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Password entropy: what the bits mean

Bits measure how many guesses it would take to find a password. This guide explains the formula, when it holds and when it misleads.

Updated . 6 min read.

What password entropy is

It is a way of counting how many different passwords the same method could have produced. If a password has n bits, there were 2n equally likely possibilities. Each extra bit doubles the attacker’s work: 80 bits is not “a little more” than 70, it is 1,024 times more.

The term comes from Claude Shannon’s information theory, and for passwords it is used in a very specific sense: it measures the method used to create the password, not the password itself.

The formula

If a password has L symbols and each is chosen at random, with equal probability, from N possible ones:

bits = L × log₂(N)

A symbol can be a character or a whole word. These are the most common values of N:

Symbol setNBits per symbol
Digits (0–9)103.32
Lowercase264.70
Upper and lowercase525.70
Letters and digits625.95
Letters, digits and 32 symbols946.55
Words from a Diceware list7,77612.92

Our generator makes one more adjustment: if you tick several character types, it requires at least one of each, which rules out some combinations. We subtract those using the inclusion–exclusion principle, so the figure you see is exact.

Examples

  • Random 4-digit PIN: 4 × 3.32 = 13.3 bits. About 10,000 possibilities.
  • 8 characters of all four types: about 51 bits. It sounds like a lot, but at 10 billion guesses per second it is exhausted in a day.
  • 16 characters of all four types: 104.6 bits. Out of reach of any foreseeable attack.
  • 6-word passphrase: 6 × 12.92 = 77.5 bits.

The generator shows the exact bits of what it creates, updated whenever you change a setting.

Password generator

When the figure misleads

The formula only holds if every symbol was truly chosen at random. Applied to a password a person made up, it produces meaningless numbers:

Chelsea1985! has 12 characters of all four types. The formula would say 12 × 6.55 ≈ 79 bits, “strong”. But an attacker does not try random combinations: they try capitalized words followed by a year and a symbol. That route has a few hundred million candidates, under 30 bits, and they are exhausted in less than a second.

That is why our checker does not just apply the formula: it looks for words, names, dates and keyboard walks, and estimates how many guesses it would take following those patterns. For a password that already exists, it is a far more realistic estimate.

The same goes for badly calculated passphrases. Many sites treat velvet-canyon-lantern-pebble as 28 random characters and give it more than 150 bits. But it is 4 words from a known list: 51.7 bits.

How many bits you need

BitsLevel on our meterGood for
under 40Very weakOnly behind an attempt limit (a PIN)
40 to 69WeakAccounts with two-factor authentication on a service that stores passwords properly
70 to 99StrongAny account
100 or moreVery strongMaster passwords, encryption, keys that must last decades

What that means in time, for several attack scenarios, is in the table of how long it takes to crack a password.

Frequently asked questions

How many bits should a strong password have?

For an ordinary account, 70 bits or more. For whatever protects everything else (your password manager’s master password, disk encryption), 90 or more. On our meter, 70 is the step from “weak” to “strong” and 100 from “strong” to “very strong”.

Why does every website give a different figure for the same password?

Because some calculate entropy as if the password were random (length times bits per character) and others try to estimate how someone looking for patterns would attack it. For a password a person chose, only the second approach makes sense, and it always comes out lower.

Does adding a symbol add many bits?

If the password is random, each character adds about 6.5 bits with the full set; adding symbols to the set raises it from 5.95 to 6.55 bits per character. If you chose the password yourself, putting a ! at the end adds almost nothing, because it is the first thing tried.

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