Across most of London more cafés than pubs are within a 10-minute walk - but not everywhere. Here is the map type that shows it, Your formula (map algebra: a ratio, a share or a difference), its three shapes and what it refuses.
Across most of London, more cafés than pubs are within a 10-minute walk - from Notting Hill and the West End to Holloway, Stratford and Streatham. The clear exceptions are the run of hexes just east of the center, toward Stepney, and places such as Brixton, Peckham and Wimbledon, where pubs come out ahead. One map shows it: café minus pub, worked out for every hex - one hexagon, about 350 m across.
That map is Your formula, the ninth map type. You pick two or more counts - the parts - and how to put them together - the shape: A per B, A as a share of a set or A minus B. Nothing is typed; every part comes from the same lists as every other map. GIS calls arithmetic between maps, worked out location by location, map algebra; these three shapes are its everyday results - a ratio, a share and a difference.
Your formulathe field's term: Map algebra: a ratio, a share or a difference
Café minus pub, within a 10-minute walk. Red: more cafés than pubs. Blue: more pubs than cafés. Light gray: about as many. Darker is a bigger difference. Near-black hexes have no data.
The idea, in one sentence
Pick the counts, pick the shape, and get one value per hex. Each shape answers a different question about the same two things:
A minus B
Which is there more of, and by how many? The second part taken from the first, in their own unit - places, people or m³.
A per B
How many of A for each B? The first part divided by the second, times the Number you pick: per 1, 100, 1 000, 10 000 or 100 000.
A as a share of a set
What part of the whole is A? A divided by A and up to five other parts added together, shown as a percent.
Where to click
Open the map-type picker. Your formula sits in its own group at the bottom, Put together, with the line A per B · a share of a set · A minus B and the question “What divided by, shared in, or minus what?”
Where to click
Map type
Your formula
Shape: A minus B
A: Café
B: Pub
Look at: Within a 10-minute walk
The panel for café minus pub. Each part is picked from the usual lists; the title line says the whole formula in words.
The panel has four rows, and changes with the shape:
Shape - A per B, A as a share of a set or A minus B.
The parts, A first. Their labels say what each one does: on A minus B, A: what B is taken from and B: what is taken from A; on A per B, A: what is divided and B: what A is divided by; on a share, A: the part and The set: what A is a share of, with Add a measure to the set for more.
Per, on A per B only - the Number A is counted per.
Look at - one choice for every part: Just this hex, or Within a 10-minute walk: the places you can reach on foot within 10 minutes, along streets and paths, nearer ones counting more (full weight under 3.5 min, 70% to 7 min, 40% to 10 min).
Under them, the title line reads the formula back - Café minus pub - and Clear starts again. In the app today that line also ends with a Guide link to this post; it was added after the screenshots here were taken.
Reading A minus B
A difference has a natural middle: as many of one as of the other. So the legend is built around it, as on Fair share: one color for more of A, another for more of B, and light gray between.
Three rows, in the parts' own words. The first step starts at half a place; the others are set where a quarter, half and nine tenths of the hexes with a difference fall, so every color holds part of the map.
Hover a hex and the card says the difference in words. Within a 10-minute walk nearer places count more, so a count - and a difference of two counts - comes in fractions:
A blue hex near Peckham: 3.2 fewer cafés than pubs within a 10-minute walk, once nearer ones are counted more.
A hex with neither cafés nor pubs in reach is 0 minus 0, so it reads About as many. A minus B is never adjusted for small numbers: it is a plain difference of two counts.
A per B, and the Number
Switch the shape to A per B and the same two parts become a ratio: café per pub. The Per row picks the Number A is counted per - 1, 100, 1 000, 10 000 or 100 000. Left alone, it is 1 000 when B is a census count (per 1 000 children under 10), 100 000 when B is building volume (per 100 000 m³) and 1 otherwise - one café per pub reads better than 1 000.
A per B with the Number at 1: café per pub.From 0 to 64.7 cafés per pub. The note under the bar warns that one color band spans 1.423 to 15.48 - an 11-fold range.
Café per pub, within a 10-minute walk. Most of London sits at the purple and blue end; the bright hexes are scattered, where cafés far outnumber the few pubs within reach. Gray: no pub within reach, so nothing to divide by.
That legend note is the honest lesson of every ratio: it is jumpy where B is small. With almost no pub in reach, a handful of cafés is suddenly dozens per pub; with no pub at all, there is nothing to divide by, so the ratio doesn't apply - the hex is drawn in the No data, or doesn't apply here gray. Read in Just this hex, a hex with very few of B is adjusted toward London's own ratio and the hover card says adjusted for small numbers; within a 10-minute walk the walk already pools enough places, so nothing is adjusted.
0.86 cafés per pub: fewer cafés than pubs within a 10-minute walk of this hex.
A as a share of a set
A share asks what part of a whole A makes up. Here the whole is pubs and cafés together: pub as a share of pub + café. Use Add a measure to the set to put up to five parts beside A.
A as a share of a set. The set is A plus the parts you add, so the title reads pub + café.A share runs from 0% to 100%. The colors here are cut by Equal share of hexes, so a color says how a hex ranks, not a fixed percent.
Pub as a share of pub + café, within a 10-minute walk. Inner London sits in the middle colors; the brightest and darkest hexes - mostly pubs, or mostly cafés - are mostly in outer London.54% of the pubs and cafés within a 10-minute walk of this hex are pubs.
One rule keeps a share honest: nothing in the set may be counted twice. If one of the other parts is a category that already holds A - vegan restaurant as a share of restaurant - the set is the others alone, and the title says so. If two parts sit one inside the other, the map is refused (see below). Compared with Share of its category, which always divides by a kind's own category, a set can be anything you choose - pubs and cafés belong to two different categories, Bars & Nightlife and Eat & Drink.
The math, honestly
The three shapes are one line of arithmetic each, worked out hex by hex. Here is one illustrative hex, the same two counts put together three ways:
One London hex: 12 cafés and 8 pubs within a 10-minute walk (illustrative)
Café minus pub4 more cafés than pubs
12 − 8 = +4
Café per pub (Number: 1)1.5 cafés per pub
12 ÷ 8 = 1.5
Pub as a share of pub + café40% of the set are pubs
8 ÷ 20 = 40%
Three answers, one pair of counts
+4 · 1.5 · 40%
Within a 10-minute walk each count already weighs nearer places more, so real values come with decimals. The places are those Overture Maps lists (release 2026-08-19).
Which shape to pick depends on the question. A minus B tells you how many more, so busy central hexes, with lots of both, show the biggest differences. A per B and a share tell you the balance, whatever the size, so a quiet hex with two cafés and one pub looks just like a busy one with twenty and ten.
What a part can be - and what gets refused
Every part is a count: of places (a kind, several kinds added together, or a whole category), of people (a census count, such as residents or children under 10), of building volume - or one of your data. The picker turns off what can't be one: an average or a rate is “Already a per-something number, so it can't be a part of your formula”, and anything else that isn't a count says “This isn't a count of places, people or building volume”.
The rest is checked when the map is drawn. If a formula can't be honest, the map says why instead of drawing it:
Café as a share of café + pub + bar. Pub and bar are both in the set.Pubs are already counted in bars, so the set would count every pub twice. The map refuses and says which to drop.
The other refusals, word for word as the map shows them:
A part that isn't a count - “… isn't a count of places, people or building volume, so Your formula can't use it as a part”.
The same thing on both sides - “… is on both sides, so Your formula would read the same in every hex”.
A minus B across different kinds of thing, such as cafés minus residents - “These are different kinds of numbers, so one can't be taken from the other”. A set that mixes kinds is refused the same way: they can't be added together.
Residents and residential building volume, divided either way round - the two track each other closely, “so dividing one by the other tells you nothing new”.
Your data within a 10-minute walk - “Your data is read in each hex; within a 10-minute walk isn't offered for it yet”.
Why not just use Count as?
The Amount map already divides. Its Count as row turns a count into Per 1 000 residents, Per km², Share of its category and the bases London's census publishes, such as Per 1 000 children under 10. That is a fixed list of what to divide by, chosen because each one is a sound base.
Your formula divides by anything countable: café per pub, playgrounds per 1 000 children under 10, your shops per 1 000 residents. And it does two things Count as never does - a share of a set you pick, and a difference. Where both can draw the same thing - cafés per 1 000 children under 10, say - they give the same numbers, hex for hex.
What Your formula does not do (yet)
A Your formula map can't take a Range or Only where …, can't be compared with the average and can't be tested on Clusters, and it can't be added to the Score as a factor. Standouts on A minus B rank one end only: more of A. Scout Bee can't put one together for you yet. And the parts are counts of places Overture Maps lists (release 2026-08-19) and, for people, ONS Census 2021 figures that are an estimate for each hex - a place missing from the data is missing here, and a count says nothing about how busy a place is. Treat the map as decision support, not a forecast.
Your formula puts two or more counts - the parts - together in one of three shapes; the field calls this map algebra.
A minus B: how many more of one than the other, around a middle of About as many.
A per B: a ratio, per the Number you pick - jumpy where B is small, and gray where there is none of B.
A as a share of a set: what part of a whole you choose A makes up, from 0% to 100%.
One Look at reads every part, in the hex or within a 10-minute walk.
A part must be a count, nothing is counted twice, and a refused formula says why.
Quick questions
What is Your formula?
A map type that puts two or more counts - the parts - together in one shape: A per B, A as a share of a set, or A minus B. Every part is picked from the usual lists; nothing is typed.
What can a part be?
A count of places, of people, of building volume, or one of your data. An average or a rate can't be a part, and a formula that would count something twice or mix different kinds of numbers is refused with a sentence saying why.
What is the Number on A per B?
What A is counted per: 1, 100, 1 000, 10 000 or 100 000. Left alone it is 1 000 for a census count, 100 000 for building volume and 1 otherwise.
Why are some hexes gray on A per B?
Where there is none of B there is nothing to divide by, so the ratio doesn't apply and the hex is drawn in the No data, or doesn't apply here gray. Where B is small the ratio jumps, so read the legend's note.
How is it different from Count as on the Amount map?
Count as divides by a fixed list of bases, such as Per 1 000 residents or Per km². Your formula divides by anything countable, and also draws a share of a set you pick and a difference.
See it on a real map
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