Street orientation: which cities follow a grid?

Key findings

• New York (0.85), Chicago (0.84), and Beijing (0.83) have the most ordered street networks of the 64 cities studied (orientation order out of 1).
• Barcelona is the first European city in the ranking, in 11th place (0.33).
• In France, Tours (0.21), Versailles (0.16), and Nancy (0.15) are the most ordered of the 25 cities measured; Toulouse is the least ordered (0.01).
• Toulouse has the least ordered network of the whole study (0.01): its streets run in almost every direction.
• Paris scores 0.05 (42nd of 64): its avenues are straight, but they radiate in every direction from star-shaped squares.
• Manhattan's grid is tilted 28° east of north: the 1811 plan follows the island's axis, not true north.

How to read a rose

Each petal shows the share of street length running in one direction, in 10° steps. A street runs both ways, so the rose is symmetric: the north and south petals have the same length.

A grid draws a four-armed cross. A network with no dominant direction draws an almost round shape. Each rose has its own scale: it compares shapes, not the size of cities.

The 64 cities, from most to least ordered

1. 1. New York0.85
2. 2. Chicago0.84
3. 3. Beijing0.83
4. 4. Kyoto0.74
5. 5. San Francisco0.58
6. 6. Mexico City0.56
7. 7. Washington0.54
8. 8. Montreal0.52
9. 9. Melbourne0.41
10. 10. Buenos Aires0.36
11. 11. Barcelona0.33
12. 12. Los Angeles0.21
13. 13. Tours0.21
14. 14. Prague0.16
15. 15. Versailles0.16
16. 16. Nancy0.15
17. 17. Cape Town0.13
18. 18. Lyon0.13
19. 19. Rennes0.12
20. 20. Sydney0.12
21. 21. Munich0.12
22. 22. Athens0.11
23. 23. Stockholm0.11
24. 24. Madrid0.11
25. 25. Edinburgh0.11
26. 26. Cairo0.10
27. 27. Marseille0.10
28. 28. Singapore0.10
29. 29. La Rochelle0.09
30. 30. Marrakesh0.09
31. 31. Avignon0.08
32. 32. Saint Petersburg0.07
33. 33. Florence0.07
34. 34. Brussels0.07
35. 35. Amsterdam0.07
36. 36. London0.07
37. 37. Le Havre0.07
38. 38. Angers0.07
39. 39. Grenoble0.06
40. 40. Geneva0.06
41. 41. Reims0.05
42. 42. Paris0.05
43. 43. Lille0.05
44. 44. Rome0.05
45. 45. Lisbon0.05
46. 46. Rouen0.05
47. 47. Berlin0.05
48. 48. Dublin0.04
49. 49. Saint-Étienne0.04
50. 50. Copenhagen0.04
51. 51. Brest0.04
52. 52. Tokyo0.04
53. 53. Dijon0.03
54. 54. Istanbul0.03
55. 55. Budapest0.03
56. 56. Nantes0.03
57. 57. Nice0.03
58. 58. Venice0.02
59. 59. Bordeaux0.02
60. 60. Annecy0.02
61. 61. Montpellier0.02
62. 62. Vienna0.02
63. 63. Strasbourg0.01
64. 64. Toulouse0.01

The 25 French cities

The full ranking

Method

• Data: OpenStreetMap, read from the OpenFreeMap vector tiles (OpenMapTiles schema, zoom 13) that also draw our posters. Data version: October 11, 2026.
• Area measured: a circle of 3 km radius around each city's centre (coordinates in the CSV file), roughly what a city-centre poster frames.
• Streets counted: motorways, trunk roads, primary, secondary and tertiary roads, residential and access streets, pedestrian streets. Service roads (car parks, driveways), paths, cycleways, sidewalks, steps and railways are left out.
• Computation: each segment adds its length to the 10° bin of its bearing and to the opposite bin, 36 bins in all. The Shannon entropy of that distribution, H = −Σ pᵢ ln pᵢ, is ln 36 ≈ 3.584 when bearings are spread evenly and ln 4 ≈ 1.386 for a perfect grid. The orientation order φ = 1 − ((H − 1.386) / (3.584 − 1.386))² rescales it between 0 and 1.
• Grid rotation: the mean of the bearings multiplied by four, which folds a grid's four directions into one. It is only given for cities whose order is above 0.2: below that, there is no grid to rotate.
• Check: on five cities recomputed from the more detailed zoom 14 tiles, the orientation order moves by less than 0.005.

Differences from Geoff Boeing's study: we weight each segment by its length instead of counting segments, we measure a circle around the centre instead of the administrative boundaries, and we count pedestrian streets, which are many in old town centres.

Reference paper: Boeing, G. (2019). Urban spatial order: street network orientation, configuration, and entropy. Applied Network Science, 4(1), 67. https://doi.org/10.1007/s41109-019-0189-1

Limitations

• The result depends on the chosen centre and radius: a smaller circle around Barcelona would keep only the Eixample grid and give a higher order.
• Dual carriageways (boulevards, motorways) are counted twice, as they appear in the data.
• OpenStreetMap completeness varies by country; it is very good in the cities of this study, but not equal everywhere.

Frequently asked questions

Reusing the data

The CSV file gives, for each city, the measured centre, the street length, the entropy, the orientation order, the grid rotation and the 36 shares of the histogram.

Licence: ODbL, like OpenStreetMap. Credit "MaptoWall, Street orientation, maptowall.com/en/etude/orientation-des-rues — data © OpenStreetMap contributors".