"Use a mix of upper case, lower case, numbers, and symbols" is common advice — but it's not the whole picture, and on its own it can lead people toward shorter passwords that are actually weaker than a longer, simpler one. Here's the actual math behind password strength.
Entropy: how password strength is actually measured
Entropy measures how many possible combinations exist — more bits means exponentially more combinations to search through. Two factors control it: how many characters are available at each position (the pool size), and how many positions there are (the length).
The comparison that surprises people
Consider two passwords built from the same generator logic used on this site (a pool that excludes visually confusing characters like 1, l, 0, and O):
| Password style | Pool size | Length | Entropy |
|---|---|---|---|
| 8 characters, all types (upper, lower, numbers, symbols) | 76 characters | 8 | ≈50.0 bits |
| 12 characters, lowercase only | 25 characters | 12 | ≈55.7 bits |
The 12-character lowercase-only password has more entropy than the 8-character password using all four character types — despite looking "less complex." Length has a compounding effect: each additional character multiplies the number of possible combinations, while adding another character type only increases the pool size for every position.
Why this happens, intuitively
Adding a character type (say, going from lowercase-only to lowercase+numbers) increases the pool size modestly — from 25 to roughly 33 characters, a small percentage increase applied at every position. Adding one more character to the password length, by contrast, multiplies the total combinations by the full pool size all over again. At any reasonable pool size, a few extra characters of length outweighs a richer character set on a shorter password.
This doesn't mean complexity is useless — a longer password that also uses multiple character types is stronger than either change alone. The point is that if you have to choose where to spend your effort, length is the more effective lever.
Why some characters get excluded
Password generators commonly exclude visually similar characters — 1, l (lowercase L), 0, and O are frequent examples — because they're easy to misread and mistype when a person is transcribing a generated password by hand (say, reading it off a screen and typing it into a different device). This slightly reduces the pool size, which is a deliberate usability trade-off rather than an oversight.
The bigger risk: reuse, not weak generation
A password with excellent entropy is still vulnerable if it's reused across multiple accounts. If any one of those sites is breached, attackers commonly try the same email-and-password combination against many other services — a technique called credential stuffing — regardless of how strong or randomly generated that password was. Using a unique password per account, managed through a password manager, closes this gap in a way that improving entropy on a single reused password cannot.
Try the tool
The password generator creates a cryptographically random password using your chosen length and character types, with a strength indicator based on this length-and-variety logic.
Frequently asked questions
What is password entropy?
Entropy measures password unpredictability in bits, calculated as password length multiplied by the base-2 logarithm of the character pool size. A higher entropy value means more possible combinations an attacker would need to try.
Is a longer simple password stronger than a shorter complex one?
Often, yes. A 12-character password using only lowercase letters has more entropy (roughly 56 bits) than an 8-character password mixing uppercase, lowercase, numbers, and symbols (roughly 50 bits), because length has a larger multiplying effect than adding a few more character types.
Why do password generators avoid characters like 1, l, 0, and O?
These characters look nearly identical in many fonts, which can cause transcription errors when a person reads and types a generated password manually. Removing them slightly reduces the character pool but improves usability.
Is it safe to reuse a strong password across multiple sites?
No. If any one site suffers a data breach, a reused password can be tried against other accounts (a technique called credential stuffing), regardless of how strong or random that individual password was. A unique password per site, managed with a password manager, protects against this.