Password Strength Explained: Entropy, Length, and Crack Times

Most password advice boils down to a single principle: the strength of a password is measured by its entropy — the number of possible combinations an attacker would have to try. More entropy means exponentially longer brute-force times, and the cheapest way to buy entropy is length.

Length beats complexity

Each extra character multiplies the search space by the size of the character set. Every character drawn from a 72-symbol set adds about 6.2 bits of entropy, so a 16-character password lands near 99 bits while an 8-character one from the same set is only around 49 bits. Because entropy is exponential, that is not twice as strong — it is roughly a hundred trillion times more combinations. This is why security guidance consistently favours long passphrases over short, symbol-stuffed ones.

Crack-time estimates, demystified

Crack-time estimates translate entropy into plain English — "about 3 centuries" instead of 106 bits. They assume a powerful attacker using GPUs, so treat them as a lower bound. If your password rates in centuries, it's strong enough; if it rates in hours, regenerate it.

ForgePlug's Password Generator shows both numbers live: an entropy-based strength meter and a crack-time estimate that updates as you change length or character sets. It uses your browser's cryptographically secure random API — the same source operating systems use — so results can't be predicted, and nothing you generate ever leaves your device.

Entropy only counts if the password was random

This is the caveat that undermines most entropy discussions. The formula assumes every character was chosen uniformly at random. A password a person invented does not meet that assumption, however complicated it looks, because humans draw from a small and predictable space: a word, a capital at the front, a number and a symbol at the end, a meaningful date.

Password crackers model those habits directly. They do not iterate blindly through every combination — they try dictionary words with common substitutions, then append the years people actually use, then apply known mangling patterns. A password like Summer2024! has the length and character variety a naive strength meter rewards, and falls in seconds because it sits squarely inside a pattern the attacker already enumerates. The strength number a meter shows for a human-invented password is close to fiction; for a randomly generated one, it is meaningful.

Crack time depends on something you don't control

Any crack-time estimate is really a statement about how the site stored your password, and that is entirely the site's decision. If a breached service stored passwords with a deliberately slow algorithm such as bcrypt, scrypt, or Argon2 — designed so each guess costs real time and memory — even a moderate password takes an impractical amount of effort to attack. If it stored them as unsalted SHA-256 or MD5, a GPU rig can attempt them at enormous rates, and a weak password falls almost immediately.

There is also a large distinction between online and offline attacks. Guessing against a live login form is slow and usually rate-limited or locked out after a handful of attempts, so entropy barely matters there. Entropy matters for the offline case: after a breach, when an attacker holds the password database and can guess as fast as their hardware allows, with no rate limit and no one watching. Assume that is the scenario you are defending against, because it is the one you cannot influence.

Passphrases and the numbers behind them

A randomly selected word from a standard 7,776-word diceware list contributes about 12.9 bits of entropy. Six such words come to roughly 78 bits — comparable to a random 12-character password, and vastly easier to type and remember. The critical word is randomly: the strength comes from genuine random selection, not from choosing words yourself. A phrase you composed because it was memorable is a human-chosen password again, and the entropy calculation no longer applies.

What actually breaks passwords

• Reuse — one breached site leaks the password everywhere else you used it. This is the single biggest real-world risk, and no amount of entropy protects against it.
• Human-chosen 'complex' passwords — patterns like a capitalised word plus a year and a symbol are enumerated early by cracking tools.
• Weak storage on the provider's side — you cannot control it, which is why length and uniqueness are your only levers.
• Phishing — no amount of entropy helps if you type it into a convincing fake login page.

The practical conclusion is less about any individual password than about the system around it. A password manager generates genuinely random credentials, stores a different one per site so a breach cannot cascade, and refuses to autofill on a domain that does not match — which quietly defends against phishing better than vigilance does. Add multi-factor authentication on anything that matters, since it keeps an account secure even when the password has already leaked.