Round QR codes with logos — the centre size math

A round QR code with a logo in the centre is two design choices stacked on top of each other, and each one quietly spends the same budget. Round modules already give up about 22% of the area their square counterparts fill. The centre logo then eats further into the same error-correction pool the round modules already drained. Push both at once without doing the math and you get a code that previews beautifully and fails on the bus stop.

This post is the math for that specific case: how big a round QR code with logo center can actually be, why the safe ceiling is lower than the equivalent square code, and the small set of rules that separate a code that always scans from one that mostly does. By the end you should be able to look at a round-modules-plus-logo proof and know whether it will survive print before you spend a printer dollar.

What round modules cost before the logo arrives#

Every QR code is a square grid first, a graphic second. The decoder samples the centre of each grid cell and asks one question: darker or lighter than the threshold? The shape of the cell — square, round, rounded-square — is purely cosmetic to that sampling step. The round-modules primer walks through this in detail; the short version is that a circle inscribed inside a 1×1 square covers π/4 of the square, which is 78.5%. Twenty-one and a half percent of every dark cell is now white space the cell would otherwise have filled.

That missing area matters in two places. First, the boundary between adjacent dark cells weakens. Two black squares share a full edge; two black circles touch at a single point. In dim light, with a phone held at 30cm, the decoder's contrast threshold can fall the wrong side of that point and read a chain of dark modules as several smaller blobs separated by white. Second — and this is the part most "logo with rounded QR" guides skip — the missing area lives on the error-correction side of the ledger before any logo is added. Round-module renderers that don't compensate are shipping codes that scan with measurably less headroom than the square version of the same payload, full stop.

The fix used by serious round-QR generators is oversizing — drawing each round module at roughly 105% of the cell width so circles overlap slightly at the edges. That recovers most of the lost contrast at the boundaries without disturbing the centre-sample geometry. The shootout in the round QR generator comparison walks through eight tools and which ones bother to oversize; about half don't. The half that don't will silently break your code the moment you add a logo, because the budget the logo is supposed to spend is already half-spent.

Why the centre logo math changes#

The logo size math for square QR codes lands at four practical ceilings — about 4–5% logo coverage at level L, 9–10% at M, 14–17% at Q, and 18–22% at H — assuming the worst-case headroom factor most studios use in print work. Those numbers already discount roughly a third of the error-correction budget for print drift, fingerprints, and bad light. They assume the module shape is square.

For round modules, the ceiling has to come down. The reasoning isn't a separate math model — it's the same Reed-Solomon decoder, the same ISO 18004 error-correction levels, the same percentage budget — but the round module shape spends part of the budget before the logo gets handed any. Two adjustments stack on top of each other, and the conservative move is to apply both.

The first adjustment is the boundary-contrast tax. Even with oversizing, round modules sit at the boundary between "definitely dark" and "ambiguous in dim light" more often than squares. The decoder spends some of the error-correction symbols just to clean up the noise from misread cells around the edges of dark regions. Roughly 2–3% of the redundancy at any EC level goes to that work in conditions where a square code would have spent zero. The second adjustment is the centre-logo overlap. Where the logo sits, the modules underneath are unreadable. With round modules at default size, the logo's actual coverage of the data area is slightly larger than its visible footprint suggests, because the white space around each round module gets absorbed into the logo's hit zone.

The practical ceilings, then, look like this:

• Level L (7% budget): 2–3%. A speck. Don't bother.
• Level M (15%): 6–8%. A small monogram or icon, no text.
• Level Q (25%): 11–14%. A typical logomark, no descender.
• Level H (30%): 14–18%. A logomark with a thin line of text, or a chunky monogram with breathing room.

These are roughly 70–80% of the square ceilings at the same level. That's the round-modules tax, paid up front. If a generator is letting you push the logo to 25% of a level-H round-modules code, it's selling you a code that scans at 5cm and misses at 30cm.

Step up an EC level and you reclaim a chunk of that ceiling, but a higher level also adds more modules to the code overall. At L a typical URL fits in 25×25 modules; at H the same URL needs 33×33 or more. Smaller modules at the same print size means less margin for the printer's dot gain, and a round-modules code at H printed on uncoated stock can lose to a round-modules code at Q printed on a coated proof, even with a smaller logo on the Q version. The error-correction primer covers the level-versus-print-size trade in detail. For round modules with a logo, the working rule is: H is the floor, not the ceiling. Use it.

The logo size calculator (round modules)#

Knowing the numbers is one thing; running them on your specific case is another. Drop your QR's module count and the logo footprint into the calculator below and it returns the effective budget left, the safe coverage ceiling, and a verdict.

Why most round-QR-with-logo generators get this wrong#

Three failure modes show up consistently across the tools that claim to ship round QR codes with logos. None of them are visible in the preview; all of them break print.

They don't oversize the round modules. The default circle inscribed in the cell drops to 78% coverage and stays there. The code scans fine on the bright preview screen because the camera's auto-exposure adjusts to the contrast it has. Print the same code at 25mm on uncoated stock, hand it to someone whose phone is two years old in a café with warm-tone lighting, and the contrast collapses. The fix is one parameter — module radius — and tools that don't expose it are either built on top of an old library or were never tested against print.

They cap the logo at the square ceiling, not the round one. Most generators that respect the error-correction budget at all do so by capping logo size at some fraction of the level's nominal budget — typically two thirds. They apply the same cap to square and round outputs. For round outputs that cap is too high, by the boundary-contrast tax described above. A 22% logo at level H on a square code scrapes through; the same logo on round modules at the same level fails about a third of the time in field conditions.

They round the finder patterns. Each QR code has three large finder patterns in the corners — the 7×7 nested-square structure the decoder uses to locate, align, and rotate the code. ISO 18004 defines those patterns specifically. The decoder looks for the dark-light-dark-light-dark ratio of 1:1:3:1:1 across each pattern, and "near-square" implementations get away with rounded outer edges. Implementations that draw the finders as concentric circles or with deeply curved corners trip Apple's stricter Camera-app decoder on iOS 15 and later — about 60% of the iPhone-using world is now on iOS 15+. The code looks balanced and modern in the preview and refuses to scan on more than half of the phones that pick it up. The round-QR generator comparison lists which tools commit which of these three sins; the free QR code generator avoids all three by default and the QR codes doc page covers how the error-correction control sits inside an account.

The decision sequence — round modules, centred logo#

A reliable round QR code with a logo in the centre comes out of four decisions, in order. Skip any one and the code drifts toward "scans on screen, fails on paper".

1. Pick H, not lower. Round modules eat enough of the budget on their own that L and M leave too little for the logo. Q works in controlled print conditions on coated stock. H is the safe default. Yes, this adds modules to the code and shrinks each module at the same physical size; the way to recover that is print size, not lower EC. A round-modules H code at 30mm beats the same code at 20mm every time.
2. Confirm the generator oversizes the round modules. Inspect the preview at 4× zoom. Round modules should very slightly touch their neighbours, not sit isolated with a clear ring of white around each. If the generator doesn't expose a module-radius or oversize control, assume it doesn't oversize and find a different tool. The tools shootout lists which ones do.
3. Cap the logo at the round ceiling — not the square one. Use the calculator above. For a level-H code with 5% oversizing, the safe ceiling lands around 14–18% logo coverage. Below 14% you have room to spare; between 14 and 18 you're at the edge; above 18 you're betting against your printer.
4. Test on the actual paper at the actual size. Run a one-page proof on the actual stock and scan it from 30cm with the lowest-end Android phone you can find. A code that scans on a four-year-old Android in a coffee shop will scan everywhere else. If the proof needs two attempts, the production run will need three.

The eye-shape gotcha#

Round modules and rounded eyes are two different decisions. Most "round" generators ship one option that does both — the round dots, the rounded finder patterns. That setting is also the one that most often breaks Apple's stricter decoder, because rounding the finder patterns is what fails the 1:1:3:1:1 ratio check.

The fix is to set eye/finder shape separately from module shape. Use rounded squares (gently rounded corners, not circles) for the finders; use round for the modules. The visual difference between "rounded-square finders + round modules" and "round finders + round modules" is small — the first reads as a coherent friendly QR, the second reads as a graphic designer's experiment. The scan rate on the first is comparable to a square QR; the scan rate on the second drops by 30–50% depending on the phone.

Field-test checklist#

The lab numbers above are the entry ticket. Field testing is what tells you whether your specific code will hold up. Tick each item once you've actually done it; the verdict updates as you go.

Examples — what a clean round QR with logo looks like#

The grid above is a live render of admin-curated round-modules QR designs. The ones with logos sit inside the safe ceilings the calculator returns; the centre logo never crosses 18% on any of them. Use them as the visual reference for what your own code should look like at the proof stage. If your design pushes the logo larger or rounds the finders, you've already drifted from the working examples.

Frequently asked questions#