Infinite Monkey Calculator
Estimate how long it would take a group of random-typing monkeys to produce your target text exactly.
Character count is based on exact text (including spaces and punctuation).
Example: 27 for lowercase letters + space.
What this monkey calculator does
This calculator is based on the classic Infinite Monkey Theorem: if monkeys hit keys randomly for long enough, they will eventually type any finite piece of text. While the theorem is mathematically true, the timescales are usually unimaginably large.
The tool gives you a practical estimate for that waiting time using a simple probability model. You enter a phrase, set how many symbols are available on the keyboard, then choose how many monkeys are typing and how fast each one types.
How the estimate is computed
1) Success probability for one trial
For a target text of length L and alphabet size A, the probability of typing that exact sequence in one aligned try is:
p = (1 / A)L
2) Trials per second
If you have M monkeys and each types R characters per second, the model approximates:
trials per second ≈ M × R
3) Expected waiting time
Expected time is approximately:
Expected seconds = 1 / (trials per second × p)
This is why adding one extra character can explode the waiting time—each extra character multiplies difficulty by another factor of the alphabet size.
How to use it well
- Use a realistic alphabet size for your scenario.
- Keep punctuation in mind: every additional symbol makes random matching harder.
- Short targets can still produce huge expected times.
- Use the one-day and one-century probabilities to build intuition.
Interpreting giant numbers
You may see scientific notation like 3.1 × 10^22 seconds. That is normal. Random exact matching becomes astronomically unlikely very quickly. A result this large does not mean your calculator is broken; it means combinatorics are powerful.
Important assumptions and limitations
- Keystrokes are assumed independent and uniformly random.
- All symbols in the alphabet are assumed equally likely.
- The estimate is an average expectation, not a guaranteed deadline.
- Real typing behavior (human or animal) is not truly random in this way.
Why this matters beyond monkeys
This thought experiment teaches a practical lesson used in security, search, and optimization: brute force scales badly. Whether you are evaluating password strength, random guessing, or algorithm design, growth in search space can outrun intuition.
In short: tiny increases in complexity can require extraordinary increases in time or compute power.