Calculator
Example Data Table
These examples assume a 6-sided die and classic five rolls per word unless noted.
| Dice (s) | Rolls/word (r) | Words (n) | Wordlist size (L) | Total entropy (bits) |
|---|---|---|---|---|
| 6 | 5 | 4 | 7,776 | ~51.70 |
| 6 | 5 | 6 | 7,776 | ~77.55 |
| 6 | 5 | 8 | 7,776 | ~103.41 |
| 10 | 4 | 6 | 10,000 | ~79.73 |
Formula Used
Diceware chooses one word from a wordlist. If each word is selected uniformly from L possibilities, the information entropy per word is:
Hword = log2(L) bits
For dice with s sides rolled r times per word, the list size implied by dice outcomes is:
L = sr
For n words, total entropy is:
Htotal = n · log2(L) bits
Chemistry link: microstates scale as W = Ln. A thermodynamic entropy analogue is S = kB ln(W), and because ln(W) = ln(2)·Htotal, we get:
S = kB ln(2) · Htotal
This does not mean your passphrase has a temperature—it's a useful analogy for “number of possibilities.”
How to Use This Calculator
- Choose dice sides s (usually 6) and rolls per word r (often 5).
- Enter the number of words n in your passphrase.
- Optionally enter a custom wordlist size L if you are not using dice outcomes directly.
- Select an attacker guess rate to get rough time estimates.
- Click Calculate Entropy and review bits, microstates, and entropy analogues.
- Download CSV or PDF to save the calculation with your notes.
Article: Diceware Entropy in a Chemistry Context
1) Understanding Diceware Entropy
Diceware builds passphrases from truly random dice rolls mapped to a fixed wordlist. The calculator converts that randomness into entropy in bits, a standard measure used in information theory and widely reused in scientific data integrity workflows. This standardizes strength across systems.
2) From Combinatorics to Bits
If a wordlist has N equally likely words and you select k words independently, the total search space is Nk. Entropy is H = log2(Nk) = k·log2(N), which the calculator reports as “bits per word” and “total bits.”
3) Why Chemistry Cares About Randomness
Chemistry labs increasingly depend on digital instruments, cloud notebooks, and shared repositories. Credentials with predictable patterns can expose experimental records, proprietary formulations, or instrument control panels. Strong, measurable entropy supports safer access to analytical results and collaboration data.
4) Role of Wordlist Size
A classic Diceware list contains 7,776 words (5 dice, 6 faces each). That yields about 12.9 bits per word (because log2(7776) ≈ 12.9). With smaller lists, bits per word drop quickly, so you must add more words to reach the same security level.
5) Dice Count and Phrase Length Tradeoffs
For a 7,776-word list: 6 words give about 77.6 bits, 7 words about 90.5 bits, and 8 words about 103.4 bits. The calculator also shows an estimated crack time based on an adjustable guess rate, helping you compare “one more word” versus operational convenience.
6) Adding a Separator or “Salt” Word
Optional separators (like a hyphen) can improve usability without changing entropy much if they are predictable. However, adding an extra random word is far more effective than adding a fixed digit or punctuation mark. Randomness, not complexity, is the main driver of security here.
7) Interpreting Crack-Time Estimates
Crack time depends on the attacker’s guess rate and whether offline hashing is possible. Treat the estimate as a scenario tool: choose a conservative guess rate for your threat model, and focus on the total bits. As a rule of thumb, higher entropy scales exponentially in difficulty.
8) Laboratory and Personal Security Checklist
Use physical dice or trusted hardware entropy, keep rolls independent, and avoid “favorite” words. Store passphrases in a secure manager, enable multi-factor authentication for lab systems, and rotate secrets when access changes. Document your method so teams can reproduce strong practices consistently.
FAQs
1) How much entropy does one Diceware word add?
It adds log2(wordlist size) bits. For a 7,776-word list, that is about 12.9 bits per word.
2) What if my words are not chosen uniformly?
If selection is biased, real entropy is lower than the calculator’s value. Use fair dice or a trusted random source and avoid human “random” choices.
3) Does adding a predictable digit meaningfully help?
Only a little. A fixed pattern adds minimal entropy. Adding one extra random word usually increases security far more than predictable complexity.
4) How is the crack-time estimate computed?
The calculator divides the search space (Nk) by the assumed guesses-per-second rate, then converts seconds into readable units. It is a scenario estimate, not a guarantee.
5) Is 5 or 6 words enough for research accounts?
It depends on the threat model and storage method. For many cases, 6+ words with a 7,776-word list is strong, especially with multi-factor authentication.
6) Can I use a custom wordlist?
Yes, but measure its size and ensure it is clean, unambiguous, and used with uniform selection. The calculator will reflect the entropy for your chosen size.
7) Why is this labeled under Chemistry?
Chemistry work relies on secure access to instruments, notebooks, and datasets. Entropy-based passphrases reduce the chance of credential-driven data loss or manipulation.
Professional Notes
Diceware strength relies on true randomness and uniform selection. Human-chosen words reduce entropy significantly. Protect your phrase with rate-limiting, multi-factor authentication, and strong hashing (for stored secrets).