Saved on this device

Follow your curiosity

What discovery has been shared with you?

FACTREE gives you something interesting to discover every day — and something worth talking about together.

Start with one fact. Explore it, go deeper, then follow whichever branch catches your imagination.

Choose subjects for a surprise

Exploring any topic

Begin your discovery

Your next discovery is one click away.

Choose one or more subjects above, or leave Any Topic selected and let curiosity decide.

Mathematics

Understanding Password Strength: Combinations, Character Set, and Length

Quick fact

The number of possible passwords grows exponentially with length, but only polynomially with the size of the character set. Adding one more character to a password often multiplies the number of possible combinations by the size of the character set (e.g., 94), whereas adding a new type of character might only add a few options per position.

Why this is interesting

Ever wondered why changing your password from 'password' to 'P@ssw0rd' feels secure but isn't as strong as you think? The real secret isn't just adding symbols—it's about length.