Manhattan is the easiest big city in the world to navigate, once you understand the grid — and then there is a corner of it that is among the most confusing, for reasons that are entirely historical.

Five minutes of reading here will save you an hour of standing on a corner with a phone.

The rules

Avenues run north–south. Streets run east–west. Streets are numbered from 1st Street at the bottom of the grid, increasing as you go north to 220th at the top.

Twenty streets make a mile. A north–south block is about eighty metres. So 42nd Street to 59th Street is roughly three-quarters of a mile, or fifteen minutes at a walking pace.

Crosstown blocks are much longer — roughly three times the length of a north–south block. Walking from Fifth Avenue to Eighth Avenue on 42nd Street takes about as long as walking ten blocks north. This is the single most common misjudgement visitors make.

Fifth Avenue is the dividing line between east and west. Everything with an East prefix is east of Fifth; everything with a West prefix is west of it. East 50th Street and West 50th Street are the same street and can be a mile apart in practice.

The avenues, in order

From east to west, in most of Midtown: First, Second, Third, Lexington, Park, Madison, Fifth, Sixth, Seventh, Eighth, Ninth, Tenth, Eleventh.

Lexington, Park and Madison were inserted later, which is why the numbering skips. Park Avenue was originally Fourth Avenue and still is south of 14th Street.

Some avenues have official names nobody uses. Sixth Avenue is officially Avenue of the Americas and asking for it by that name will produce a pause. Eighth Avenue above 59th Street is Central Park West, Ninth is Columbus, Tenth is Amsterdam and Eleventh is West End. On the east side above 59th, Fourth is Park and the numbering continues.

Below Houston Street on the east side, the avenues run out of numbers and become letters — A, B, C and D — which is why that area is called Alphabet City.

Finding an address

If someone gives you “620 Fifth Avenue” with no cross street, you can work out roughly where it is, but the arithmetic is fiddly and different per avenue. In practice, always ask for the cross street. New Yorkers give addresses as “Fifth and 50th” rather than by number, and that is the useful form.

For streets, the numbering starts at Fifth Avenue and increases in both directions, roughly a hundred numbers per avenue block. So 20 West 44th Street is just west of Fifth; 350 West 44th Street is around Eighth or Ninth Avenue.

The traffic direction, which matters on foot

Most avenues are one way. As a rough rule, even-numbered avenues run downtown and odd-numbered run uptown, though there are exceptions — Park, Broadway below 59th and a few others are two-way or reversed.

Most streets alternate: even-numbered streets run east, odd-numbered run west.

This matters when you cross the road. Traffic comes from one direction only on a one-way street, and the direction is not always the one your instinct expects — particularly for visitors from countries that drive on the left.

Where the grid isn’t

Broadway cuts diagonally across everything because it follows the Wickquasgeck trail, a Lenape route that predates the Dutch by centuries. Where it crosses an avenue it produces a triangular leftover lot, which is why Times Square, Herald Square, Madison Square and the Flatiron Building exist in the shapes they do.

Everything below Houston Street predates the grid. Greenwich Village was a separate settlement that fought the plan and won, so its streets follow old lanes and property lines. This is why West 4th Street crosses West 10th, 11th, 12th and 13th Streets, which is geometrically absurd and entirely real.

Lower Manhattan follows the seventeenth-century Dutch town plan, and the street names are a map of a vanished place: Wall Street was a wall, Pearl Street was the shoreline, Broad Street was a canal, Canal Street was also a canal.

Getting lost downtown is normal. The island is narrow enough there that walking in any direction for ten minutes brings you to water.

Where it came from

The Commissioners’ Plan of 1811 laid a grid of twelve avenues and 155 streets over the whole of Manhattan north of Houston, most of which was farmland, marsh and rock at the time. It made no allowance for topography, ignored existing property lines, and set aside almost no public open space — Central Park had to be carved out later, at great expense, precisely because the plan had not left room for it.

It was criticised as brutal and unimaginative and it has proved extraordinarily durable. Every corner in Manhattan tells you exactly where you are, which no organically grown city can manage.

The practical shortcuts

Lamppost plates in Central Park carry four digits. The first two are the nearest cross street; the last two tell you which side — even is east, odd is west.

Subway station entrances are frequently direction-specific and do not connect underground. Read the sign before descending.

“Uptown” means north and “downtown” means south, always, in every context — on trains, in conversation, on signs.

The sun is a decent compass here. The avenues run roughly north-north-east, tilted about 29 degrees off true north, which is why on two evenings each May and July the setting sun lines up exactly with the crosstown streets. That is Manhattanhenge, and it is worth planning around if your dates happen to fit.