Half the World Lives Inside This Circle
Draw a circle on Earth's surface that holds half of everyone alive. How small can it be? A radius of about 3,400 km, covering less than 7% of the planet's surface. It is called the Valeriepieris circle. Each figure below describes one point in time (Quah calls his result the situation "in 2015"; Arthur's paper does not give the data year), and populations shift, so today's smallest circle would differ slightly.
Drag to rotate (the flat map only turns left and right). Every circle is drawn on the sphere first and then projected, so on the flat map the same circle stretches into an oval or an irregular shape. That is what it really looks like on this kind of flat map; switch to the globe to see that it is really a perfect circle.
The answer: centred between south-west China and north-eastern Myanmar, with a radius of 3,300–3,400 km
This page uses two published results for the smallest circle (Arthur released his algorithm and code; Quah published the result and an outline of the method), and their radii are close:
| Circle | Centre | Radius | Share of Earth's surface | Population data |
|---|---|---|---|---|
| Arthur (2023) | 28.375°N, 100.625°E. The paper says “the north of Yunnan province”; reverse-geocoding the coordinates puts it in Muli Tibetan Autonomous County, Sichuan, which borders Yunnan | 3,386 km | 6.9% | SEDAC GPW v4.11, 15-arc-minute grid (about 30 km); the paper does not state the data year |
| Quah (2015) | Near Mong Khet, Shan State, Myanmar | About 3,300 km | 6.6% | Population data at about 100 km resolution; the article calls this the result "in 2015" but does not say which year the underlying population estimates are for |
The surface shares are my own calculation from the spherical-cap formula with a mean Earth radius of 6,371 km. Quah only says the centre is near Mong Khet without giving coordinates, so the map uses the coordinates of Mong Khet town. Arthur also published his software; the example in its documentation (whose input file name indicates 2020 GPW data on a 1-degree grid) gives a centre at 28.5°N, 100.5°E, a radius of about 3,377 km and about 3.99 billion people inside.
Arthur's centre is about 750 km from the town of Mong Khet (Quah published no centre coordinates, so this uses the town's coordinates and is only an order-of-magnitude guide). The known difference is the resolution of the population data (about 30 km for Arthur, about 100 km for Quah); Arthur's paper does not give the data year and Quah did not publish his full method, so the sources do not say where the gap mainly comes from. Taipei is about 2,110 km from Arthur's centre and about 2,290 km from the Quah centre marked on this page, so it is inside both circles. Tokyo (about 3,750 km from Arthur's centre and about 4,190 km from Quah's) is outside both. Jakarta is about 3,900 km from Arthur's centre, so it is outside; measured from the centre marked on this page with Quah's approximate radius, it is inside Quah's circle, only about 90 km from the edge, but his centre and radius are approximate, so the map marks it as "near edge" rather than deciding. Try them in the menu above.
Where the question came from
- 2013: Myers's original map. Ken Myers posted a map on Reddit (as user valeriepieris, as Arthur's paper also notes) circling an area where more people live inside than outside. It was centred in the South China Sea with a radius of about 4,000 km, and the circle took its name from his username. According to Wikipedia, it was drawn on a Winkel Tripel map, so it is not a true circle on the sphere, and the sources we found say only "South China Sea" with no coordinates (we did not read the original Reddit post). The map on this page can only show it approximately.
- 2015: Quah finds a smaller circle. Economist Danny Quah redid the calculation with great-circle distances and gridded population data, confirmed Myers's claim, and found a smaller circle centred near Mong Khet, Myanmar, with a radius of about 3,300 km. Quah judged Myers's original guess “remarkably close” to his 2015 optimum.
- 2023: Arthur turns it into an analysis tool. Rudy Arthur's paper in Geographical Analysis treats the circle as a “spatial median”, gives a fast algorithm and open-source code, and produces the result in the table above.
Common mix-ups
- 4,000 km is not the smallest circle. Two circles discussed here have a 4,000 km radius: Myers's 2013 original, and geographer Alasdair Rae's 2022 “Yuxi Circle”. The Yuxi Circle answers a different question: draw a 4,000 km circle around cities worldwide (about 1,500 circles) and see which one holds the most people. The winner is Yuxi in Yunnan, with about 4.32 billion people, over 55% of the world (2020 WorldPop data). A 4,000 km circle has about 40% more area than a 3,386 km one, so the two should not be confused.
- 6.9% is of Earth's whole surface, not of its land. A large part of the circle is sea (the Bay of Bengal and the South China Sea).
- The circle is not crowded everywhere. Sparsely populated places such as the Tibetan Plateau (Lhasa is about 940 km from Arthur's centre) and Mongolia (Ulaanbaatar, about 2,240 km) are inside too. Arthur's paper attributes the small radius to the very high populations of northern India, southern China and the rest of south-east Asia, which together make up half the world.
- Circles drawn directly on an ordinary flat map are wrong. Most flat maps do not preserve distance (on a Mercator map, for example, the same 3,400 km looks stretched at high latitudes), so a circle drawn as a circle on one is not a circle on the sphere; the radius has to be measured as a great-circle distance (or on an azimuthal equidistant map centred on the circle). Quah's 3,300 km is a great-circle distance on the sphere.
Sources
- Arthur, R. (2023). Valeriepieris Circles for Spatial Data Analysis. Geographical Analysis, 56(3), 514–529. doi:10.1111/gean.12383; preprint arXiv:2307.16728 (centre and radius in Table 1; published online December 2023, volume and pages as listed in Wikipedia's references)
- Arthur, R. valeriepieris (Python package). PyPI (example result; the input file name indicates 2020 data on a 1-degree grid)
- Quah, D. (2016). The World’s Tightest Cluster of People. Global Policy. Article (Wikipedia's references also list a 2015 version on an LSE blog)
- Rae, A. & Pacis, T. (2022). The Yuxi Circle: The World’s Most Densely Populated Area. Visual Capitalist. Article (authors and title as listed in Wikipedia's references; we could not access the original, and the figures on this page follow Wikipedia and nchstats)
- Wikipedia: Valeriepieris circle (background on Myers's original map)
- Base map: world-atlas (Natural Earth 1:110m); drawn with d3-geo
Last updated: 2026-10-20