Collatz Sequence Calculator

Work out collatz sequence instantly with clear inputs, formula shown and shareable results.

About Collatz Sequence Calculator

The Collatz rule halves even numbers and maps odd n to 3n + 1. Every tested starting value eventually reaches 1, but no proof exists — this is the Collatz conjecture.

Formula

Collatz step

n → n/2 if n is even, otherwise n → 3n + 1

Worked example

With the default values below, Collatz Sequence Calculator returns Steps to reach 1 of 111. Change any input above and every figure here is recalculated in your browser.

Inputs used

Starting numberminimum 1: 27
Maximum stepsaccepts 1–5,000: 500

Results

Steps to reach 1: 111
Highest value reached: 9,232
Terminated: Yes, the sequence reached 1
Start of the sequence: 27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → 214 → 107 → 322 → 161

Step by step

1Values used
2Collatz step
3Steps to reach 1= 111
4Highest value reached= 9,232
5Terminated= Yes, the sequence reached 1
6Start of the sequence= 27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → 214 → 107 → 322 → 161

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How long is the sequence from 27?

111 steps, peaking at 9232 — famously long for such a small start.

Is the conjecture proved?

No. It has been verified past 2⁶⁸ by computer but remains open, and Erdős remarked mathematics is not ready for such problems.