Ask three tools for a string of characters and all three will give you one. Ask where that string came from and the answers stop resembling each other.
A nickname comes out of two word lists somebody wrote by hand. A WiFi password comes out of an alphabet whose size you pick and a length you pick, which between them decide everything. An anagram comes out of the letters you typed yourself, and no tool can add a letter you did not bring. Three blanks filled in, three completely different places the answer was hiding.
That difference is not academic. It decides whether the tool can run out, whether two people can get the same answer, and whether the result is yours or the generator's.
Three tools, three ways of filling in a blank
The Nickname Generator holds 554 words split into a pair of lists for each of six styles. It draws one opener and one ending, joins them and trims to fit. Every name it can ever produce is one of 12,817 word pairs, and the styles are not equal: Cool has the thinnest pool at 1,672 pairs and Edgy the deepest at 2,650.
The WiFi Password Generator holds no words at all. It has three alphabets, of 56, 62 and 76 characters, and it draws one character at a time. Its space is not a list, it is a power, and you set the exponent yourself when you choose the length.
The Anagram Generator holds nothing. Its entire universe is whatever you typed into the box, rearranged. That sounds like the smallest of the three, and sometimes it is, and sometimes it is not.
The same three tools, side by side
The table below is the whole argument of this article. The last two rows are where the methods stop being variations on a theme.
| Parameter | Nickname Generator | WiFi Password Generator | Anagram Generator |
|---|---|---|---|
| Where the space comes from | Two word lists per style | An alphabet and a length | The letters you typed |
| Size of that space | 1,672 to 2,650 pairs | 56, 62 or 76 raised to the length | 1 to 2.4 quintillion |
| Who decides how big it is | The tool, then you trim it | You, completely | The word, completely |
| Does length help | Yes, and a short limit hurts badly | Yes, more than anything else | It is not yours to change |
| What repetition does | Nothing | Nothing | Divides the total, by 1,152 for MISSISSIPPI |
| Can two runs agree | Only by coincidence | Effectively never | The count always, the sample rarely |
| Can it run out | Yes, 86 names at a 4 character limit | Not in any human timescale | Yes, AA has exactly one arrangement |
| Is the answer knowable in advance | No | No | The count is exact |
| Does the result belong to you | No, anyone can draw the same name | Yes, and that is the point | It was already yours |
| What it is actually for | A public identity | A private secret | A property of a word |
Put all three on the same scale and the gap is embarrassing
There is one unit that fits all three: bits. A pool of 1,024 possibilities is 10 bits, a pool of a million is about 20. It answers the question of how much surprise a single result actually carries, regardless of whether it is made of words, letters or symbols.
| One result from | Possibilities | Bits of surprise |
|---|---|---|
| Anagram of LEVEL | 30 | 4.9 |
| Nickname, gaming, 4 character limit | 86 | 6.4 |
| Nickname, gaming, no limit in the way | 2,024 | 11.0 |
| Anagram of MISSISSIPPI | 34,650 | 15.1 |
| Nickname with two digits appended | 202,400 | 17.6 |
| Anagram of SCHOOLMASTER | 119,750,400 | 26.8 |
| WiFi password, 16 characters, no look-alikes | too large to write | 93 |
| WiFi password, 32 characters with symbols | too large to write | 200 |
Read the last two rows against everything above them. The most surprising thing the nickname generator can produce carries 17.6 bits. A perfectly ordinary WiFi password carries 93. The password space is roughly 4.9 times ten to the twenty-second larger than every nickname the tool can make with digits switched on.
Which is exactly as it should be. Nobody is trying to guess your username.
When you want the machine to invent
The name is taken and you need another one this minute. This is the classic case for invention, and the digits switch is the cheapest fix in the whole tool. Two characters of word traded for a hundred times more candidates: at a limit of eight, the pool goes from 1,686 to 65,800. Nothing about rearranging your own letters helps here, because your own letters are what is already taken. Style pages worth starting from: gaming, cool and anime.
You are protecting something. A password has to be unguessable to somebody who wants it, which rules out anything derived from words you would think of. WPA2 turns the passphrase into a key with 4,096 rounds of PBKDF2, so every guess is expensive by design, and a random 16 character passphrase puts the whole question out of reach. The choice you are really making there is how painful it will be to read out to a guest, which is why one of the three alphabets drops the six look-alike characters and costs only 0.15 bits per character to do it.
You want a second identity that leads nowhere. An anagram of your own name is a terrible disguise, because the letters are the giveaway. A drawn name shares nothing with you at all. Cute and fantasy pools are the deepest ones that stay comfortable on a public profile, at 2,376 and 1,935 pairs.
When you want nothing but a reshuffle
The answer has to stay tied to the input. A puzzle, a crossword clue, a name that has to be derived from a real one. Invention is useless here by definition: the whole point is that the letters do not change. ASTRONOMER and MOON STARER both report 907,200 arrangements, and identical counts are what being an anagram means.
You need a number, not a string. This is the case the other two tools cannot serve at all. "How many ways can the letters be arranged" is a question with one right answer, and the arithmetic behind it is the length factorial divided by the factorial of each repeat. MISSISSIPPI is the example every textbook uses: eleven letters suggest 39,916,800, the four I, four S and two P divide that by 1,152, and the honest answer is 34,650. Shorter words fall harder: LEVEL has 30 and BANANA has 60, against the 120 and 720 their lengths alone would give.
You want to see the whole space, not a sample. A short word with repeats runs out, and the tool says so rather than quietly handing you a short list. Longer ones do not: BOOKKEEPER holds 151,200, COMMITTEE 45,360 and STATISTICS 50,400.
The verdict, and it is not universal
Nobody should pick one of these methods and use it for everything. The question is not which is better, it is which blank you are filling in.
| What you need | Use | Why |
|---|---|---|
| Something nobody can guess | WiFi Password Generator | It is the only one of the three whose space is large enough for the word "unguessable" to mean anything |
| A name to put in front of people | Nickname Generator | Word lists produce something pronounceable, which random characters never will |
| A name derived from one you already have | Anagram Generator | It is the only one that cannot introduce a letter you did not choose |
| An exact count for homework | Anagram Generator | The other two have no deterministic answer to report |
| Test data that looks like text | Either generator | Both produce plausible letter distributions, unlike a random character string |
One last figure, because it makes the difference concrete. Draw one gaming nickname per second with digits switched on and you will have seen the entire pool of 202,400 in 2.3 days. Do the same with a 16 character password and the sun will have gone out first. Both tools return five results and a button that says generate again, and only one of them has anything left to give you.
Tools discussed in this article
Nickname Generator - five usernames per run from six styles, with a length ceiling, optional digits, a separator and mixed capitals. Style pages: gaming, fantasy, cool, cute, edgy and anime.
WiFi Password Generator - passphrases for a WPA2 or WPA3 router from 12 to 32 characters, with an alphabet that drops the six look-alike characters, and entropy reported in bits instead of an invented crack time.
Anagram Generator - rearranges a word or phrase and reports exactly how many distinct arrangements exist. Worked pages: MISSISSIPPI, BANANA, BALLOON, ASSESSMENT and DORMITORY.
More generator tools
Password Generator - for accounts rather than routers, with a strength rating and a character mix you control.
Random Number Generator - draws from a range you set, when the blank you are filling in is a number.
Color Generator - palettes in HEX, RGB and HSL, the same idea applied to color values.
And two calculators for the arithmetic behind the third table: Factorial Calculator for the numbers the anagram counts are built on, and Combinations and Permutations Calculator for the same formula applied to plain numbers instead of letters.