)?
Points on the prime meridian (0° longitude) have their antipodes on the 180th meridian, which roughly follows the International Date Line in the Pacific Ocean. Points on the 180th meridian have their antipodes on the prime meridian, which passes through Greenwich, England.