Where the Borders Are Straight: Ruler Lines, Rivers and Mountains on Every International Land Border, and Who Drew the Longest Straight Lines

I classify every international land border in Natural Earth's 1:10 million boundary lines, 233,534 km between 170 countries and territories, into ruler-straight stretches, rivers and lakes, mountains and other lines, using an explicit geometric test for straightness (every vertex within 1 km of a great circle or rhumb line over at least 50 km), Natural Earth rivers and lakes, and the ETOPO5 elevation grid. 19.4% of the world's land border length is straight, 20.9% follows water and 24.7% runs through mountains. Africa holds 53.8% of all straight border length and the largest share of mostly straight borders, but by share of length North America (45.9%) is straighter than Africa (30.2%) under all 12 sensitivity settings, largely because of the border between Canada and the United States. For the 40 longest straight segments I compile, from published sources, the agreement that set each line, its year and the powers involved: 21 of 40 dated lines were set between 1880 and 1914, and the United Kingdom was party to 21. Straightness depends strongly on map scale: the same method finds 25.4% straight on the 1:50 million lines and 83.6% on the 1:110 million lines. Interactive version: https://maps.tristanhotham.com/straight-borders/. Data and code: https://github.com/Tristan-Hotham/straight-borders. Blog post: https://blog.tristanhotham.com/2026/10/31/straight-borders/. Licences: text, figures and derived data CC BY 4.0; code MIT. Natural Earth and ETOPO5 are public domain. I wrote the text, with drafting and editing assistance from Claude (Anthropic), which also helped prepare the analysis code. I reviewed and checked all text and results.