Find Entropy of a Number - Calculate the Complexity or Entropy of a Number

Entropy is a measure of surprise. In the world of information theory, the entropy of a string of digits tells you how unpredictable, how information-rich, that string is - expressed in bits per symbol by Claude Shannon’s classic formula H = -sum p log2 p. For a number, that question becomes: do the digits spread themselves evenly like a shuffled deck, or crowd into a few favourites like a nursery rhyme? The answer exposes structure that is invisible at a glance.

Find Entropy of a Number computes the Shannon entropy of any digit string - an integer, a decimal, a phone number, a hash - by counting the frequency of each digit 0 to 9 and folding those frequencies into bits per symbol. Alongside the headline entropy it reports how many distinct digits appear, the per-digit count table, an evenness estimate against the theoretical maximum of log2(10) = 3.3219 bits, and a plain-language complexity verdict: low, moderate or high. Numbers are analysed one per line, up to 1000, and every result row copies or downloads as text. All of it runs locally in your browser - nothing is uploaded, stored or logged.

• True Shannon entropy: Bits per symbol via H = -sum p log2 p over digit frequencies.
• Per-digit counts: A full 0-9 frequency table for every number.
• Distinct-digit count: How many different values actually appear.
• Evenscore: An estimate of uniformity against the 3.3219-bit maximum.
• Complexity verdict: A low / moderate / high reading in plain words.
• Full decimal support: Analysess digits across integers and decimals alike.
• Batch mode: Up to 1000 numbers, one per line.
• Free and private: Everything runs in the browser; nothing is uploaded or logged.

1. Enter your numbers - one per line. Integers, decimals, hashes or any digit string all work.
2. Generate - the tool counts each digit and computes the Shannon entropy.
3. Read the headline - bits per symbol, the percentage and the verdict.
4. Study the table - per-digit counts and distinct-digit totals.
5. Copy or download - the full analysis is yours.

1 - No surprise, low entropy. Enter 11111111: every digit is the same, the frequency is a lone peak, and the entropy is exactly 0 bits per symbol - the most predictable string possible.

2 - A natural mix. Enter 1234567890: all ten digits appear exactly once, producing the theoretical maximum of about 3.32 bits per symbol - evenly surprising throughout.

3 - A daily real number. Enter a year like 2024: three digits appear once and one twice - a modest score reflecting its mild repetition, ranked well below a perfect shuffle.

4 - Phone-number pattern. Enter A-like patterns such as 5551234: the repeating 5 and the 3-2-1 run tilt the balance toward the predictable end of the scale.

5 - Very long and even. A long random decimal spread across all ten digits scores near the maximum - a live demonstration that genuine randomness fills every symbol evenly.

• Quantifies randomness: Turn a gut feeling about a number into bits.
• Structure revealer: See repetition and bias that the eye misses.
• Context-free: Works on any digit string - no base or size restrictions.
• Per-digit clarity: The frequency table explains the score.
• Batch friendly: Analyse hundreds of numbers at once.
• Private and free: Everything runs in the browser; nothing is uploaded or logged.