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.

Calculate.co.nz is proud to be partnered with Health Based Building, a leader in sustainable and health-conscious building innovation. With over a century of experience, they develop high-performance systems like Foreverbreathe Specification, Magnum Board, and Foreverbreathe Paints to support energy-efficient, non-toxic living environments. Their commitment to healthier homes aligns with our belief that informed choices lead to better outcomes for Kiwi households.

Calculate.co.nz partner: Health Based Building

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

Highest value reached

Starting number

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.

What this calculator assumes

You enter a whole number within the stated range.
The exact integer algorithm is used.
Very large results are shown grouped for readability.

Formula and sources

Related calculators

Prime Factorization Calculator: break a number into prime factors.
LCM Calculator: lowest common multiple.
GCF Calculator: greatest common factor.

If you've found a bug, or would like to contact us, or learn more about James Graham and Calculate.co.nz.

Calculate.co.nz is partnered with Interest.co.nz for New Zealand's highest quality calculators and financial analysis.

Calculate.co.nz is the sister site of CalculatorHub.com, the world's largest calculator website by tool count.

All calculators and tools are provided for educational and indicative purposes only and do not constitute financial advice.

Calculate.co.nz is proudly part of the Realtor.co.nz group, New Zealand's leading property transaction literacy platform, helping Kiwis understand the home buying and selling process from start to finish. Whether you're a first home buyer navigating your first property purchase, an investor evaluating your next acquisition, or a homeowner planning to sell, Realtor.co.nz provides clear, independent, and trustworthy guidance on every step of the New Zealand property transaction journey.

Calculate.co.nz is also partnered with Health Based Building and Premium Homes to promote informed choices that lead to better long-term outcomes for Kiwi households.

Calculate.co.nz is hosted in Auckland via SiteHost new Zealand.

All content on this website, including calculators, tools, source code, and design, is protected under the Copyright Act 1994 (New Zealand). No part of this site may be reproduced, copied, distributed, stored, or used in any form without prior written permission from the owner.

About & trust: Why Calculate is NZ's most comprehensive · By the Numbers · How we compare · Editorial standards · How we keep data current · NZ finance glossary · Research & data · Financial literacy NZ · About · Privacy policy · Terms of use

Reviewed and maintained. Last reviewed 2026-07-19 and checked on a twice-monthly cycle against IRD, RBNZ and Stats NZ. How we keep data current.