Merkle Tree Proof Size Calculator
Calculate Proof Sizes
Enter the number of transactions (for Bitcoin) or accounts (for Ethereum) to see estimated proof sizes.
Bitcoin Binary Merkle Proof
Estimated proof size: -
Based on SHA-256 hashing and binary tree structure
Ethereum Merkle-Patricia Proof
Estimated proof size: -
Based on Keccak-256 hashing and radix trie structure
Key Differences
- Binary trees rebuild entire structure on update; Merkle-Patricia trees only update affected path
- Binary tree proofs are smaller (150 bytes for 10k transactions); Merkle-Patricia proofs are larger (1-2 KB)
- Merkle-Patricia trees support exclusion proofs (proving something doesn't exist)
Bitcoin doesn’t need to know who owns what. It just needs to prove a transaction happened. Ethereum needs to know who owns what, how much, and what rules their smart contracts follow. That’s why Bitcoin uses a simple binary Merkle tree, and Ethereum uses a far more complex Merkle-Patricia tree. One isn’t better than the other-they solve completely different problems.
How Binary Merkle Trees Work in Bitcoin
Imagine you have 100 transactions in a Bitcoin block. You can’t store all of them in the block header-it’s too big. So you take each transaction, hash it with SHA-256, and pair them up. You hash each pair together. Then you take those hashes and pair them again. Keep doing this until you’re left with one final hash: the Merkle root.If even one transaction changes, even by a single bit, that Merkle root changes completely. That’s the magic. It’s like a digital fingerprint of the whole block. Light wallets, like those on your phone, don’t need to download the whole blockchain to verify a payment. They just ask a full node for the Merkle proof-a short list of hashes that connect their transaction to the root. If the math checks out, the transaction is real.
Bitcoin’s Merkle tree is binary, meaning every node has exactly two children. If you have an odd number of transactions, the last one gets duplicated. Simple. Predictable. Efficient. It’s designed for one thing: proving that a transaction was included in a block. Nothing more. And it does that better than anything else.
Why Ethereum Needs Something More
Ethereum isn’t just about sending ETH. It’s about running code-smart contracts-that change state. Your balance, your NFT ownership, your DeFi position, your token allowance-all of it is stored as data. And that data changes every few seconds. A binary Merkle tree can’t handle that.Why? Because binary trees are static. If you want to update one account’s balance, you’d have to rebuild the entire tree. That’s not feasible when millions of accounts are changing constantly. Ethereum needed a data structure that could efficiently store, update, and verify states without rebuilding everything.
Enter the Merkle-Patricia tree. It’s a hybrid: part radix trie, part Merkle tree. A radix trie is like a phonebook organized by prefixes. If you’re looking for account 0x742..., the tree follows the digits one by one-like navigating a map. This makes lookups fast, even with millions of accounts.
Each node in the Merkle-Patricia tree holds a hash of its children. Change one account? Only the path from that account to the root needs to be updated. The rest stays the same. And because it’s Merkle-secured, any change still produces a new state root-so everyone can verify the new state is legitimate.
Key Differences at a Glance
| Feature | Binary Merkle Tree | Merkle-Patricia Tree |
|---|---|---|
| Primary Use | Verifying transactions in blocks | Storing and verifying account states |
| Structure | Binary tree (two children per node) | Radix trie with Merkle hashing |
| Data Type | Fixed transactions | Dynamic key-value pairs (accounts, storage) |
| Update Efficiency | Rebuild entire tree | Update only affected path |
| Hash Function | SHA-256 | Keccak-256 (Ethereum’s hash) |
| Proof Type | Inclusion proof only | Inclusion and exclusion proofs |
| Used By | Bitcoin, Litecoin, most UTXO chains | Ethereum, Polygon, BSC, other EVM chains |
Proofs: More Than Just Verification
With a binary Merkle tree, you can only prove something exists. Did this transaction happen? Yes or no. That’s enough for Bitcoin.Ethereum needs more. It needs to prove something doesn’t exist. For example: "My balance is $0. Is that true?" Or: "This contract doesn’t have a storage slot at position 123." That’s called an exclusion proof.
Merkle-Patricia trees make exclusion proofs possible because of their trie structure. The tree has empty branches. If a key isn’t there, the path ends in a null node. That null node can be hashed and included in a proof, letting you prove something is missing. You can’t do that with a binary tree-it assumes everything is present.
Performance and Storage Trade-Offs
Binary Merkle trees are lean. A proof for a single transaction in a block of 10,000 transactions might be 150 bytes. Fast to generate. Fast to verify. Minimal bandwidth. Perfect for mobile wallets.Merkle-Patricia trees are heavier. A single state proof-say, proving your ETH balance-is often 1-2 KB. That’s because the trie path can be long, and each step needs a hash. For a state with 10 million accounts, the tree can grow to hundreds of gigabytes. That’s why Ethereum nodes need powerful hardware.
But here’s the catch: if you tried to use a binary tree for Ethereum’s state, you’d need to rebuild the entire tree every time a single account changes. That’s not just slow-it’s impossible at scale. The Merkle-Patricia tree’s efficiency in updates makes Ethereum’s entire model possible.
Implementation Difficulty
Building a binary Merkle tree? A weekend project for any developer who knows how to hash data. Bitcoin’s code is open. There are libraries in every language. You can write one in Python in under 50 lines.Merkle-Patricia trees? That’s a different level. You need to understand radix tries, nibble encoding, node compression, hash collisions, and how to handle empty branches without bloating storage. Ethereum’s implementation took years to stabilize. Even now, bugs in MPT handling have caused network upgrades to fail.
Most developers don’t build MPTs from scratch. They use libraries like Go-Ethereum’s trie package or Solidity’s built-in state management. But understanding how they work is critical for anyone building on Ethereum-especially if you’re working on Layer 2s, zk-proofs, or stateless clients.
What’s Next?
Bitcoin’s Merkle trees won’t change. They’re perfect for their job. The focus now is on making SPV proofs faster and smaller for mobile users.Ethereum is pushing hard to make Merkle-Patricia trees more efficient. The goal? Reduce storage, speed up sync times, and shrink proof sizes. Projects like stateless clients and Verkle trees (a newer alternative using polynomial commitments) are already in testing. Verkle trees could replace MPTs entirely in the next few years-offering smaller proofs and faster verification.
But for now, Merkle-Patricia trees are the engine behind every Ethereum transaction, every NFT sale, every DeFi trade. They’re the reason Ethereum can do what Bitcoin never could: run a global computer.
Frequently Asked Questions
Can Bitcoin use Merkle-Patricia trees?
Technically, yes-but it would be overkill. Bitcoin’s model relies on immutable transactions and doesn’t need to track account states. A Merkle-Patricia tree adds complexity, storage overhead, and slower verification for zero benefit. Bitcoin’s binary Merkle tree is simpler, faster, and perfectly suited to its purpose.
Why does Ethereum use Keccak-256 instead of SHA-256?
Ethereum chose Keccak-256 because it was selected as the SHA-3 standard by NIST in 2015. It’s faster in software implementations and offers better resistance to certain cryptographic attacks compared to SHA-256. It’s also the hash used throughout Ethereum’s stack-from transaction signing to smart contract execution. Consistency matters.
Do all blockchains use one or the other?
Most fall into one camp. UTXO-based chains like Bitcoin, Litecoin, and Dash use binary Merkle trees. Account-based chains like Ethereum, Solana, and Avalanche use variations of Merkle-Patricia trees or similar trie structures. Some newer chains experiment with alternatives like Verkle trees or hash graphs, but these two remain the dominant models.
Can I verify my Ethereum balance without downloading the whole chain?
Yes, but it’s more complex than Bitcoin’s SPV. You need a full node or a trusted provider to give you a Merkle-Patricia proof of your account state. Lightweight wallets like MetaMask rely on third-party nodes for this. True stateless verification-where you verify proofs yourself with minimal data-is still experimental and not yet mainstream.
What’s the difference between a Merkle tree and a Patricia tree?
A Merkle tree is a cryptographic structure that hashes data up to a root for verification. A Patricia tree (or radix trie) is a data structure optimized for key-based lookups using prefixes. A Merkle-Patricia tree combines both: it uses the Patricia trie’s structure to organize key-value pairs, then hashes each node to create a Merkle root. One handles organization, the other handles security.
There are 21 Comments
Clarice Coelho Marlière Arruda
so like... bitcoin is just a fancy ledger, and ethereum is like a whole computer? that makes so much sense now. i always thought they were just different coins, not totally different beasts.
Brian Collett
the fact that bitcoin's tree is so simple is why it's so damn secure. no fancy optimizations, no edge cases, just hash everything and trust the math. sometimes simple is the most powerful.
Allison Andrews
the exclusion proof concept blew my mind. it's not just about proving something exists-it's about proving it doesn't. that's philosophical in a cryptographic way.
Wayne Overton
ethereum is overengineered
Alisa Rosner
OMG YES!! 🙌 The Merkle-Patricia tree is like a super-smart filing cabinet 🗂️-you don't have to reorganize the whole drawer just to move one paper! So elegant! 🤯
MICHELLE SANTOYO
they say 'different tools for different jobs' but honestly? Ethereum is just trying to be everything and ending up as a bloated mess. Bitcoin knew its lane and stayed in it. 🤷♀️
Lena Novikova
you people don't get it-Bitcoin's simplicity is why it's still alive. Ethereum's tree is a nightmare to debug and costs millions in gas every time someone messes up a storage slot. We're paying for complexity
Olav Hans-Ols
really appreciate this breakdown. i used to think all blockchains were just different flavors of the same thing. now i see it's like comparing a bicycle to a hybrid car-same goal, totally different engineering.
Kevin Johnston
🔥 This is the best explanation I've ever read! Ethereum's MPT is like a living organism that grows and adapts. Bitcoin's tree? A rock-solid statue. Both beautiful in their own way! 🙏
Dr. Monica Ellis-Blied
It is imperative to recognize that the architectural divergence between these two systems reflects not merely technical preference, but fundamentally distinct ontological commitments to decentralization, verifiability, and scalability. The binary Merkle tree upholds absolute immutability; the Merkle-Patricia tree enables dynamic, stateful computation-thereby redefining the very nature of consensus.
Herbert Ruiz
Bitcoin doesn't need this. End of story.
Frech Patz
Is there any research on how Merkle-Patricia trees scale under 100M+ accounts? I've heard the storage overhead becomes prohibitive even on enterprise nodes.
Rosanna Gulisano
Verkle trees are the future and you all are clinging to relics
Sheetal Tolambe
So cool to see how different cultures of blockchain evolved. Bitcoin = minimalist, Ethereum = maximalist. Both brilliant in their own way. India is watching this closely for our own digital rupee design!
gurmukh bhambra
you think this is about tech? nah. this is about who controls the ledger. mpt lets them freeze accounts. binary tree? no one can touch your coins. this is surveillance vs freedom.
Sunny Kashyap
ethereum is just a scam. bitcoin is real money. why do you waste time on this? go work
james mason
Let’s be honest-Merkle-Patricia trees are the reason Ethereum can’t scale. It’s not the gas fees. It’s the data structure. Anyone who thinks this is ‘innovation’ is confusing complexity with sophistication.
Anna Mitchell
thank you for writing this. i’ve been trying to understand the difference for months. now it just clicks.
Pranav Shimpi
you missed one thing-MPT's nibble encoding is why it's so hard to implement right. i tried building one in rust and spent 3 weeks debugging a single null node bug. it's not for beginners.
jummy santh
As a Nigerian developer who has worked with both systems in fintech applications, I must say that Bitcoin's binary Merkle tree is a masterpiece of restraint. In regions with unreliable infrastructure, simplicity is not a limitation-it is survival. Ethereum’s state tree, while powerful, demands bandwidth and compute power that many of our communities simply do not possess. This is not a critique of Ethereum, but a celebration of Bitcoin’s humility in design.
Kirsten McCallum
Bitcoin’s tree is elegant. Ethereum’s is a Rube Goldberg machine built by engineers who thought ‘more features’ meant ‘better.’
Write a comment
Your email address will not be published. Required fields are marked *