Block Weight & The 4:1 Witness Discount

Rather than executing a risky hard fork to increase the raw 1 MB block size limit, SegWit introduced a new mathematical metric called Block Weight, measured in Weight Units (WU).

By redesigning how block capacity is calculated, SegWit effectively increased Bitcoin's transaction throughput while keeping UTXO storage costs sustainable.

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⚖️ Defining Block Weight

Under SegWit rules, the strict 1,000,000-byte limit was replaced with an absolute block weight limit:

$$\text{Maximum Block Weight} = 4,000,000 \text{ WU}$$

For any transaction, its overall weight in Weight Units is calculated using a dual-factor formula:

$$\text{Transaction Weight} = (\text{Base Size} \times 3) + \text{Total Size}$$

The Variables Explained:

• Base Size (bytes): The size of the transaction excluding all witness data (metadata, inputs, outputs, amounts, and legacy scriptSigs).
• Total Size (bytes): The complete physical size of the transaction including all witness data (signatures and public keys).

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🧮 Mathematical Proof of the 4:1 Witness Discount

We can rewrite the Weight formula to isolate the non-witness bytes and the witness bytes.

Let $\text{Base}$ represent non-witness bytes, and let $\text{Witness}$ represent witness bytes. Since $\text{Total Size} = \text{Base} + \text{Witness}$:

$$\text{Weight} = (\text{Base} \times 3) + (\text{Base} + \text{Witness})$$

$$\text{Weight} = 4 \cdot \text{Base} + \text{Witness}$$

This algebraic expansion reveals the core economic engine of SegWit:

1. Every non-witness byte contributes exactly 4 Weight Units to the block capacity.
2. Every witness byte contributes only 1 Weight Unit to the block capacity.

This mathematically establishes a 4:1 witness discount. Because signatures are four times cheaper than output scripts, transactions with large signatures (such as complex multisig scripts) are heavily incentivized.

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🚀 Scaling the Virtual Block Size (vByte)

To make fee estimations consistent between legacy and SegWit transactions, wallets measure transaction sizes in Virtual Bytes (vBytes):

$$1 \text{ vByte} = 4 \text{ Weight Units}$$

$$\text{Transaction vSize} = \frac{\text{Transaction Weight}}{4}$$

📈 Real-World Capacity Limits

Because witness data occupies a substantial portion of any transaction, this discount effectively expands Bitcoin's on-chain capacity:

• Standard Tx Mix: Typically yields a virtual block size of 1.6 MB to 2.2 MB of raw transaction data.
• Extreme Witness Mix: If a block is packed with transactions containing massive witness payloads (such as large multisig spends or inscriptions), the physical block size can scale up to 4.0 MB on-chain, while still strictly satisfying the 4,000,000 WU limits!
• Legacy Node Safety: Because legacy nodes are stripped of the witness data before blocks are relayed to them, they see the block size as strictly under 1 MB, ensuring they never reject the block.