Password entropy explained: how many random bits keep you safe

Guide · Updated 2026-11-10

What makes a password hard to guess, how bits of entropy are counted, and how to use the password generator to make long random passwords on your own device.

Open the Password generator Free, in your browser, nothing uploaded.

The password generator makes random passwords on your own device, from 8 to 128 characters, using the characters you choose. It tells you how many bits of randomness each one carries, so you can see at a glance whether a password is fit for an email account or a bank login. It is for anyone setting up a new account, IT staff handing out first-time logins, and students learning why “P@ssw0rd1” is a poor choice. To test a password you already use, try the password strength checker; to confirm a downloaded file has not been changed, the hash checker compares fingerprints; and for random labels that are not secrets, the UUID generator makes IDs.

What it is

An attacker who steals a scrambled password list tries guesses, very fast, until one matches. Your defence is a password with so many possibilities that the guessing never finishes.

If each character is picked at random from a pool of P characters, and the password has L characters, the number of possible passwords is P to the power L. Entropy measures this in bits:

entropy = L × log2(P)

Each bit doubles the attacker’s work.

Two things matter about that formula. Length counts more than variety, because L multiplies while P only sits inside a logarithm. And the formula holds only when every character is truly random. A password you invent has far fewer bits than the formula suggests, because people follow patterns.

The generator uses crypto.getRandomValues, the browser’s secure random source, and a method called rejection sampling: random numbers that would make some characters slightly more likely are thrown away and drawn again, so every character in the pool is equally likely.

When you ask for at least one character from each ticked set, a few possible passwords are ruled out. The tool counts exactly how many remain (by inclusion-exclusion: all passwords, minus those missing a set, plus those missing two, and so on), so the bits shown are a touch lower than L × log2(P).

How to use it

1. Type a Length from 8 to 128. It starts at 20.
2. Type How many passwords you want, from 1 to 100. It starts at 5.
3. Under Use these characters, tick any of lower case, upper case, digits and symbols. Untick symbols if a site will not accept them.
4. Tick Leave out look-alikes if the password will be read aloud or copied from paper, and keep At least one from each ticked set for sites that insist on a digit or a symbol.
5. Read the line above the list: the bits of randomness, a rating (weak, fair, strong or very strong) and the size of the pool.
6. Press Copy beside a password, or Copy all for the whole list. Make new ones draws a fresh set; changing any setting does the same.

A worked example

A site allows letters and digits but no symbols, and a maximum of 16 characters. Set Length to 16, untick Symbols, and keep the other two boxes as they are.

The pool is 26 + 26 + 10 = 62 characters. With no rules, entropy is 16 × log2(62) = 16 × 5.954 = 95.3 bits. Requiring a lower case letter, a capital and a digit removes a tiny share of passwords, and the tool shows 95.2 bits, rated strong.

Now tick Leave out look-alikes. That removes o and l from the lower case, O and I from the capitals, and 0 and 1 from the digits, leaving 24 + 24 + 8 = 56 characters. The line now reads 92.8 bits: you gave up about 2.4 bits for easier reading.

To see what that means, imagine an attacker making a trillion (10^12) guesses a second. On average they need to search half the possibilities. For the 95.2-bit password that is 2^95.2 ÷ 2 ÷ 10^12 seconds, roughly 710 million years. Compare a random 8-letter, lower-case-only password: 8 × log2(26) = 37.6 bits, found on average in about 0.1 seconds.

If the site allowed 20 characters, the same three sets would give 119.0 bits, rated very strong.

Where it is used

• Password managers: make a new random password for every account and let the manager remember it, so one leak does not open the rest.
• Wi-Fi keys: a long password with look-alikes left out is easy to type into a smart TV or a printer.
• First-time logins at work: IT staff can make a batch for new starters, then ask each person to change theirs.
• Teaching security: the bits figure shows students, in numbers, why length beats clever substitutions.

Common mistakes

• Editing the password to make it memorable. Swapping a few characters for your initials removes randomness. Keep it exactly as made and store it in a password manager.
• Reusing one strong password. Strength does not help if one site leaks it and the same password unlocks others. Make one per account.
• Choosing the minimum length. If a site accepts 64 characters, use 20 or more. Extra length costs you nothing when a manager types it.
• Thinking symbols are required. Four more random letters add more strength than adding symbols to a short password. Untick symbols freely where they cause trouble.

Questions people ask

Can the website see the passwords it makes? No. They are built by code running in your browser and are never sent anywhere or saved; close the tab and they are gone.

Why does the bits number drop when I tick “each set”? Because a few passwords, such as ones with no digit, are now not allowed. Fewer possibilities means slightly fewer bits, though the change is tiny at normal lengths.

Should I change passwords every few months? Current guidance from NIST says to change one when there is a reason, such as a leak, rather than on a timer. A long random password kept in a manager can stay as it is.