Collatz Conjecture Calculator

This Collatz conjecture calculator applies the famous 3n plus 1 rule to any whole number and shows you how the sequence behaves before it settles at 1. The process is simple: if your number is even, halve it; if it is odd, triple it and add one; then repeat on whatever number you get, over and over. The Collatz conjecture, one of the most famous unsolved problems in mathematics, claims that every positive whole number eventually reaches 1 this way, no matter how large or how wildly the sequence rises and falls first. Mathematicians have verified this for enormous ranges of numbers using computers, yet nobody has ever proved it holds for every number, which is why it keeps mathematicians busy decades after it was first proposed. Enter any starting number from 1 up to one billion and the calculator runs the full sequence, returning the total number of steps taken to reach 1, the highest value the sequence climbs to along the way, and your original starting number for reference. Try 27, a famous example that takes 111 steps and peaks above 9,000 despite starting so small, to see how unpredictable the sequence can be. Below the calculator you will find the formula written out, a worked example starting from 6, answers to common questions about hailstone numbers, and the assumptions the calculator makes.

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Starting number (1 to 1,000,000,000)

111 steps

Highest value reached9,232

Starting number27

The formula

Apply the map: if n is even, n becomes n/2; if n is odd, n becomes 3n + 1. Repeat until you reach 1. The number of applications is the total stopping time, and the conjecture is that this is always finite.

Worked example

Starting at 6: 6, 3, 10, 5, 16, 8, 4, 2, 1, which is 8 steps, peaking at 16. The number 27 famously takes 111 steps and peaks at 9232. Enter 27 to see it.

Frequently asked questions

What is the Collatz conjecture?

The claim that the 3n+1 process reaches 1 from every positive starting number. It is unproven but verified for very large ranges.

Why are these called hailstone numbers?

Because the values rise and fall repeatedly, like hailstones in a cloud, before finally settling to 1.

Does every number really reach 1?

It is conjectured to, and checked far beyond a billion, but there is no general proof.

Who this calculator is for

This calculator is for students, programmers and anyone exploring number theory.