Password Entropy Explained: How to Measure Password Strength

Quick answer: Password entropy describes how unpredictable a password is under a particular generation model. It is commonly expressed in bits. For a password created by independently choosing each character uniformly from an alphabet of 62 symbols, entropy can be calculated as H = L × log₂(62), where L is the number of characters. Under those assumptions, a 16-character password has approximately 95.3 bits of entropy.

However, this formula does not accurately measure every password. A human-created password may follow patterns, even when it contains many characters, and a real-world attack may involve phishing, stolen credentials, or weaknesses unrelated to guessing.

Understanding password entropy helps explain why secure randomness, sufficient length, and unique credentials matter.

What Is Password Entropy?

Password entropy is a measure of uncertainty associated with a password-generation process.

When a generator can produce many different passwords with equal probability, an attacker who does not know the selected password faces a large space of possibilities.

Entropy provides a convenient way to express the size of that space.

What Does Entropy Mean in Bits?

A bit of entropy represents a doubling of the number of equally likely possibilities.

For a uniformly random secret:

Each additional bit doubles the theoretical search space.

For example, a uniformly random secret with 80 bits of entropy has 2²⁰—or 1,048,576—times as many possibilities as a uniformly random secret with 60 bits.

That does not mean every real-world attack takes proportionally longer. The result depends on what the attacker knows and what method they use.

Shannon Entropy vs Min-Entropy

There are different mathematical definitions of entropy.

Shannon entropy measures average uncertainty across a probability distribution.

Min-entropy focuses on the probability of the most likely outcome, which can be especially relevant when considering an attacker's best initial guess.

For a uniform distribution across N possible passwords, both values equal log₂(N).

For a nonuniform distribution, such as passwords manually selected by humans, they can differ substantially.

This is one reason that assigning a single precise entropy value to a human-chosen password is difficult.

How Is Password Entropy Calculated?

For a password generated uniformly at random from a fixed character set, a common formula is:

H = L × log₂(N)

Where:

1. H = entropy in bits
2. L = password length
3. N = number of possible characters at each position
4. log₂ = logarithm to base 2

The formula assumes independent, uniformly distributed character selections from the same alphabet at every position.

Example: 16-Character Random Password

Suppose a generator selects 16 characters independently and uniformly from:

1. 26 lowercase letters
2. 26 uppercase letters
3. 10 digits

The alphabet contains 62 characters.

The calculation is:

H = 16 × log₂(62)

H ≈ 95.27 bits

This is a theoretical value for the defined generation process.

It does not prove that an arbitrary 16-character password found online has 95.27 bits of entropy.

Why Does the Character Set Matter?

When selection is truly uniform and independent, increasing the number of possible characters at each position increases the search space.

Consider three example alphabets:

For the same length, a randomly generated password using the larger alphabet has more theoretical entropy.

However, adding extra character types does not automatically improve the security of a password chosen by a person.

For example, changing a common password from password to P@ssw0rd introduces predictable substitutions. It does not make the resulting secret equivalent to a random selection from a large alphabet.

When Does the Simple Formula Become Inaccurate?

The formula H = L × log₂(N) only applies under its stated assumptions.

A generator may produce a different distribution if it:

1. Guarantees at least one character from each selected category.
2. Excludes visually similar characters.
3. Uses different alphabets at different positions.
4. Selects characters with a biased algorithm.
5. Applies formatting or structural constraints.
6. Uses a restricted or nonuniform source of randomness.

Such generators can still be secure, but their actual output distribution must be considered when estimating entropy.

For constrained generators, calculating the exact output probabilities or defensible lower bounds is more appropriate than automatically applying the unrestricted formula.

Password Entropy by Length: Comparison Table

The following table uses a single model: characters selected independently and uniformly from 62 possible symbols.

These values are mathematical estimates, not observed password-cracking results.

Is a 12-Character Random Password Strong?

A uniformly random 12-character password drawn from 62 symbols has approximately 71.45 bits of theoretical entropy.

That represents a very large number of possible credentials, but its suitability still depends on the system and threat model.

Current NIST SP 800-63B requires a minimum of 15 characters for passwords used as a single authentication factor within its scope.

A longer random password is preferable when supported.

How Much Entropy Does a 16-Character Password Have?

Under the 62-character uniform random model, a 16-character password has approximately 95.27 bits of theoretical entropy.

This makes 16 randomly generated characters a practical default for many accounts.

But a human-created 16-character password cannot automatically be assigned the same value.

Does a 24-Character Password Offer More Security?

Under an identical, uniform generation model, a 24-character password has a vastly larger theoretical search space than a 16-character password.

A password manager can make longer credentials convenient, especially for accounts that do not require frequent manual entry.

However, an attacker who obtains the password through phishing or malware does not need to search its theoretical space.

For a more detailed discussion of recommended lengths, see How Long Should a Password Be?.

Is More Password Entropy Always Better?

More entropy means greater unpredictability under the model being measured.

But entropy is not the same as comprehensive account security.

Entropy Does Not Prevent Phishing

A sophisticated phishing website may trick a user into revealing a password.

If the attacker receives the actual credential, its theoretical guessing difficulty is irrelevant to that attack.

This is why phishing-resistant authentication methods, such as appropriately implemented passkeys, provide advantages beyond password complexity.

Entropy Does Not Prevent Password Reuse

A long random password reused across multiple websites can still create a serious risk.

If one service exposes the credential, attackers may try it on other services.

Use a different password for every account.

For a practical creation workflow, see How to Create a Strong Password.

Entropy Does Not Guarantee Secure Storage

A password's resistance to offline guessing can depend on how the service stores and verifies it.

Properly salted, computationally expensive password hashing increases the cost of testing guesses after a database compromise.

Poor credential handling can undermine security even when users choose strong passwords.

Password Entropy vs Password Cracking Time

Password entropy and estimated cracking time are related concepts, but they are not interchangeable.

A simple offline guessing model might estimate the time required to exhaust a search space as:

Maximum search time = total candidate passwords ÷ guesses per second

For a uniformly random password with N equally likely possibilities, the expected number of guesses in a fixed-order exhaustive search is approximately (N + 1) ÷ 2.

Real attacks are more complicated.

Online Guessing vs Offline Guessing

In an online attack, the attacker submits guesses to a login service.

Rate limiting, multifactor authentication, account lockouts, and monitoring may restrict the number of attempts.

In an offline attack, the attacker may have obtained password hashes and can test candidates without interacting with the login website.

Offline guessing speed depends heavily on the password hashing algorithm, its configuration, the attacker's resources, and other technical conditions.

Why Many Password Cracking Charts Are Misleading

Some charts show enormous cracking times without explaining the assumptions.

A useful estimate should disclose the candidate distribution, guessing strategy, verification cost, and whether the displayed time represents an average or worst-case search.

A precise number with unclear assumptions can create a false sense of security.

The safer conclusion: Entropy describes uncertainty in a defined model. It does not predict the time needed for every possible attack.

Random Passwords vs Passphrases: Entropy Comparison

A passphrase can be generated by selecting several independent words from a predefined wordlist.

For a uniformly random selection from a list of W words, the formula is:

H = K × log₂(W)

Where K is the number of words.

Example: A 7,776-Word List

Suppose a generator selects words independently and uniformly from a list containing 7,776 distinct words.

These values assume that each word is chosen independently and uniformly from the full list, with repetitions allowed.

If the generator prevents repetition or changes the selection process, the exact calculation changes.

Are Passphrases Better Than Random Passwords?

Neither format is universally better.

Random-character passwords are convenient when stored by a password manager.

Random multiword passphrases may be easier to memorize and type.

A passphrase based on personal memories, familiar quotations, or a meaningful sentence does not have the same entropy as a sequence of independently sampled words.

Use the Passphrase Generator to explore the different format options.

How Do Password Strength Checkers Estimate Entropy?

Some password strength tools estimate security from length and the available character set.

Others attempt to identify common words, keyboard patterns, predictable dates, and known password structures.

These are different approaches.

Theoretical Entropy Estimators

A theoretical entropy estimator describes the uncertainty associated with an assumed generation method.

It is especially useful when evaluating a secure random password generator with a documented output distribution.

It should not automatically assign the same entropy to a human-created string that happens to have the same length and character types.

Pattern-Based Password Strength Estimators

Pattern-aware tools attempt to estimate how easily an attacker might guess a particular password.

They can identify obvious weaknesses such as common words and sequences, but their results remain model-dependent.

No strength meter can guarantee that a password is unknown to attackers or that an account cannot be compromised.

What Does PasswordGenerating.com's Checker Measure?

The Password Strength Checker has been presented as an estimator for generated-password settings.

Before interpreting its output as a measured security level, review the assumptions and ensure they match the deployed generation algorithm.

If the generator guarantees characters from different categories, a simple independent-selection calculation may overstate or mischaracterize the actual distribution.

A trustworthy calculator should explain its limitations rather than display an unjustified security guarantee.

How to Increase Password Entropy Safely

For new passwords, use a cryptographically secure generation process.

1. Increase Random Password Length

Under the same uniform generation model, every additional character increases entropy.

For most accounts, 16 or more randomly generated characters is a practical default when supported.

2. Select Characters Using Secure Randomness

Avoid manually inventing patterns or relying on ordinary pseudorandom functions unsuitable for cryptographic use.

The Web Crypto API provides cryptographically strong random values for browser applications, but generation logic must also avoid bias.

3. Use Unique Credentials

A new password should be unique to the account where it is used.

This does not increase the entropy of one password, but it reduces risk across multiple accounts.

4. Store Passwords Securely

Use a reputable password manager to save long, random credentials.

Keep your master password and account recovery methods secure.

5. Enable Multifactor Authentication

Even a highly unpredictable password can be exposed through phishing, malware, or account compromise.

Use additional authentication, especially phishing-resistant options where available.

What Does NIST Say About Password Entropy?

NIST SP 800-63B recognizes the difficulty of estimating the entropy of human-selected passwords.

Its guidance emphasizes length, checking new passwords against commonly used or compromised values, secure storage, and protections against repeated guessing attempts.

The current standard requires covered password verifiers to enforce at least 15 characters for single-factor passwords and permits a minimum of eight when passwords are used as part of multifactor authentication.

It also rejects mandatory character-composition rules and arbitrary periodic password changes.

Important: NIST does not provide a universal minimum entropy-bit score that makes every human-chosen password secure.

Key Takeaways

Password entropy is useful when the generation model is clearly defined.

For uniformly random passwords, the formula H = L × log₂(N) provides a straightforward theoretical estimate.

But entropy values should never be confused with guarantees of security or exact cracking times.

Choose passwords that are long, randomly generated, unique, and stored safely. Use MFA or passkeys where available.

To create your next unique credential, visit the Password Generator.

Frequently Asked Questions

What is password entropy in simple terms?

Password entropy measures uncertainty in how a password was selected. Higher entropy represents a larger effective space of possibilities under the assumed model.

How do you calculate password entropy?

For a password made from independent, uniformly random character selections, use H = L × log₂(N), where L is the password length and N is the alphabet size.

How many bits of entropy is a strong password?

There is no universal number that guarantees security for every situation. Adequacy depends on the generation process, attack model, password storage, and other account protections.

How much entropy does a 16-character password have?

A 16-character password generated uniformly from 62 symbols has approximately 95.27 bits of theoretical entropy. A human-chosen password of the same length may have substantially less effective unpredictability.

Is 80 bits of entropy enough?

Eighty bits represents an enormous theoretical search space for a genuinely uniformly generated secret. However, no single entropy threshold guarantees safety against phishing, theft, weak storage, or every guessing scenario.

Is password entropy the same as password strength?

Not exactly. Entropy describes uncertainty under a model, while practical password strength also depends on predictability, compromises, verification systems, and attack methods.

Does adding symbols always increase entropy?

Only if the generation process actually increases the uncertainty of the output. Predictable manual symbol substitutions may provide little benefit.

How many bits of entropy does a passphrase have?

It depends on the wordlist, number of words, selection probabilities, and constraints. With independent uniform selections from 7,776 words, six random words provide approximately 77.55 bits.

Can a password strength checker know the exact entropy of my password?

Generally, no. A tool can calculate theoretical entropy for a known random-generation model or estimate guessability, but it cannot infer the full selection history of an arbitrary human-created password.

Sources and Further Reading

1. NIST SP 800-63B — Authentication and Authenticator Management
2. OWASP Authentication Cheat Sheet
3. MDN — Crypto.getRandomValues()
4. OWASP Password Storage Cheat Sheet

Methodology: Numerical entropy values are derived from the explicitly stated independent, uniform random-selection models. They are not measurements of human-selected password distributions, results of penetration testing, or guarantees against compromise.