Formula & Calculator
Seed Phrase Entropy
Calculates the cryptographic security strength of a wallet recovery seed phrase based on its word count and the size of the wordlist used.
Interpretation
Entropy (bits) = Number of Words × log₂(Wordlist Size). The security of a seed phrase in bits. Used to assess wallet security.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Entropy | Seed phrase entropy | bits |
| Number of Words | Number of words in the seed phrase | |
| Wordlist Size | Size of the standard wordlist (BIP-39 = 2048) |
What it means
Seed phrases (mnemonic) are used to generate private keys. The entropy is the number of possible combinations. For BIP‑39, a 12‑word phrase from a 2048‑word list gives 128 bits of entropy. This is used to evaluate the security of a wallet. Understanding entropy helps users choose secure seed lengths and to avoid insecure wallets.
Worked example
Seed Phrase Entropy – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Word Count | 12 |
| Wordlist Size | 2048 |
| Parameter | Value |
|---|---|
| Words | 24 |
| Wordlist | 2048 |
Common mistakes
- Seed phrase entropy: Number of words × log₂(wordlist size).
- BIP‑39: Standard wordlist size is 2048 (2^11).
- Entropy: 12 words ≈ 128 bits; 24 words ≈ 256 bits.
- Security: Higher entropy means stronger protection.
Applications
Seed phrase entropy measures the security strength of a recovery seed phrase by multiplying the number of words by the log₂ of the wordlist size. This indicates the number of possible combinations and the difficulty of brute‑forcing. Higher entropy means stronger security. Users and wallet providers use this to assess the safety of their seed phrases. Understanding entropy is crucial for wallet security.
- Assessing the security of a seed phrase
- Choosing the appropriate number of words (12, 24)
- Understanding the risk of brute‑force attacks
- Security education for crypto users
- Educational understanding of cryptographic entropy
Frequently Asked Questions
Entropy = Number of Words × log2(Wordlist Size). For a 12-word BIP-39 seed with a 2048-word list, entropy = 12 × 11 = 132 bits (though the actual entropy is 128 bits due to checksum). This indicates the brute-force resistance.
128 bits of entropy is considered secure against any feasible brute-force attack with current technology. It would take billions of years to crack with existing computational power.
A 24-word phrase has 256 bits of entropy, which is even more secure. However, 128 bits is already secure, so the main advantage is future-proofing against quantum computers.
It is more secure, but it is also longer and more cumbersome to store and enter. For most users, 12 words are sufficient. The choice depends on your risk tolerance.
It is not recommended because humans are bad at generating randomness. Always use a wallet that generates a cryptographically secure seed phrase.
Never store it digitally. Write it down on paper or metal and store it in a secure location (e.g., a safe). Consider splitting it into multiple parts for redundancy.
The checksum is a small part of the seed phrase that validates the phrase's integrity. It reduces the effective entropy slightly (e.g., from 132 bits to 128 bits for a 12-word phrase).
The probability of two people generating the same seed phrase is astronomically low due to the enormous entropy. It is not a practical concern.