https://www.johndcook.com/blog/2025/10/31/smaller-qr-codes/

John D. Cook
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Text case changes the size of QR codes

Posted on 31 October 2025 by John

Let's make a QR code out of a sentence two ways: mixed case and upper
case. We'll use Python with the qrcode library.

>>> import qrcode
>>> s = "The quick brown fox jumps over the lazy dog."
>>> qrcode.make(s).save("mixed.png")
>>> qrcode.make(s.upper()).save("upper.png")

Here are the mixed case and upper case QR codes.

[qr_mixed_upper]

The QR code creation algorithm interprets the mixed case sentence as
binary data but it interprets the upper case sentence as alphanumeric
data.

Alphanumeric data, in the context of QR codes, comes from the
following alphabet of 45 characters:

0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:

Since 452 = 2025 < 2048 = 2^11 two alphanumeric characters can be
encoded in 11 bits. If text contains a single character outside this
alphabet, such as a lower case letter, then the text is encoded as
ISO/IEC 8859-1 using 8 bits per character.

Switching from mixed-case text to upper case text reduces the bits
per character from 8 to 5.5, and so we should expect the resulting QR
code to require about 30% fewer pixels. In the example above we go
from a 33 x 33 grid down to a 29 x 29 grid, from 1089 pixels to 841.

Application to Bitcoin addressess

Bech32 encoding uses an alphabet of 32 characters while Base58
encoding uses an alphabet of 58 characters, and so the former needs
about 17% more characters to represent the same data. But Bech32 uses
a monocase alphabet, and base 58 does not, and so Bech32 encoding
requires fewer QR code pixels to represent the same data as Base58
encoding.

(Bech32 encoding uses a lower case alphabet, but the letters are
converted to upper case before creating QR codes.)

Related posts

  * Base 32 and Base 64 encoding
  * Two meanings of QR code
  * Dithered QR codes

Categories : Math
Tags : Coding theory Cryptocurrency
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John D. Cook

John D. Cook, PhD

My colleagues and I have decades of consulting experience helping
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John D. Cook

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