Pi me a River

Is the average sinuosity of the world's rivers equal to π?

What is this?

There is a hypothesis that the average sinuosity of the world's rivers should be equal to π (3.141593). Numberphile produced a video discussing the idea and stated that there didn't seem to be any recorded data to actually check to see if it is true. This project aims to solve that.

Sinuosity is the ratio of the river's length to the straight-line distance between its source and mouth. For example, the Amazon is 6992.0km long and has a direct straight-line distance of 3026.7km, giving it a sinuosity of 6992.0 / 3026.7 = 2.31, notably less than π.

Notes on accuracy

This data has been crowd sourced and so is potentially guesswork and estimations. It is often difficult to find the exact source of a river, and indeed many rivers have multiple sources that are debated. Furthermore some named rivers are tributaries to larger rivers and different lengths are given depending on how you look at the data.


With 280 rivers the average sinuosity is 1.916233, with a standard deviation of 0.730769.

This is a difference of 1.22536 from π, or an error of 39.004415%.


Length vs Sinuosity


The code for this project is available at github. If you are interested in getting involved, either just submit your local river to the right or contribute and discuss via github.


I intend to continue updating the site with some interface improvements and potentially importing a massive set of data on rivers to improve the accuracy of the results.

Add your river

pimeariver.com is undergoing a major rebuild which will involve importing the river data for the entire globe from Open Street Map.

In the meantime adding your own rivers has been disabled to prevent the data from being spammed. Sorry for any inconvenience, you can follow the updates progress on github.


  1. Amazon (Brazil, Peru, Colombia)
  2. Nile (Ethiopia, Sudan, Egypt, Uganda, Democratic Republic of the Congo, Kenya, Tanzania, Rwanda, Burundi, South Sudan)
  3. Yangtze (China)
  4. Yenisei (Mongolia, Russia)
  5. Yellow River (China)
  6. Parana (Argentina, Brazil, Paraguay)
  7. Lena (Russia)
  8. Mekong (China, Myanmar, Laos, Thailand, Cambodia, Vietnam)
  9. Niger (Guinea, Mali, Niger, Benin, Nigeria)
  10. Missouri (United States)
  11. Mississippi (United States)
  12. Volga (Russia)
  13. Ob (Russia)
  14. Madeira (Bolivia, Brazil)
  15. Indus (Pakistan, India, China)
  16. Yukon (Canada, United States)
  17. Rio Grande (United States, Mexico)
  18. Lower Tunguska (Russia)
  19. Brahmaputra (China, India, Bangladesh)
  20. Danube (Germany, Austria, Slovakia, Hungary, Croatia, Serbia, Bulgaria, Moldova, Ukraine, Romania)
  21. Sao Francisco (Brazil)
  22. Amur (Russia, China)
  23. Salween (China, Burma, Thailand)
  24. Euphrates (Iraq, Syria, Turkey)
  25. Fraser (Canada)
  26. Nelson-Saskatchewan (Canada)
  27. Zambezi (Zambia, DR Congo, Angola, Namibia, Botswana, Zimbabwe, Mozambique, Malawi, Tanzania)
  28. Ganges (India, Bangladesh)
  29. Kolyma (Russia)
  30. Murray (Australia)
  31. Murray River (Australia)
  32. Ural (Russia, Kazakhstan)
  33. Amu Darya (Afghanistan, Tajikistan, Turkmenistan, Uzbekistan)
  34. Pearl River (China, Vietnam)
  35. Arkansas (United States)
  36. Slave River (Canada)
  37. Colorado (United States, Mexico)
  38. Syr Darya (Kyrgyzstan, Uzbekistan, Tajikistan, Kazakhstan)
  39. Oranjerivier (Lesotho, South Africa, Namibia)
  40. Red River of the South (United States)
  41. Dnjepr (Russia, Belarus, Ukraine)
  42. Orinoco (Venezuela)
  43. Columbia River (United States, Canada)
  44. Songhua (China)
  45. Peace (Canada)
  46. Middle Tunguska (Russia)
  47. Kama (Russia)
  48. Angara River (Russia)
  49. Mackensie (Canada)
  50. Churchill (Canada)
  51. Ohio (United States)
  52. Oka (Russia)
  53. Godavari (India)
  54. Krishna (India)
  55. Yamuna (India)
  56. Athabasca (Canada)
  57. Brazos (United States)
  58. Narmada (India)
  59. Ottawa River (Rivière des Outaouais) (Canada)
  60. Rio Grande aka Rio Bravo (United States, Mexico)
  61. Rhine (Luxembourg, Belgium, Italy, Germany, Austria, Switzerland, France, Netherlands, Liechtenstein)
  62. Saint Lawrence River (Canada)
  63. Cumberland (United States)
  64. Elbe (Czech republic, Germany)
  65. Vistula (Poland)
  66. Apure (Venezuela, Columbia)
  67. Tagus (Spain,Portugal)
  68. Loire (France)
  69. Usumacinta (Guatemala, Mexico)
  70. Tisza (Ukraine, Romania, Hungary, Slovakia, Serbia)
  71. Sava (Slovenia, Croatia, Bosnia and Hercegovina, Serbia, Montenegro, Albania)
  72. Meuse (France, Belgium, Netherlands)
  73. Neman (Lithuania, Belarus, Russia)
  74. Ebre (Espanya)
  75. Oder (Czech Republic, Poland, Germany)
  76. Rhone (France, Switzerland)
  77. Warta (Poland)
  78. Seine (France)
  79. Pripyat (Belarus, Ukraine)
  80. Bug (Poland, Belarus, Ukraine)
  81. Kaveri (India)
  82. Drava (Italy, Austria, Slovenia, Hungary, Croatia)
  83. Susquehanna (United States)
  84. Jon Vander Hill (United States)
  85. Guadalquivir (Spain)
  86. Potomac (United States)
  87. Po (Italy)
  88. Glomma (Norway)
  89. Garonne (Spain, France)
  90. Bow River (Canada)
  91. Shilka (Russia)
  92. James (United States)
  93. Moselle (France, Germany, Luxembourg)
  94. Dalälven (Sweden)
  95. Main (Germany)
  96. Tumen River (China, North Korea, Russia)
  97. Torne älv (Sweden, Finland)
  98. Inn (Austria, Germany, Switzerland, Italy)
  99. Hudson River (United States)
  100. Moskva River (Russia)
  101. St. Johns River (United States)
  102. Motagua (Guatemala)
  103. Narew (Poland, Belarus)
  104. San (Poland, Ukraine)
  105. Maritsa (Bulgaria, Greece, Turkey)
  106. Beas (India)
  107. Doubs (France, Switzerland)
  108. Mur (Austria, Slovenia, Croatia)
  109. Weser (Germany)
  110. Gasconade (United States)
  111. Sacramento (United States)
  112. Loa (Chile)
  113. Slave (Canada)
  114. Vltava (Czechia)
  115. Waikato River (New Zealand)
  116. Klamath River (United States)
  117. Saale (Germany)
  118. Adige (Italy)
  119. Tevere (Italy)
  120. Tiber (Italy)
  121. Tundzha (Bulgaria, Turkey)
  122. Klarälven (Norway, Sweden)
  123. Tarn (France)
  124. Bio Bio (Chile)
  125. Büyük Menderes (Turkey)
  126. Ems (Germany, Netherlands)
  127. Iskar (Bulgaria)
  128. Neckar (Germany)
  129. Shannon (Ireland)
  130. Morava (Czechia, Slovakia, Austria)
  131. Severn (United Kingdom)
  132. Meramec (Missouri) (United States)
  133. Thames (England)
  134. Thames (United Kingdom)
  135. Brisbane River (Australia)
  136. Mahaweli (Sri lanka)
  137. Mahaweli (Sri Lanka)
  138. Illinois River (United States)
  139. Tyne (United Kingdom)
  140. Pilica (Poland)
  141. Eger (Czechia, Germany)
  142. Citarum (Indonesia)
  143. Werra (Germany)
  144. Trent (United Kingdom)
  145. Madison River (U.S.A)
  146. Isar (Germany, Austria)
  147. Aare (Switzerland)
  148. Plyussa (Russia)
  149. Grand River (Canada)
  150. Arda (Bulgaria, Greece)
  151. Trinity River (California) (United States)
  152. Manning River (Australia)
  153. Great Miami River (United States)
  154. Vaigai (India)
  155. Jordan (Israel,Jordan)
  156. Maipo (Chile)
  157. Arno (Italy)
  158. Saar (France, Germany)
  159. Big River (Missouri) (United States)
  160. Piave (Italy)
  161. Great Ouse (United Kingdom)
  162. Mogami River (Japan)
  163. Lippe (Germany)
  164. Altmühl (Germany)
  165. Ruhr (Germany)
  166. Holston River (United States)
  167. Fulda (Germany)
  168. Wye (United Kingdom)
  169. Byskeälven (Sweden)
  170. Aller (Germany)
  171. Huron River (Michigan, United States)
  172. Bharathapuzha (Nila) (India)
  173. Cahabón (Guatemala)
  174. Simojoki (Finland)
  175. Barrow (Ireland)
  176. Eider (Germany)
  177. merrimack (united states)
  178. Suir (Ireland)
  179. Aroostook (United States, Canada)
  180. Pai (Thailand, Burma)
  181. Little Miami River (United States)
  182. Muskingum (United States)
  183. Eder (Germany)
  184. Siuslaw River (United States)
  185. Clyde (United Kingdom)
  186. Gudenåen (Denmark)
  187. Volturno (Italy)
  188. Penobscot (United States)
  189. Hase (Germany)
  190. Amper (Germany)
  191. Nolin (United States)
  192. Milwaukee River (United States)
  193. Vohandu (Estonia)
  194. Jackson (United States)
  195. Sieg (Germany)
  196. Stanislaus (United States)
  197. Santa Ana River (United States)
  198. Rideau (Canada)
  199. Nore (Ireland)
  200. Soča (Slovenia, Italy)
  201. Tees (United Kingdom)
  202. River Avon (United Kingdom, Warwickshire)
  203. Preto (Brazil)
  204. Kankakee (United States)
  205. Kalajoki (Finland)
  206. The Charles River (United States)
  207. Liffey (Ireland)
  208. IJssel (Netherlands)
  209. Freiberger Mulde (Czech Republic, Germany)
  210. Ure (United Kingdom)
  211. Swale (United Kingdom)
  212. slaney (ireland)
  213. Tittabawassee (United States)
  214. Derwent (United Kingdom)
  215. Don (United Kingdom)
  216. Aire (United Kingdom)
  217. Simeto (Italy)
  218. Mapocho (Chile)
  219. Oulujoki (Finland)
  220. Oker (Germany)
  221. Nacimiento (United States)
  222. Vantaanjoki (Finland)
  223. Suur Emajogi (Estonia)
  224. Blies (Germany, France)
  225. Ciliwung (Indonesia)
  226. Wharfe (United Kingdom)
  227. Georges River (Australia)
  228. Innerste (Germany)
  229. Svartån (sweden)
  230. Lee (Ireland)
  231. Stör (Germany)
  232. Ouse (United Kingdom)
  233. Emscher (Germany)
  234. Jordan(Utah) (United States)
  235. Pegnitz (Germany)
  236. Narva (Estonia, Russia)
  237. Neva (Russia)
  238. Kennet (United Kingdom)
  239. Swan River (Australia)
  240. Lea (or Lee) (United Kingdom)
  241. San Jacinto River (United States)
  242. Haune (Germany)
  243. Cam (United Kingdom)
  244. River Irwell (England)
  245. Lek (Netherlands)
  246. Humber (United Kingdom)
  247. Etobicoke Creek (Canada)
  248. Odense Å (Denmark)
  249. Lein (Germany)
  250. Dill (Germany)
  251. Menomonee (United States)
  252. River Yare (England)
  253. Detroit River (United States, Canada)
  254. Esk (United Kingdom)
  255. Venoge (Switzerland)
  256. Meža (Austria, Slovenia)
  257. Almont (France)
  258. Duessel (Germany)
  259. Eckbach (Germany)
  260. Oswego (United States)
  261. Arlau (Germany)
  262. Bünz (Switzerland)
  263. Limmat (Switzerland)
  264. Wietze (Germany)
  265. Rheidol (United Kingdom)
  266. Nidelva (Norway)
  267. Potamos Germasogeias (Cyprus)
  268. Perfume River (Vietnam,Hue)
  269. Yarkon (Israel)
  270. Maroglio (Italy)
  271. Pasig River (Philippines)
  272. Steinach (Germany)
  273. Aalbek (Stör) (Germany)
  274. Kam Tin River (Hong Kong)
  275. Mystic River (United States)
  276. Lam Tsuen River (Hong Kong)
  277. Kleinwaltersdorfer Bach (Germany)
  278. Storåna (Norway)
  279. Bain (United Kingdom)
  280. Fiumefreddo (Italy)