Collatz Conjecture Calculator
Generate the Collatz sequence for any number using the 3n+1 rule, and see how many steps it takes to reach 1 and the highest value reached.
Last reviewed by the Radiatus Cloud team
Generate the Collatz 3n+1 sequence and count the steps to reach 1.
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Explore the Collatz conjecture
The Collatz conjecture is one of the most famous unsolved problems in mathematics. Starting from any positive integer, you repeatedly apply a simple rule: if the number is even, halve it; if it is odd, multiply by three and add one. The conjecture states that this process always eventually reaches one, no matter which number you start with. This calculator generates the full sequence, counts the steps to reach one, and reports the highest value the sequence climbs to along the way.
Starting from twenty-seven, the sequence takes one hundred and eleven steps and soars as high as nine thousand two hundred and thirty-two before descending to one.
A simple rule, a deep mystery
Despite its childlike simplicity, no one has proved that the Collatz process always terminates, and it has been verified by computer for astronomically large numbers without a single exception found. The sequence is sometimes called the hailstone sequence because the values bounce up and down like hailstones in a cloud before finally falling. Exploring different starting numbers reveals surprisingly varied and unpredictable behaviour.
The calculator includes a safety limit, but the conjecture holds for every number ever tested, so the sequence reliably reaches one. All calculation happens locally in your browser.
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Frequently Asked Questions
What is the Collatz conjecture?
It states that repeatedly halving even numbers and tripling-plus-one odd numbers always eventually reaches one, for any positive starting integer.
Has the conjecture been proved?
No. It remains unproven, though it has been verified by computer for enormous numbers without any counterexample ever being found.
Why is it called the hailstone sequence?
Because the values rise and fall unpredictably, like hailstones bouncing up and down in a cloud, before eventually dropping to one.
What does the highest value tell me?
It is the peak the sequence reaches, which can be far larger than the starting number, illustrating the wild swings before it settles to one.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter a positive integer to generate its Collatz sequence.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.