# Mask patterns 0 to 7 — the eight formulas and why they exist

> A QR code's data region is XORed with one of eight mask patterns, chosen to avoid misleading shapes: large same-colour areas, poor dark-light balance, and runs that mimic the finder patterns' 1:1:3:1:1 signature. The masks are fixed formulas over row and column, and the chosen one is recorded in the format information.

Source: https://useqr.app/docs/spec/mask-patterns-0-to-7 · Last reviewed 2026-08-21 · UseQR is free forever, MIT licensed, no signup.

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## Why masking exists

Data is arbitrary, and arbitrary data sometimes draws exactly what a scanner must not see:
a solid dark slab that swallows the local threshold, a checkerboard-free expanse with no
edges to lock onto, or — worst — a run of modules in the **1:1:3:1:1 ratio that imitates a
[finder pattern](/docs/spec/finder-patterns)** and sends the detector chasing a false
corner. An unmasked symbol would scan well for some payloads and terribly for others,
with the difference invisible to the person generating it.

[Masking](/glossary/mask-pattern) fixes the distribution, not the data: XOR the data
region with a fixed, decoder-known pattern so the *printed* modules look statistically
tame whatever the payload. XOR is self-inverse, so the decoder applies the same pattern
once more and the original bits fall out. Nothing is encrypted, nothing is lost.

## The eight formulas

For a module at row *i*, column *j* (counted from 0, top-left), the module is **flipped**
when the condition holds:

| Mask | Condition | Visual character |
|---|---|---|
| 0 | (i + j) mod 2 = 0 | Checkerboard |
| 1 | i mod 2 = 0 | Horizontal stripes |
| 2 | j mod 3 = 0 | Vertical bars, every third column |
| 3 | (i + j) mod 3 = 0 | Diagonal stripes |
| 4 | (⌊i/2⌋ + ⌊j/3⌋) mod 2 = 0 | Coarse brick pattern |
| 5 | (i·j) mod 2 + (i·j) mod 3 = 0 | Grid lattice |
| 6 | ((i·j) mod 2 + (i·j) mod 3) mod 2 = 0 | Dense weave |
| 7 | ((i+j) mod 2 + (i·j) mod 3) mod 2 = 0 | Diagonal lattice |

Two rules govern their application:

- **Only the data and error-correction region is masked.** Function patterns — finders,
  separators, [timing](/docs/spec/timing-patterns), alignment — and the
  format/version fields are never touched; their geometry *is* the specification.
- **Exactly one mask covers the whole symbol.** The 3-bit mask number is stored in the
  [format information](/docs/spec/format-information), read before any data, so the
  decoder knows precisely what to undo.

## How one is chosen

The encoder is supposed to render the symbol all eight ways and score each with four
[penalty rules](/docs/spec/mask-selection-penalty-scores) measuring runs, blocks,
finder-lookalikes and dark/light imbalance; the lowest total wins. Because the choice
depends on the payload, the same data at the same version can legitimately wear different
masks from different generators — the main reason
[two tools produce different-looking codes](/docs/spec/why-two-generators-produce-different-codes)
for identical input. Any of the eight is *valid*; the scoring only optimises scannability.

Decoders do not care which mask was picked — they read the mask number from the format
bits and un-XOR. A "wrong" (suboptimally chosen) mask costs scan robustness at the
margins, not correctness. This is also why hand-rolled encoders that hard-code mask 0
still produce working codes, and why you should judge any generator by whether its output
[decodes cleanly under stress](/validate) rather than by which patterns it favours.

## FAQ

### What is a mask pattern in a QR code?
One of eight fixed XOR patterns applied to the data region so the printed modules avoid problem shapes — big same-colour areas, imbalance, and runs that imitate finder patterns. The decoder reads the mask number from the format information and reverses it.

### Why are there exactly eight mask patterns?
The standard defines eight formulas — enough variety that at least one scores well on any payload, while the mask number still fits in the 3 bits reserved for it in the format information.

### Does masking encrypt the QR code data?
No. Masking is a reversible XOR with a public, standardised pattern, applied purely to improve scannability. Anyone decoding the symbol removes it mechanically; it provides zero secrecy.

### Are the finder patterns masked too?
No. Masking applies only to the data and error-correction region. Finder, separator, timing and alignment patterns, plus the format and version fields, keep their fixed appearance — that fixedness is what scanners rely on.

## Try it

- https://useqr.app/url
- https://useqr.app/validate
- https://useqr.app/scan