Math Calculators

Collatz Conjecture Calculator

Apply the Collatz conjecture rules to a starting number and count how many steps it takes to reach 1.

Steps to reach 1 —

Peak value reached —

Sequence —

About the Collatz Conjecture Calculator

The Collatz conjecture takes any positive whole number and repeatedly applies a simple rule: halve it if it's even, or triple it and add one if it's odd. The (unproven) conjecture claims every starting number eventually reaches 1.

Formula: next = n/2 if n is even, next = 3n + 1 if n is odd

Small starting numbers can still produce surprisingly long sequences with high peaks — 27, for example, takes over 100 steps and climbs past 9,000 before falling to 1.