How to create a strong password: length, entropy, and what actually matters

What a strong password actually is

A strong password has three properties, and missing any one of them undoes the other two. It is unpredictable, meaning nobody can guess it from your name, birthday, pet, or favorite team. It is long enough that trying every possibility is not practical. And it is unique, meaning no other account shares it.

The third property is the one people skip. Attackers rarely sit down and guess your password from scratch. When one website is breached, the stolen email and password pairs get tried against banks, email providers, and shopping sites. That is why a perfectly random password reused in two places is only as safe as the weaker of the two sites.

It also helps to separate two kinds of guessing. In an online attack, the attacker types guesses into a login form, and the service can slow or lock them out. In an offline attack, the attacker has stolen the service's file of password fingerprints and can test guesses on their own hardware as fast as it will go, with no lockouts. Long random passwords are mainly insurance against the offline case, because nothing else is stopping the attacker there.

The entropy math you can do yourself

Entropy measures unpredictability in bits. Each extra bit doubles the number of guesses an attacker needs. For a password where every character is chosen uniformly at random from a set of N possible characters, the number of possible passwords is N raised to the length, and the entropy is length x log2(N).

Here is the arithmetic for common cases, calculated directly:

• Lowercase letters only (26 characters): log2(26) = 4.70 bits per character. 16 characters = 75.2 bits.
• Letters and digits (62 characters): log2(62) = 5.95 bits per character. 8 characters = 47.6 bits, 12 = 71.5 bits, 16 = 95.3 bits, 20 = 119.1 bits.
• Letters, digits, and 26 symbols (88 characters): log2(88) = 6.46 bits per character. 8 characters = 51.7 bits, 12 = 77.5 bits, 16 = 103.4 bits.
• Digits only (10 characters): log2(10) = 3.32 bits per character. A 6-digit PIN = 19.9 bits, which is exactly 1,000,000 possibilities.
• Number of combinations: 62^8 is about 2.2 x 10^14, 62^16 is about 4.8 x 10^28, and 88^16 is about 1.3 x 10^31.

Length versus complexity

Look at what symbols buy you. Moving from a 62-character set to an 88-character set raises the per-character value from 5.95 to 6.46 bits, a gain of about 0.5 bits. Across 16 characters that is 8.1 extra bits. Adding two more characters to the 62-character version gains 2 x 5.95 = 11.9 bits. So an 18-character letters-and-digits password (107.2 bits) beats a 16-character password that uses symbols (103.4 bits).

The same pattern holds at the extreme. A 20-character password that is all lowercase letters has 94.0 bits, which beats a 12-character password drawn from all 88 characters (77.5 bits). Every character you add multiplies the guessing work by the whole size of the set, while adding a character type only enlarges the set a little.

This matches current federal guidance. NIST SP 800-63B-4, the Digital Identity Guidelines for authentication, tells services to require a minimum of 15 characters when a password is the only authenticator, and eight when it is used as one factor of several. It also says services should allow passwords of at least 64 characters and should not impose composition rules such as requiring a mix of character types. CISA's consumer guidance likewise asks for at least 16 characters. Note that the NIST text sets rules for the services that check passwords. It is not a personal checklist, but it shows where the experts landed: length, not decoration.

None of this means symbols are bad. Some sites still demand them, and a random password with symbols is perfectly good. The point is that when you have a choice, extra length is the cheaper way to get strength.

What the numbers mean in practice

To make bits feel concrete, assume an offline attacker who can test one trillion guesses per second. That rate is an illustration chosen to be generous to the attacker, not a measurement. Real speeds depend heavily on how the service stores passwords, and a deliberately slow storage method cuts them by orders of magnitude. On average an attacker finds the password after trying half the possibilities, so the expected time is N^L / 2 divided by the rate.

• 8 characters, 62-character set: 2.2 x 10^14 possibilities, about 109 seconds on average.
• 8 characters, 88-character set: about 30 minutes.
• 12 characters, 62-character set: about 51 years.
• 12 characters, 88-character set: about 3,400 years.
• 16 characters, 62-character set: about 7.6 x 10^8 years.

Where the entropy formula breaks down

The formula is only true when every character is chosen at random. Human-made passwords are not. A password like Summer2026! looks like it has four character types and ten characters, but it follows a pattern thousands of people use: a word, a year, a symbol. Attackers try those patterns first, so its real strength is a tiny fraction of the nominal calculation. Replacing letters with lookalike symbols, adding a 1 at the end, or capitalizing the first letter barely changes the effective strength because everyone does it.

Reuse is the other place the math stops mattering. A 100-bit password stored in plain text on a breached site is exposed regardless of its entropy. This is why uniqueness and a good source of randomness matter more than squeezing out more bits once you are past roughly 16 random characters. Beyond that point, the realistic risks are phishing, malware, and reuse, none of which longer passwords fix.

Passphrases: the memorable option

Some passwords you have to type from memory, such as the one that unlocks your password manager or your computer. For those, a passphrase works well. CISA suggests a memorable phrase of four to seven unrelated words. The key word is unrelated, and the words have to be picked randomly, by dice or software, not by you choosing words you like.

If each word comes from a list of 7,776 words (the size of a list built from five rolls of a six-sided die, 6^5), each word adds log2(7,776) = 12.92 bits. Four words give 51.7 bits, five give 64.6, six give 77.5, and seven give 90.5. So a six-word random passphrase has about the same strength as 12 fully random characters from an 88-character set, while being far easier to type. A song lyric, a famous quote, or a sentence about your life does not count, because those come from a much smaller pool of possibilities than a random word list.

Using the Password Generator

The Password Generator on EveryFix lets you set a length from 4 to 128 characters (the default is 16) and switch four character groups on or off: uppercase letters, lowercase letters, numbers, and symbols. The first three are on by default and symbols are off, so the default password draws from a 62-character set and carries 95.3 bits. Turning symbols on adds 26 symbol characters for an 88-character set.

The randomness comes from crypto.getRandomValues in your browser, the Web Crypto API's secure random source, not Math.random. The tool fills a block of 32-bit random numbers, then maps each one to a character by taking the remainder when divided by the set size. That mapping has a theoretical bias of about two parts in a hundred million, which is far too small to matter. The code falls back to Math.random only if the browser has no crypto support at all, which is not expected in modern browsers. The password is generated on your device and is not sent anywhere.

Two behaviors are worth knowing. First, the Strength label is a quick rule of thumb, not an entropy calculation. It reads Strong at 12 or more characters with at least three character types, and Moderate at 8 or more with at least two. A 128-character lowercase-only password therefore shows only a Weak label even though it has about 600 bits of entropy. When in doubt, trust the bits. Second, the generator picks every character independently, so it does not guarantee that each selected type appears. A 16-character password from the 62-character set has about a 6 percent chance of containing no digit, because (52/62)^16 = 0.06. If a site insists on one, just generate again.

The related tools solve different problems. The UUID Generator makes random identifiers for databases and software, not passwords you would type. The Hash Generator computes SHA fingerprints of text, and hashing a weak password gives a long string that is no harder to guess than the original input.

Password managers and multifactor authentication

Nobody can memorize dozens of unique 16-character random passwords, which is the reason password managers exist. CISA describes a password manager as a program that generates, stores, and fills in your passwords, so you only need to remember one strong master password, ideally a passphrase. NIST's guidance also tells services that they must allow password managers and autofill, and that they should permit pasting into the password field.

Multifactor authentication, or MFA, is the safety net for the day a password leaks or is phished. CISA recommends turning it on for every account or app that offers it, including banking, email, and social media. Authenticator apps generate a new code every 30 seconds, and a code sent by text is another option. Protect your email account especially well: whoever controls it can usually reset your other passwords.

Finally, change a password when there is a reason to, not on a calendar. NIST says services should not force periodic changes, and requires a change if there is evidence the password has been compromised. Forced rotation mostly produces predictable variants like Summer1!, then Summer2!.