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About this tool
Visualize the Shannon entropy of any text or probability distribution you enter.
Shannon Entropy Explorer computes H = -sum(p * log_b p) for either a string of text or a list of probabilities, and reports the result in bits, nats or hartleys depending on the logarithm base you pick. Alongside the entropy it gives the maximum possible entropy for that number of outcomes, the normalised ratio between the two, the perplexity, and a per-outcome table of probability and self-information. It is for students and engineers who want to see where a distribution's uncertainty actually comes from rather than just a single number.
Open Shannon Entropy Explorer on AltFTool — it loads instantly in your browser.
Switch between the 'Text symbols' and Probabilities tabs, then type into 'Text or comma-separated probabilities' — the Examples row loads abracadabra or 'Fair four outcomes' (0.25, 0.25, 0.25, 0.25).
Set 'Logarithm base' to '2 · bits', 'e · nats' or '10 · hartleys'; the entropy recomputes on every keystroke, and counts or percentages are divided by their total so your list need not sum to 1.
Read the entropy in the Result panel with Maximum entropy, Normalized entropy and 'Perplexity (base 2)' below it and an Outcome / Probability / Information table, then use Copy or Download, which saves shannon-entropy-explorer.txt.
Every result comes with log_b(n), the maximum entropy for that many outcomes, so 2.04 bits means something instead of floating free.
Enter counts, weights or percentages in any scale and they are divided by their total, so the list does not have to sum to 1.
The table gives each symbol's probability and its -log_b p surprisal, which is where you see one rare event dominating the total.
About 2.0404 bits per character. It has 5 distinct symbols with counts a=5, b=2, r=2, c=1, d=1 over 11 characters, against a maximum of log2(5) = 2.3219 bits, giving a normalised entropy of roughly 0.879.
Only the logarithm base: base 2 gives bits, base e gives nats, and base 10 gives hartleys. The underlying uncertainty is identical — one nat is about 1.4427 bits and one hartley is about 3.3219 bits — so switching base rescales the number without changing what it means.
It is H divided by the maximum log_b(n), so it runs from 0 to 1 and says how close your distribution is to uniform. A value of 1 means every outcome is equally likely; a value near 0 means one outcome dominates and observing the result tells you almost nothing new.
No. It measures the character-frequency entropy of the text you paste, treating each character as an independent draw — so a memorable phrase can score well here while still being trivial to guess, because real attackers use dictionaries and known patterns, not symbol frequencies. Judge password strength by how it was generated, not by this figure.