How big is a square?

TLDR: they’re about a mile wide.

The squares (or tiles to use the usual term in mapping software) that are imported into VeloViewer are the “level 14” tiles from the OpenStreetMap  . To get to level 14, you start at level 0 which is one tile representing the whole world. You then zoom in to split that tile into 4 equal-sized tiles, each with a side half the length of the first tile. This gets you level 1. Then you zoom in again splitting those four tiles into four tiles each, making a total of 16 tiles covering the whole world at level 2, each with a length of a quarter of the length of the original. Do this splitting procedure 12 more times and you get 4 to the power 14 tiles (268,435,456 tiles) covering the world. The length of the tile is half each time.

This means, at the equator, the size of a tile S = (circumference of the earth)/2^14.

But I don’t ride at the equator, as we get further away from there, the tiles get smaller as they head towards the North Pole, where they vanish to nothing. In fact the formula for the width of the tile harks back to school and trigonometry:

Size = Circumference of Earth * cos(latitude) / 2^14
     = 40,075km * cos(51.5 degrees) / 16,384
     = 1.523km
     = 0.95 miles.

But it’s best just to say “about a mile”.

Edited to add: OpenStreetMap has a page all about zoom levels


Ride report: Goring north

As the nearest unfilled squares are 25 miles away as the crow flies, my old habit of starting and ending my rides at home is becoming more and more of a problem. I would put a “one new square” ride into the route planner, and it would come back at me with 100km ride. That’s sort of fine, but my boys are growing up and having more and more activities to go to… my long-suffering but enormously patient wife wants me home sometimes.

The solution is to head out on a train somewhere and then ride home. Even with Britain’s notorious public transport system this is usually a little quicker than me riding. This weekend though I was blocked in almost all directions – engineering works into London, and on the lines out of Woking down to Petersfield and Basingstoke meant the ONLY option was to head to Reading. [Bikes are not allowed on replacement bus services].

The route out of Reading took me over the river and onto the A4074 which heads up straight up a 13%-in-places lump called St. Peters. Hill. I got to the top without being passed by a car and thought wow I must be in good form if the cars aren’t squeezing past me in frustration. Turns out the lady behind was just incredibly patient, so I gave her the thumbs up as she finally passed as part of my resolution to thank the nice drivers rather than just bawl at the usual ones. She burst out laughing.

Anyway I soon turned off down the nice roads over to Goring – no surprise someone has put the whole 7.7 miles as a segment – the final stretch is a sharp descent with twists and turns so never in month of Sundays am I going to get close to the top-end, being the lily-livered descender that I am.

Heading north out of Goring, still on the east of the Thames I bag the first new square of the day at 12 miles. Wedged as I am between the western end of the Chilterns and the river, I have high hopes for a great clear November view. Sadly as I turn east at South Stoke I realise it is fairly featureless farmland and, more importantly, the wind is actually a fairly strongly easterly and I am 30 miles due west of home. Damn those trains forcing me to Reading! About five minutes later the puncture fairy visited AGAIN. Inner strength, rule 5, blah blah blah.

The alignment of roads and squares turns out not to be so good here and I have to execute three “nubbins” at Ipsden, Well Place and somewhere in the middle of nowhere to get all the missing squares. Heading east of Ewelme I pick up square 9 of the day and immediately hit the Chilterns Wall. From Wallingford to Princes Risborough there must be about 20 roads heading up this ridge. And the only one that doesn’t get above 10% for a sustained period is the M40, where the motorway builders just cut straightforward. Looking at VeloViewer, I think the route up to Cookley Green (Swyncombe Hill) was my 10th different route up. Road was pretty good, but had high hedgerows spoiling the view. Inevitably, after a few miles of empty road, a car trailed inches from by back wheel, and shoved me off the road to the extent I put a foot down :/. No thumbs up to him..

At the top of the hill I swing back round again to get square 10. This has no public roads, being dominated by the former site of Ewelme Park (a royal hunting ground on ground original owned by Geoffrey Chaucer’s son). I didn’t quite establish if the current Ewelme Park House is ever open to the public, but fortunately its fine main entrance road is a bridleway, so I happily cycled down it to get into the square.

All new squares backed, after an aboutturn I was soon back on familiar roads. I joined the main Henley-Oxford at Nettlebed and despite going what I thought was quite fast on the lovely descent, my 23.8mph average for this segment still puts me at 3483rd out of 4490. I can blame the headwind, but I really am a lousy descender.

From there it was my standard back from Henley – up Remenham Hill (no PR, damn my fit self from last Summer), then through Cockpole Green (dammit, I still smile every time), Warrens Row and White Waltham before hitting Drift Road. 14.21 for the Drift Road segment against a PR of 11.26… really must mumble something about a headwind.

Strava :

New squares: 10

Minimum squares for project 50: 211

Where can you cycle?

Tips and links for figuring how to fill a tile:

  • Get the VeloViewer Strava plugin for Chrome ( ). Among many snazzy features, this plugin allows you to overlay your completed squares when designing routes in the Strava RouteBuilder.
  • Big caveat! RouteBuilder and the other mapping sites such as RideWithGPS and GarminConnect do not always “know” which roads are private.
  • A good first approximation is use Google StreetView. If the StreetView car has been down a road, it is very likely to be a public road and also suitable road bikes.
  • In my area of the world, this simple approach gets me to about 90% of squares. But all is not lost! Just because a road is not open to public motor traffic, it may open as a bridleway. Google Maps and Open Street Map are not particularly good at marking bridleways. The OS maps are better but chargeable (spend £4 for one month and build a bank of routes to keep you going?). However most county councils will keep a copy of their “definitive map” of rights of way online


  • Remember it is legal to cycle on bridleways, restricted by-ways and ‘BOATs’ – ‘byways open to all traffic’. It is not legal to cycle on footpaths. I would like to know if there is ambiguity or problem in wheeling a bicycle along a footpath – there are some squares where I fear I need to do this!
  • For roads that are not public roads but are public bridleways, you often see signs saying simply “private” and you might fear that you are trespassing. In the cases where there is a public bridleway, you are not – some landowners simply don’t like to make it too obvious there is a public right of way for walkers, horse-riders and cyclists over their land. I have taken to printing out copies of the “definitive map” and bringing them on rides; just in case I get into a “discussion” with someone I meet out there – I want to prove that I made a good faith effort to stay on permitted routes.

I’m not sure ramblers tend to like cyclists all that much (gross generalisation!) but in many ways we share a common cause in being aware of and exercising our rights. Their rights of way FAQ is handy. Question 11 is about cycling – note it states that a cyclist cycling on the pavement (footway) can be fined on the spot thanks to the Fixed Penalty Offences Order 1999. As far as I know this is still true – even though Robert Goodwill (Transport Minister with responsibility for cycling) re-iterated in 2014 that cyclists should not be fined “to escape dangerous sections of road” – Telegraph article


One set of squares I have visited many many times are those on my commute from the north-west corner of Surrey to the centre of London. The route takes me to Staines, then along the A30 as far  the Clockhouse Roundabout at Bedfont and I then follow the A315 through Hounslow, Isleworth, Brentford, Chiswick and Kensington before heading along South Carriage Drive, around Hyde Park Corner, past Buckingham Palace, around Trafalgar Square before joining the East-West Superhighway at the Hungerford Bridge. [*]

I.e. my commute is exactly along the route on which Cycling Superhighway 9, first proposed in 2010, is supposed to be built. The route was kicked into the long grass in 2013, but as of 2016 the new Sadiq Kahn administration has announced a new consultation.

This is mostly good, but they aren’t even going to try to convince the good Tory councillors that it would be make sense for CS9 to join up to the EWSH at Hyde Park. Instead the consultation will be on a route from Olympia (at the western edge of K&C) down to Hounslow. On the upside, this consultation has some hope of succeeding – the consultation on a two-way cycle track on the north side of the Hammersmith gyratory has already gone through). On the downside, it is pretty horrible that we would end up forcing cyclists through the black hole of Kensington High Street – a mile long stretch of road where there have been at least 94 accidents in the last four years – search for yourself at – and which is a nightmare for cyclists especially at rush hour.

In letters obtained by AlexInTheCities, RBKC councillors said

  • “ our biggest concern [about CS9 on KHS] is that it would change quite fundamentally the experience of using the street for pedestrians. Pedestrians value the ability to cross the High Street at virtually any point along its length, by taking advantage of the central reservation strip”

The idea that this road is somehow pleasant for pedestrians at the moment is totally laughable. The road is full of hard-accelerating vans, buses, lorries, taxis, Ubers, and Kensington folk in their Land Rovers and Mercs as well as cyclists. Motorists by turns gaze down at their phones, jump out of side roads and accelerate through as the lights turn green.

Such a shame that dysfunctional government between this borough and the Mayor of London/TfL is going to people in danger for years to come.


[*] It’s 24 miles and normally takes me about 85 minutes in the rush hour (I still don’t fully understand how I got my PB of 65 minutes, though the fact it was at 5am with a gale force tailwind partially explains it)

Analysing the squares yourself

To get hold of the raw what-squares-have-I-visited data, I open the Veloviewer summary page in Google Chrome and press Ctrl+Shift+I to switch to developer mode. Then type copy(d3.values(explorerTiles)) to copy the data to the clipboard. Copy it into a text editor – it is pretty self-explanatory JSON format.

Lots of other data is available this way – not just the explorerSquares variable.

Once you have copied the JSON the attached Python script (unfortunately saved as .doc due to a WordPress limitation) will do a bit of analysis on it. You will probably want to mess with the last three lines of the script

  • filename – the path where you saved the JSON down to
  • The last two arguments to parse_visited_squares – these are the co-ordinates of the square you want to define as your origin. I have chosen 8146,5439 which is the top-left of my current square in the Chilterns, Oxfordshire, UK.
  • The last argument to number_to_complete. This is the biggest square you want to analyse. It should be bigger than the biggest square you have down so far. I chosen 50.


Output looks like a bit like this:

For N=39 the square with top-left at (0, 0) is complete!
For N=40 the square with top-left at (0, 0) is complete!
For N=41 the minimal solution needs 7 squares to be visited
The top left square must be (-2, -1) and the following squares are needed:
 (3, -1)
 (33, -1)
 (34, -1)
 (35, -1)
 (36, -1)
 (37, -1)
 (38, -1)
For N=42 the minimal solution needs 15 squares to be visited
The top left square must be (-2, -2) and the following squares are needed:
 (3, -1)
 (33, -2)
 (33, -1)
 (34, -2)
 (34, -1)
 (35, -2)
 (35, -1)
 (36, -2)
 (36, -1)
 (37, -2)
 (37, -1)
 (38, -2)
 (38, -1)
 (39, -2)
 (39, -1)


Explorer square links

Collected links for square exploring

About this

I am a nerdish type who likes riding my bike. Things like Strava and its spin-off VeloViewer are perfect for me. Spend all morning riding a bike and then all afternoon looking how far I went, how slowly, had I been there before, how many feet I did climb before my heart rate hit 180bpm etc etc.

I also one of those “ticker” or “collector” types who can’t help but make lists of things to complete and then try to complete them (I blame my Dad who climbed all of the “Wainwrights” in the Lake District and charted his progress for years on the kitchen wall).

When Ben Lowe of Veloviewer introduced the “max explorer” square to Veloviewer, I knew I had found my “Wainwrights”. Whenever I upload a ride to Strava, Veloviewer detects whether I have been in any new Google maps squares and paints them green in the “activities” window. And if I have been to all the squares that make up a big square of squares, it surrounds that square in blue. The size of that big blue square is my max explorer square. As I write, mine is 26×26:

ExplorerSquareFeb16To really fuel my dorkish listish tickish desire, Ben also puts together a global leaderboard of the squares with the biggest blue squares. At the time of writing I’m sixth, stranded behind four Belgians and an American. This blog tracks all the muddy fields and dead end roads I’ve cycled up to try to beat the four Belgians and an American.