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Password Entropy Calculator

Calculate the entropy and strength of a password based on character set size and length.

Reviewed by Christopher FloiedPublished Updated

This free online password entropy calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Minimum: 0

Number of characters in the password

Number of possible characters at each position

Results

Password Entropy

74 bits

Total Combinations

1.94e+22

Brute Force Time (10B/sec)

1.94e+12 seconds

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Password Entropy Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Password Entropy Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Password Entropy Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • •Use the Password Entropy Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

About This Calculator

The Password Entropy Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the entropy and strength of a password based on character set size and length. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.

About Password Entropy Calculator

The Password Entropy Calculator measures the strength of a password based on its length and the size of the character set used. Entropy, measured in bits, quantifies the unpredictability of a password. Higher entropy means more possible combinations and greater resistance to brute-force attacks. Security experts recommend a minimum of 60 bits of entropy for important accounts and 80+ bits for critical systems.

The Math Behind It

Password entropy measures the information content of a password in bits. It is calculated as the logarithm base 2 of the total number of possible passwords: E = L * log2(C), where L is the password length and C is the number of possible characters at each position. A password with 1 bit of entropy has 2 possible values. Each additional bit doubles the number of possibilities. At 40 bits of entropy, there are about 1 trillion possibilities. At 80 bits, there are about 10^24 possibilities. The character set size depends on what characters are used. Lowercase letters provide 26 options per character. Adding uppercase doubles it to 52. Adding digits brings it to 62. Including symbols (such as !@#$%^&*) increases it further. The full printable ASCII set provides 95 options per character position. Password length has a more significant impact on entropy than character set size because it appears as the exponent. Increasing a 10-character password to 12 characters with the same character set adds more entropy than keeping 10 characters and adding symbols. Modern password cracking can test billions of passwords per second using GPUs. A password with 40 bits of entropy can be cracked in seconds. Fifty bits takes hours, sixty bits takes months, and eighty bits is considered infeasible with current technology. This calculator assumes truly random passwords. Human-chosen passwords are far weaker because people use patterns, dictionary words, and predictable substitutions that attackers exploit.

Formula Reference

Password Entropy

E = L * log2(C)

Variables: E = entropy in bits, L = password length, C = character set size

Worked Examples

Example 1: 12-character password with mixed characters

A 12-character password using alphanumeric characters plus symbols (72 character set).

Step 1:Bits per character: log2(72) = 6.17 bits
Step 2:Total entropy: 12 * 6.17 = 74.0 bits
Step 3:Combinations: 72^12 = 1.94 * 10^22
Step 4:Crack time at 10B/sec: 1.94 * 10^22 / 10^10 = 1.94 * 10^12 seconds = ~61,500 years

The password has 74 bits of entropy and would take over 61,000 years to crack by brute force at 10 billion guesses per second.

Common Mistakes & Tips

  • !Assuming entropy calculations apply to human-chosen passwords; they only apply to randomly generated passwords.
  • !Equating password length with security without considering the character set size.
  • !Ignoring that dictionary attacks and pattern-based attacks bypass brute-force entropy calculations entirely.

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Frequently Asked Questions

How many bits of entropy do I need?

For general accounts, 50-60 bits is adequate. For email and financial accounts, aim for 70+ bits. For encryption keys and critical systems, 80+ bits is recommended. Using a password manager allows you to easily generate and store high-entropy passwords.

Is a longer password always better?

Yes, for randomly generated passwords. Each additional character multiplies the number of possible combinations. A 16-character lowercase password (75 bits) is stronger than a 10-character full-ASCII password (66 bits). However, human-chosen long passwords may use predictable patterns that reduce effective entropy.