How Strong Is Your Password? Length, Randomness and Entropy Explained

Password advice has changed. For years, sites told us to add a capital letter, a number and a symbol. Today the security consensus is simpler: make it long, make it random, and never reuse it. This guide explains why with a little arithmetic, so you can judge any password yourself.

What "entropy" means

Entropy measures how many guesses an attacker would need, expressed in bits. Each extra bit doubles the number of possibilities. For a password picked completely at random, the entropy is:

If each character is chosen at random from a pool of 94 (letters, digits and symbols), every character adds about 6.55 bits. A pool of only 26 lowercase letters adds about 4.7 bits per character.

Length beats complexity

Compare passwords made of randomly chosen characters:

• 8 characters from 94 symbols: about 52 bits.
• 12 characters from 94 symbols: about 79 bits.
• 16 characters from 94 symbols: about 105 bits.
• 12 lowercase letters only: about 56 bits.
• 16 lowercase letters only: about 75 bits.

A 16-letter lowercase password is stronger than a 10-character password with every character type, simply because it is longer. Each added character multiplies the work by the pool size.

How long would guessing take?

Suppose an attacker who has stolen a database of weakly protected password hashes can try 10 billion guesses per second, which is possible with specialist hardware against fast hashes. On average they find the password after trying half the possibilities:

• About 38 bits (8 random lowercase letters): roughly 10 seconds.
• About 52 bits (8 random characters of all types): about 3 days.
• About 56 bits (12 random lowercase letters): about 55 days.
• About 79 bits (12 random characters of all types): roughly 800,000 years.
• About 105 bits (16 random characters): far beyond any realistic timescale.

Well-run sites use slow hashing that limits guesses to thousands per second, which makes each of those figures many times longer. But you cannot see how a site stores passwords, so choose a strong one anyway.

Randomness matters more than the symbols

The arithmetic above only applies to passwords chosen at random by a computer. Human-made passwords are far weaker than they look. "P@ssw0rd!" has all four character types but is on every attacker's list, and substitutions like a→@ and o→0 are the first thing cracking software tries. Names, dates, keyboard patterns and dictionary words fall quickly.

• Never build a password from personal details.
• Do not add a number to the end of a word and call it done.
• Let a generator choose it, such as the Password Generator, which uses your browser's secure random number generator and never sends the password anywhere.

Passphrases: random words

A passphrase made of random words from a large list is a good option when you have to type or remember it. With a list of 7,776 words (as in the Diceware method), each word adds about 12.9 bits: four words give about 52 bits, five give about 65, six give about 78 and seven give about 90. The words must be chosen randomly, not picked because they sound nice.

What to do in practice

• Use a password manager, and let it generate a long random password for every account. You then need to remember only one strong master passphrase.
• Use at least 16 characters for important accounts such as email, banking and your password manager.
• Never reuse a password. If one site is breached, reused passwords open your other accounts.
• Turn on two-factor authentication wherever it is offered, ideally with an authenticator app or security key.
• Check a password with the Password Strength Checker before you rely on it.

Put this into practice with the tools: create a password with the Password Generator, test it with the Password Strength Checker, and protect a sensitive document with the PDF Password Protector. If you forget a document password later, remember that a modern encrypted PDF cannot be recovered, so keep the password in a password manager.