# Antipode Calculator

Created by Davide Borchia
Reviewed by Anna Szczepanek, PhD
Last updated: Jun 05, 2023

Digging a tunnel through the center of the Earth would bring you to your antipode: let's find out where it lies with our antipode calculator! Here you will learn a little bit of history, what the antipode of a point is, and how to find the antipode using a tiny bit of math.

## What is an antipode?

The antipode is the diametrically opposite point of a given location on a sphere. In the past, the question "what is an antipode?" had many interesting answers. The Greeks knew the Earth was spherical, and the polymath Erathostenes calculated its diameter with an error of only about $1000\ \text{km}$: impressive! Knowing the size of the planet, they were enthralled by the idea of landmasses on the other side of the globe, where people would live in the opposite direction of them: "anti" means "opposite" and "pous" means "foot".

In the middle ages, people had wilder imaginations, and instead of a land where people were standing upside-down, the term antipode came to mean upside-down people, with feet in place of their heads and vice versa!

Terra Australis, the hypothetical continent on the other side of the globe, was depicted in various ways, attracting explorers until it was clear that it was not much different to the one they came from. In later years, antipodes lost their mystical connotation and settled more as a curious feature of our planet.

## How to calculate the antipode of any point?

A point on the surface of a planet is uniquely identified by the pair of coordinates $(\theta, \varphi)$:

• The latitude ($\theta$) indicates the north-south position of the point, divided into 180 degrees, from +90° at the North Pole to -90° of the South Pole, passing through 0° at the equator.
• The longitude ($\varphi$) gives information on the east-west position. There is no geographical indicator for $\theta = 0\degree$; it was arbitrarily fixed in 1884, choosing the Royal Observatory in Greenwich, London, as its reference point — you can go there and take a picture claiming to be in both hemispheres at the same time! If the point is located in the Western Hemisphere, then the longitude varies from $0\degree$ to $-180\degree$; in the Eastern Hemisphere, the value is positive between $0\degree$ and $180\degree$, for a total of $360\degree$. Latitude and longitude on Earth. The easiest way to identify points on the Planet. Via Wikimedia Commons Djexplo/ CC0

And here is how to find the antipode $(\theta_\text{a}, \varphi_\text{a})$ to a point $(\theta,\varphi)$!

• The latitude of the point, with a change of sign: $\theta_\text{a}= −\theta$
• The longitude of the point transformed according to:
• $\varphi_\text{a} = \varphi + 180\degree\ \textrm{if}\ \varphi \leq 0$
• $\varphi_\text{a} = \varphi - 180\degree\ \textrm{if}\ \varphi \>0$

That's how we calculate the antipode of a point! Easy, right?

Coordinates can get messy; do we use decimals or minutes and seconds — and weren't those time units?! If you want to find out more, try our coordinates converter!

Earth is a blue planet: landmasses cover less than $30\%$ of the surface of the globe. In consequence, it's highly likely that the antipode of a given point lies in the middle of an ocean! Only $15\%$ of the land has a land antipode, and most of the rest falls into the Pacific Ocean.

The Pacific Ocean itself is so big it contains its own antipode! And speaking of containing the opposite point: the Sun never did set over the British Empire, as Britain and New Zealand are almost antipodal.

In 2020, two men (one in New Zealand and the other in Spain) by placing bread slices on the exact coordinates of two antipodal points. They didn't manage to finish eating it, apparently.

Another interesting fact! At every moment, there is at least one pair of antipodal points on Earth with the same temperature — we know this thanks to the . Choose a pair of antipodal points, $a$ and $b$. Now move around the globe following the great circle (the biggest line you can draw on Earth connecting $a$ and $b$, which would then contain pairs of antipodal points). After half a turn, $a$ and $b$ would switch position. This means that at a certain point $c$ of the great circle, the pair of antipodal points had the same temperature. Don't believe us? Take a look at the picture representing the variation of temperature from $a$ to $b$ (red line) and the variation from $b$ to $a$ (blue line)! The Borsuk-Ulam theorem in action. Even if the two lines follow different paths, there is a point ccc at which they meet.

## How does our antipode calculator work?

In our antipode calculator, we have a list of countries and cities with more than 100,000 inhabitants (fewer than that, and you wouldn't find yours!):