# Entropy Calculator

Measure the randomness of any data — Shannon entropy (bits/symbol), Min-Entropy (worst-case guess work), alphabet size, duplicate rate, and an average brute-force cracking time at a chosen hash rate. Rates data as Strong (≥128-bit min-entropy), Medium (64-127), or Weak (<64).

> Canonical page: https://elysiatools.com/en/tools/entropy-calculator

- **Category:** Security

- **Keywords:** entropy, shannon entropy, min-entropy, randomness, brute force, cracking time, password strength, key analysis, security

## Overview

This tool measures **how random your data actually is**. Paste a password, key, token, or any bytes, and it quantifies unpredictability with two complementary metrics plus a concrete cracking estimate.

**Two entropy metrics — and why Min-Entropy matters for rating:**

- **Shannon entropy** (H): the classic `−Σ p·log₂ p` average information per symbol. It reflects average uncertainty and is useful for compression and communication theory. But it can be *misleading* for security: a value like `aaaaaaaaaaX` (one rare symbol among many common ones) scores a moderate Shannon entropy even though an attacker guessing the most common symbol hits often.
- **Min-Entropy** (H∞ = `−log₂(max p)`): the *worst-case* guess work — based solely on the single most probable symbol. It upper-bounds an attacker's best single-guess success rate and is the conservative metric for security, so **it is what the Strong/Medium/Weak rating uses**.

**Cracking estimate.** Average time = `2^(min-entropy) / guessRate / 2` (half the keyspace on average). You pick the attacker's hash rate — from a slow CPU (10⁶/s) to a GPU farm (10¹²/s) or a custom rate — to frame the estimate realistically.

**Rating thresholds** (total Min-Entropy):
- **Strong** ≥ 128 bits → average crack time in the millions+ of years
- **Medium** 64–127 bits
- **Weak** < 64 bits → shown in red

**Analysis Mode:**
- **Auto** (default): character-level when the input is <128 bytes and all printable, else byte-level.
- **Byte-level**: treats each byte as a symbol — right for binary keys/hashes.
- **Character-level**: treats each Unicode character as a symbol — right for passwords/passphrases.

This tool does **not** maintain a weak-password dictionary — rating is purely algorithmic, based on the actual symbol distribution of whatever you paste. Use it to sanity-check generated keys, evaluate passphrase strength, or compare two tokens' randomness.

## Inputs

- **Data** (textarea): Paste the data to analyze — a password, key, token, or any text/bytes.
- **Analysis Mode** (select)
- **Guess Rate (for cracking estimate)** (select)
- **Custom Guess Rate (h/s)** (number): e.g. 1e13

## When to use

- When evaluating the cryptographic strength of generated API tokens, SSH keys, or passwords.
- When comparing the randomness of different token generation algorithms to detect predictability.
- When auditing passphrases to ensure they meet minimum security thresholds against brute-force attacks.

## How it works

- Paste your password, key, token, or raw bytes into the data input field.
- Select the analysis mode (Auto, Byte-level, or Character-level) and choose the target attacker guess rate.
- The tool calculates the Shannon entropy, Min-Entropy, alphabet size, and duplicate rate of the input.
- It outputs a security rating (Strong, Medium, or Weak) along with an estimated average brute-force cracking time.

## Use cases

- Auditing generated API keys to ensure they have at least 128 bits of Min-Entropy.
- Testing the randomness of custom passphrase generation scripts.
- Estimating brute-force resistance of passwords against high-performance GPU farms.

## Frequently asked questions

### What is the difference between Shannon entropy and Min-Entropy?

Shannon entropy measures average uncertainty, which can overestimate security. Min-Entropy measures the worst-case scenario based on the most frequent symbol, providing a safer security metric.

### How is the security rating determined?

The rating is based on total Min-Entropy: Strong is 128 bits or more, Medium is 64 to 127 bits, and Weak is under 64 bits.

### When should I use Byte-level instead of Character-level analysis?

Use Byte-level analysis for binary keys, hashes, or raw byte streams, and Character-level analysis for text-based passwords or passphrases.

### Does this tool check my password against a database of leaked credentials?

No, the analysis is purely algorithmic and evaluates randomness based on the symbol distribution of the input data.

### How is the average cracking time calculated?

It is calculated as 2 raised to the power of the Min-Entropy, divided by the selected guess rate, and then divided by 2 to represent guessing half the keyspace.

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