Distance from A 3 Paris Porte De Bagnolet to Peripherique

N A 3 Paris Porte De Bagnolet → Peripherique
Road distance
11,704.1 km
Metro routes · M1 / M3 / M6
A 3 Paris Porte De Bagnolet to Peripherique is a full long-distance road trip, covering about 11,704.1 km in roughly 136 hrs 16 min. It also crosses a provincial boundary.
Geodesic Direct point-to-point reference
9,591.6 km
Road multiplier Route-to-direct distance ratio
1.22×
Navigation steps Instruction count in route set
294
Info Travel board
Travel time
136 hrs 16 min
Start point
Place de la Porte de Bagnolet
Return: 32 min
Rolling runtime Engine-calculated drive duration
8176 min
Average velocity Distance over route runtime
85.9 km/h
Stop-adjusted ETA 68 planned rest stops
153 hrs 16 min
Fuel Service sign
Estimated fuel cost - 7.2 L/100km
93 Petrol R26.52 / litre
R22,348.36
95 Petrol R26.63 / litre
R22,441.06
Diesel 500ppm R32.30 / litre
R27,219.16
Diesel 50ppm R32.50 / litre
R27,387.70
93 Petrol R26.52 / litre
R29,487.42
95 Petrol R26.63 / litre
R29,609.73
Diesel 500ppm R32.30 / litre
R35,914.17
Diesel 50ppm R32.50 / litre
R36,136.55
93 Petrol R26.52 / litre
R38,799.24
95 Petrol R26.63 / litre
R38,960.17
Diesel 500ppm R32.30 / litre
R47,255.48
Diesel 50ppm R32.50 / litre
R47,548.09
See more fuel details from A 3 Paris Porte De Bagnolet to Peripherique
🧭 Route vector
Compass bearing
59° ENE
Forward azimuth heading
Return heading Reverse azimuth
239° WSW
Coordinate delta Lat / Lon shift
South-West
Start coords Origin point
48.8645, 2.4087
End coords Destination point
22.5601, 114.0169
Taxi Local commuter
Taxi fare estimate
Check local taxi rank
Long-distance caution
Route class Operational trip category
Local shared
Calculating arrival…
Travel modes
A 3 Paris Porte De Bagnolet → Peripherique
🚗
Car
11,704.1 km
136 hrs 16 min
Road route
🏍️ Estimate
Two-wheeler
11,704.1 km
~180 hrs 3 min
65 km/h avg
🧭 Google
Navigate now
Peripherique
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Estimate
Flight
11,704 km
~23 hrs 24 min
↑ 112 hrs 51 min faster · Search →
Route

Route overview

Live map, directions, tolls and route services.

Map Directions Tolls Trip planning
Route map

Live map

Start, destination and route line.

11,704.1 km 136 hrs 16 min
Start A 3 Paris Porte De Bagnolet
Finish Peripherique
Map key
Start point
Destination
Driving route
Navigation sign

Turn-by-turn directions

Route directions
🏙️
Directions from A 3 Paris Porte De Bagnolet to Peripherique via M6 and M3 and M1
Metro arterial routes M6 M3 M1
  1. Head on Place de la Porte de Bagnolet
    0.1 km
  2. Continue onto Avenue de la Porte de Bagnolet
    0.3 km
  3. Keep slight left at the fork towards A 3: Lille
    6.6 km
  4. Keep slight left at the fork
    8.9 km
  5. Keep slight left at the fork towards A 1
    1.6 km
  6. Take the exit ramp slight left towards A 1: Lille
    0.7 km
  7. Merge slight left onto Autoroute du Nord
    121.3 km
  8. Keep slight right at the fork towards A 2: Cambrai
    77.1 km
  9. Continue straight
    36.9 km
  10. Keep slight right at the fork onto Autoroute de Wallonie towards E42
    3.1 km
  11. Keep slight left at the fork
    0.0 km
  12. Merge slight left onto Autoroute de Wallonie
    0.6 km
  13. Keep slight right at the fork
    0.0 km
  14. Merge slight right onto Autoroute de Wallonie
    138.2 km
  15. Continue straight onto König Baudouin Autobahn - Autoroute Roi Baudouin
    11.5 km
  16. Continue straight
    10.4 km
  17. Take the exit ramp slight right towards A 4
    0.3 km
  18. Keep slight left at the fork towards A 4: Köln
    0.7 km
  19. Merge slight left
    51.1 km
  20. Take the exit ramp slight right
    0.1 km
  21. Keep slight left at the fork towards A 1: Dortmund
    0.8 km
  22. Keep slight left at the fork towards A 1: Dortmund
    0.1 km
  23. Merge slight left
    106.1 km
  24. Take the exit ramp slight right towards A 2: Oberhausen
    0.4 km
  25. Keep slight right at the fork towards A 2: Hannover
    0.9 km
  26. Merge slight left
    179.4 km
  27. Keep slight left at the fork towards A 2: Berlin
    22.1 km
  28. Keep slight left at the fork towards A 2: Berlin
    19.8 km
  29. Take the exit ramp slight right towards B 444: Peine
    0.2 km
  30. Keep slight left at the fork towards Peine-Ost
    1.8 km
  31. Keep slight left at the fork towards A 2: Berlin
    0.5 km
  32. Merge slight left
    97.1 km
  33. Take the exit ramp slight right towards B 189: Magdeburg-Zentrum
    0.1 km
  34. Continue straight
    0.2 km
  35. Keep slight left at the fork towards B 189: Stendal
    0.4 km
  36. Keep slight left at the fork towards A 2: Berlin
    0.3 km
  37. Continue straight
    0.2 km
  38. Merge slight left
    89.2 km
  39. Merge slight right
    18.5 km
  40. Keep slight left at the fork towards A 10: Frankfurt (Oder)
    46.5 km
  41. Take the exit ramp slight right towards A 12: Warschau (Warszawa)
    0.9 km
  42. Continue straight
    510.6 km
  43. Continue straight
    2.4 km
  44. Take the exit ramp slight right towards S7
    1.1 km
  45. Continue straight
    106.1 km
  46. Keep slight left at the fork towards Białystok
    96.4 km
  47. Take the exit ramp slight right towards 8
    0.3 km
  48. At the roundabout, take the 3rd exit onto Aleja Tysiąclecia Państwa Polskiego
    0.1 km
  49. Continue onto Aleja Tysiąclecia Państwa Polskiego
    6.5 km
  50. Take the exit ramp slight right towards 19: Kuźnica PL/BY
    33.1 km
  51. Continue straight onto Grodzieńska
    4.0 km
  52. At the roundabout, take the 2nd exit
    0.1 km
  53. Continue
    0.4 km
  54. At the roundabout, take the 1st exit
    0.0 km
  55. Continue
    0.2 km
  56. Continue straight
    9.4 km
  57. At the roundabout, take the 2nd exit
    0.1 km
  58. Continue
    3.1 km
  59. Turn left onto Graniczna
    0.1 km
  60. Continue straight onto Topolowa
    0.2 km
  61. At the end of the road, turn right onto Tadeusza Kościuszki
    0.3 km
  62. Turn right
    0.5 km
  63. Continue slight right
    0.2 km
  64. Continue straight
    0.1 km
  65. Keep slight right at the fork
    0.1 km
  66. Keep slight left at the fork
    1.8 km
  67. At the roundabout, take the 2nd exit
    0.0 km
  68. Continue
    0.1 km
  69. Continue straight
    27.6 km
  70. Take the exit ramp slight right towards M6: Ліда
    228.5 km
  71. Take the exit ramp slight right towards M3
    0.6 km
  72. Keep slight left at the fork
    0.4 km
  73. Merge slight left
    45.3 km
  74. At the roundabout, take the 1st exit
    0.1 km
  75. Continue
    15.2 km
  76. Continue straight
    9.0 km
  77. Take the exit ramp slight right towards M1: Масква
    0.3 km
  78. Merge slight left
    160.1 km
  79. Continue straight
    62.6 km
  80. Continue straight onto «Беларусь»
    117.9 km
  81. Continue straight onto «Беларусь»
    8.3 km
  82. Continue straight onto «Беларусь»
    1.8 km
  83. Keep slight right at the fork onto «Беларусь»
    28.2 km
  84. Go straight
    214.0 km
  85. Keep slight right at the fork
    2.3 km
  86. Merge slight left onto «Беларусь»
    8.4 km
  87. Turn slight right
    1.7 km
  88. Merge slight left onto «Беларусь»
    5.4 km
  89. Turn slight right
    0.8 km
  90. Merge slight left onto «Беларусь»
    2.3 km
  91. Continue straight onto Минское шоссе
    31.2 km
  92. Keep slight left at the fork onto Минское шоссе
    6.8 km
  93. Continue straight onto 27-й км, Минское шоссе
    1.0 km
  94. Continue straight onto Минское шоссе
    4.5 km
  95. Turn slight right towards Зона отдыха
    1.7 km
  96. Merge slight left onto Минское шоссе
    3.1 km
  97. Continue straight onto Можайское шоссе
    0.1 km
  98. Continue slight left onto Можайское шоссе
    5.0 km
  99. Continue straight onto Кутузовский проспект
    5.4 km
  100. Turn slight right towards М-3
    0.2 km
  101. Keep slight right at the fork towards М-3: 3-е Кольцо-направо
    0.4 km
  102. Go straight onto Третье транспортное кольцо
    0.3 km
  103. Keep slight left at the fork onto Третье транспортное кольцо
    6.0 km
  104. Continue straight onto Третье транспортное кольцо
    5.8 km
  105. Keep slight left at the fork onto Третье транспортное кольцо
    0.6 km
  106. Keep slight left at the fork onto Юго-Восточная хорда
    4.0 km
  107. Keep slight right at the fork
    0.5 km
  108. Go straight onto Северо-Восточная хорда
    6.5 km
  109. Continue straight onto Косинское шоссе
    4.1 km
  110. Continue straight onto Северо-восточная хорда
    4.7 km
  111. Continue straight onto «Восток»
    740.1 km
  112. Continue make a U-turn onto «Восток»
    56.0 km
  113. Take the exit ramp slight right
    0.6 km
  114. Continue straight
    0.2 km
  115. Merge slight left
    7.8 km
  116. Keep slight right at the fork
    6.6 km
  117. Keep slight right at the fork
    34.9 km
  118. Continue straight onto Алексеевское - Альметьевск
    143.0 km
  119. Continue straight
    0.4 km
  120. Continue make a U-turn
    1.7 km
  121. Turn right
    9.1 km
  122. Turn slight right
    0.0 km
  123. Go straight
    7.5 km
  124. Turn left
    2.7 km
  125. Merge slight left
    0.2 km
  126. Take the exit ramp slight right towards Р-239: Актюбинск
    5.0 km
  127. At the roundabout, take the 1st exit onto Объездной тракт
    0.0 km
  128. Continue onto Объездной тракт
    48.4 km
  129. Continue straight onto улица Газинура Гафиатуллина
    3.3 km
  130. Turn left onto улица Джалиля
    0.9 km
  131. Continue slight right onto улица Ленина
    8.0 km
  132. At the roundabout, take the 2nd exit
    0.2 km
  133. Continue
    0.1 km
  134. Continue straight
    19.9 km
  135. At the roundabout, take the 2nd exit onto «Урал»
    0.1 km
  136. Continue onto «Урал»
    510.2 km
  137. Turn slight right towards 75К-171: Черновское
    0.1 km
  138. Continue straight
    0.4 km
  139. Turn slight right
    1.3 km
  140. Continue straight
    16.2 km
  141. Turn left onto улица Ленина
    1.0 km
  142. Turn right onto улица Труда
    1.3 km
  143. Continue straight onto Больничная улица
    0.4 km
  144. Continue straight
    35.2 km
  145. Turn right
    25.9 km
  146. Continue straight
    4.4 km
  147. At the roundabout, take the 2nd exit
    0.1 km
  148. Continue
    1.0 km
  149. At the roundabout, take the 2nd exit
    0.2 km
  150. Continue
    0.0 km
  151. Continue straight
    0.5 km
  152. Merge slight left
    3.7 km
  153. Go straight
    29.1 km
  154. Keep slight right at the fork towards А-310: Кустанай
    0.1 km
  155. Merge slight left
    42.8 km
  156. Turn right
    13.1 km
  157. Turn slight right
    0.1 km
  158. Turn left
    0.1 km
  159. Turn left
    0.1 km
  160. At the end of the road, turn right
    0.1 km
  161. Turn right
    0.0 km
  162. Keep slight left at the fork
    0.2 km
  163. Merge slight left
    0.4 km
  164. Continue straight
    41.0 km
  165. Turn left
    5.6 km
  166. Continue left
    1.8 km
  167. Turn right
    115.8 km
  168. Keep slight left at the fork
    9.2 km
  169. Turn right onto Абай даңғылы
    1.1 km
  170. Turn left onto Тәуелсіздік көшесі
    3.6 km
  171. At the roundabout, take the 1st exit
    0.0 km
  172. Continue
    3.2 km
  173. Keep slight left at the fork
    251.9 km
  174. Continue right
    14.9 km
  175. At the roundabout, take the 3rd exit
    0.2 km
  176. Continue
    15.6 km
  177. Go straight
    66.7 km
  178. Merge slight right
    87.4 km
  179. Continue right
    3.4 km
  180. Turn left
    109.2 km
  181. At the roundabout, take the 1st exit
    0.0 km
  182. Continue
    133.1 km
  183. Take the exit ramp straight towards Петропавл
    0.4 km
  184. Merge slight left onto Астана айналма жолы
    22.4 km
  185. Take the exit ramp slight right
    0.3 km
  186. Merge slight left onto шоссе Алаш
    5.1 km
  187. Continue straight onto Астана — Ерментау
    2.3 km
  188. Continue straight onto Астана — Павлодар
    10.7 km
  189. Continue straight onto р.Коянды
    255.3 km
  190. Continue straight onto Шидерты-Экибастуз
    56.1 km
  191. Continue straight onto Экибастуз-Павлодар
    73.0 km
  192. Take the exit ramp slight right towards Р45: Курчатов
    0.4 km
  193. Merge slight left
    10.7 km
  194. Take the exit ramp straight
    0.3 km
  195. Continue straight
    15.7 km
  196. Take the exit ramp slight right
    0.5 km
  197. Merge slight left onto Павлодар - Семей
    263.2 km
  198. Continue straight onto Ленина
    1.9 km
  199. Continue straight onto Павлодар - Семей
    51.3 km
  200. Continue straight onto Шугаев көшесі
    1.5 km
  201. Turn right onto Гагарин көшесі
    1.4 km
  202. At the roundabout, take the 1st exit onto Тұрлыханов даңғылы
    0.1 km
  203. Continue onto Тұрлыханов даңғылы
    2.6 km
  204. At the roundabout, take the 3rd exit onto Бозтаев көшесі
    0.4 km
  205. Continue onto Бозтаев көшесі
    2.7 km
  206. Continue straight onto Титов көшесі
    1.6 km
  207. At the end of the road, turn right onto Семей — Қалбатау
    153.7 km
  208. Take the exit ramp slight right towards А3
    5.6 km
  209. Continue straight onto Қалбатау - Алматы
    278.5 km
  210. Keep slight left at the fork onto Таскескен - Бақты (Қытай шекарасы)
    187.2 km
  211. Continue straight
    2.9 km
  212. Turn right
    11.3 km
  213. Continue straight onto 奎塔高速
    205.3 km
  214. Take the exit ramp slight right
    0.6 km
  215. Keep slight right at the fork
    0.8 km
  216. Merge slight left onto 奎阿高速
    43.0 km
  217. Keep slight left at the fork onto 五克高速
    206.5 km
  218. Turn right
    0.8 km
  219. Turn left
    0.7 km
  220. Keep slight left at the fork
    0.8 km
  221. Merge slight left onto 连霍高速
    212.8 km
  222. Keep slight left at the fork onto 连霍高速
    118.1 km
  223. Keep slight left at the fork onto 连霍高速
    1,164.5 km
  224. Keep slight left at the fork onto 连霍高速 towards 武威
    444.1 km
  225. Keep slight right at the fork onto 连霍高速
    5.1 km
  226. Keep slight right at the fork onto 连霍高速
    1.8 km
  227. Merge slight left onto 京藏高速
    19.6 km
  228. Keep slight left at the fork onto 连霍高速
    0.2 km
  229. Keep slight right at the fork onto 连霍高速
    3.1 km
  230. Keep slight left at the fork onto 连霍高速
    17.3 km
  231. Take the exit ramp slight right onto 连霍高速 towards 定西
    34.3 km
  232. Continue straight onto 青兰高速
    9.8 km
  233. Continue straight onto 连霍高速
    48.7 km
  234. Keep slight left at the fork onto 青兰高速
    180.6 km
  235. Keep slight left at the fork onto 青兰高速 towards G70
    1.2 km
  236. Merge slight left onto 青兰高速
    100.6 km
  237. Take the exit ramp slight right
    1.0 km
  238. Merge slight left onto 上海 - 霍尔果斯
    4.6 km
  239. Go straight
    68.0 km
  240. Turn left
    25.4 km
  241. Take the exit ramp left
    0.9 km
  242. Keep slight right at the fork
    0.3 km
  243. Merge slight left onto 福银高速
    92.8 km
  244. Continue straight onto 银百高速
    18.5 km
  245. Take the exit ramp slight right
    0.5 km
  246. Keep slight left at the fork
    1.6 km
  247. Merge slight left onto 西安绕城高速
    26.2 km
  248. Take the exit ramp slight right
    0.4 km
  249. Keep slight left at the fork
    1.7 km
  250. Merge slight left onto 沪陕高速
    18.9 km
  251. Take the exit ramp slight right onto 蓝田县联络线
    20.4 km
  252. Continue straight onto 福银高速
    45.1 km
  253. Take the exit ramp slight right onto 福银高速
    301.8 km
  254. Continue straight onto 汉十高速
    32.6 km
  255. Take the exit ramp slight right
    0.1 km
  256. Keep slight right at the fork
    0.8 km
  257. Merge slight left onto 二广高速
    16.6 km
  258. Continue straight onto 襄阳汉江四桥
    4.6 km
  259. Continue straight onto 襄荆高速
    197.5 km
  260. Continue straight onto 二广高速
    66.9 km
  261. Continue straight onto 国家高速G55
    91.3 km
  262. Continue straight onto 沅水特大桥
    9.1 km
  263. Take the exit ramp slight right
    0.3 km
  264. Keep slight left at the fork
    1.1 km
  265. Merge slight left onto 长常北线高速
    125.3 km
  266. Take the exit ramp slight right
    0.4 km
  267. Keep slight right at the fork
    0.7 km
  268. Merge slight right
    390.4 km
  269. Keep slight left at the fork onto 许广高速
    0.2 km
  270. Continue straight onto 临连高速
    4.3 km
  271. Continue straight onto 广连高速
    231.0 km
  272. Take the exit ramp slight right
    0.5 km
  273. Keep slight left at the fork
    2.0 km
  274. Merge slight left onto 大广高速
    5.0 km
  275. Keep slight right at the fork
    0.8 km
  276. Continue straight onto 珠三角环线高速
    5.2 km
  277. Take the exit ramp slight right
    0.4 km
  278. Keep slight right at the fork
    0.6 km
  279. Merge slight left onto 从埔高速
    25.1 km
  280. Merge slight left onto 京港澳高速
    5.4 km
  281. Take the exit ramp slight right onto 京港澳高速 towards G4
    0.7 km
  282. Keep slight left at the fork onto 京港澳高速
    0.4 km
  283. Keep slight left at the fork onto 京港澳高速 towards G4
    53.8 km
  284. Keep slight left at the fork onto 京港澳高速 沈海高速
    38.5 km
  285. Take the exit ramp slight right towards G107: 北环大道
    0.3 km
  286. Keep slight right at the fork towards G107: 北环大道
    0.0 km
  287. Keep slight left at the fork towards G107: 北环大道
    0.2 km
  288. Keep slight right at the fork
    0.3 km
  289. Go straight onto 南海大道
    1.0 km
  290. Turn slight right towards G107: 北环大道(东)
    0.3 km
  291. Go straight onto 北环大道辅路
    0.4 km
  292. Take the ramp slight left
    0.2 km
  293. Merge slight left onto 北环大道
    8.7 km
  294. You have arrived at your destination
    0.0 km
Navigation sign

Tolls on this route

R
Tolls found 0
Known total
Main toll road M6 - Chapman's Peak Drive
We found matching toll-road records for this route, but no tollgate point was close enough to the route line to display as a confirmed route toll.
M6 - Chapman's Peak Drive M6 - Chapman's Peak Drive M6 - Chapman's Peak Drive M6 - Chapman's Peak Drive
Stop Stopover sign
Halfway point
5,843.1 km
Île-de-France to 广东省
Mid-route position Road corridor partition
50 / 50
Time partition Start / finish split
68 hrs 8 min • 68 hrs 8 min
Waypoint reference Nearest route marker
Île-de-France to 广东省
Vec Consumption & emissions
Consumption & emissions profile
842.7 L needed
Moderate efficiency • 7.2 L/100km baseline
CO2 emitted Estimated tailpipe output
1,946.6 kg
Fuel mass Approximate tank weight
632.0 kg
Cost per km Based on 95 Petrol
R1.92
Directness index As-the-crow-flies ratio
82%
Solar data
Daylight window at Peripherique
00:-18 – 12:58
Outside daylight hours
Solar noonHighest sun position
Total daylightUsable driving light
13 hrs 16 min
Light remainingUntil sunset
Expired
SunriseDawn break
00:-18
Fin Tax & wear
Wear & SARS deduction
R48,923.32
Single trip SARS allowance
SARS rate R4.18/km fixed rate
R4.18/km
Tyre wear Estimated tread cost
R234.08
Service wear Oil & filter allocation
R2,340.83
Total trip wear Excludes fuel & tolls
R51,498.24
Nav Maneuver index
Navigation complexity
Very High (338)
Turn difficulty rating
Roundabouts Multi-path navigation
16
Lane merges Yield required
40
Complex forks Path selection
66
Highway exits Deceleration zones
52
Route atlas

Atlas Route Specification

Route sheet

ZA-ATLAS
Origin A 3 Paris Porte De Bagnolet Start: Place de la Porte de Bagnolet 48.86450, 2.40874
Midpoint
5,843.1 km
Total: 11,704.1 km
Midpoint 5,843.1 km
11,704.1 km 136 hrs 16 min
Destination Peripherique 22.56013, 114.01687

Route sheet

Route class Interprovincial corridor
Province span Île-de-France to 广东省
One-way road span 11,704.1 km
Return-cycle span 23,408.3 km
Traversal time 136 hrs 16 min
Maneuver count 294
Maneuver density 2.5 /100 km
Midpoint chainage 5,843.1 km

Coordinate frame

Start 48.86450, 2.40874
Midpoint 51.86201, 75.75658
End 22.56013, 114.01687
Route support

Route FAQ

Tap a question to expand the answer and keep the section compact while browsing the route page.

Questions 9
How far is A 3 Paris Porte De Bagnolet from Peripherique? +
A 3 Paris Porte De Bagnolet is about 11,704.1 km from Peripherique by road.
How long does it take from A 3 Paris Porte De Bagnolet to Peripherique? +
The drive usually takes about 136 hrs 16 min depending on traffic, stops, and road conditions.
Is it possible to drive from A 3 Paris Porte De Bagnolet to Peripherique in one day? +
It is possible, but for many travellers this is better treated as a very long same-day trip or an overnight trip.
Is taxi available from A 3 Paris Porte De Bagnolet to Peripherique? +
Taxi may be available, but for this route it is better to confirm the latest fare at the local taxi rank.
What's the estimated fuel amount from A 3 Paris Porte De Bagnolet to Peripherique? +
Using an estimated consumption of 7.2 L/100km for this route, 93 Petrol is about R22,348.36 (R26.52 / litre), 95 Petrol is about R22,441.06 (R26.63 / litre), Diesel 500ppm is about R27,219.16 (R32.30 / litre), Diesel 50ppm is about R27,387.70 (R32.50 / litre). Actual fuel spend can vary by vehicle, traffic and driving style.
Are there any tollgates from A 3 Paris Porte De Bagnolet to Peripherique? +
No tollgates are currently matched for this route.
What is the route verdict for this trip? +
Very long trip: This is a demanding long-distance route. Treat it as a serious travel day and consider an overnight stop.
Is there a long-trip warning on this route? +
This is a long trip. Plan rest stops, avoid driving tired, and be careful with late-night travel.
Is there a road note for this route? +
This is a longer road trip, so a fuel or rest stop is recommended. Take a short break about every 2 hours if possible. This route crosses a provincial boundary. This route looks more local or regional, but always check signs and road conditions on the day.
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Route Locations

Start area
A 3 Paris Porte De Bagnolet, Île-de-France
Suburb: Not available
Road: Not available
Postal code: Not available
Destination area
Peripherique, 广东省
Suburb: Not available
Road: Not available
Postal code: Not available

Distance comparisons

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