Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Students · Huffman Coding

Huffman Coding for a Merkle tree

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a Merkle tree live below — adjust the inputs and watch it respond, right in your browser.

Huffman CodingLive

optimal lossless compression

Codebook (shorter = more frequent)

×5

1 bit

×1

100

3 bit

×1

101

3 bit

×2

110

3 bit

×2

111

3 bit

Controls

Text to compress

Huffman coding gives frequent symbols short codes and rare ones long codes, minimizing the total bits — the optimal prefix code. It builds a tree by repeatedly merging the two least frequent nodes, so no code is a prefix of another and decoding is unambiguous. It is the compression step inside ZIP, JPEG, MP3, and countless file formats.

▶ Run in Python

Data Inspector

Symbols5

Huffman bits23

Fixed-length bits33

Compression70%

Governing equation

L = i \sum p_{i} ℓ_{i} = 2.09 bits/sym \geq H = - i \sum p_{i} lo g_{2} p_{i}

Reading this result: Huffman packs this text into 23 bits versus 33 fixed-length — a 30% saving, earned by giving the most frequent symbol (a, ×5) the shortest code.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders General version →

More with Huffman Coding

Huffman Coding for an RSA key Huffman Coding for a password hash Huffman Coding for a digital signature Huffman Coding for a Diffie-Hellman exchange Huffman Coding for a block cipher Huffman Coding for a hash collision Huffman Coding for a one-time pad Huffman Coding for a Caesar cipher

Frequently asked questions

Is this good for students?: Yes — this version of "Huffman Coding for a Merkle tree" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.