# Collatz Conjecture Calculator

URL: https://speedycalculator.com/calculators/math/collatz-conjecture/
Last updated: 2026-10-30

> The Collatz conjecture calculator follows the 3n + 1 rule from any starting number and reports the number of steps to reach 1 (stopping time), the highest value reached and the full sequence.

## Inputs

- Starting number

## Results

- Steps to reach 1
- Highest value reached
- Sequence

## Formula

```
n → n/2 if n is even,  n → 3n + 1 if n is odd
```

## Explanation

The Collatz conjecture says that this simple rule eventually reaches 1 from every positive starting number. It has been checked beyond 2⁶⁸ but never proved – Paul Erdős said "mathematics is not yet ready for such problems".

### How to use the Collatz Conjecture Calculator

- **Starting number**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Enter a positive whole number. Exact big-integer arithmetic is used, so even huge numbers are followed correctly.

## Worked example

Inputs — Starting number: 27.

Results — **Steps to reach 1 = 111**; Highest value reached = 9232; Sequence = 27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → 214 → 107 → 322 → 161 → 484 → 242 → 121 → 364 → 182 → 91 → 274 → 137 → 412 → 206 → 103 → 310 → 155 → 466 → 233 → 700 → 350 → 175 → 526 → 263 → 790 → 395 → 1186 → 593 → 1780 → 890 → 445 → 1336 → 668 → 334 → 167 → 502 → 251 → 754 → 377 → 1132 → 566 → 283 → 850 → 425 → 1276 → 638 → 319 → 958 → 479 → 1438 → 719 → 2158 → 1079 → 3238 → 1619 → 4858 → 2429 → 7288 → 3644 → 1822 → 911 → 2734 → 1367 → 4102 → 2051 → 6154 → 3077 → 9232 → 4616 → 2308 → 1154 → 577 → 1732 → 866 → 433 → 1300 → 650 → 325 → 976 → 488 → 244 → 122 → 61 → 184 → 92 → 46 → 23 → 70 → 35 → 106 → 53 → 160 → 80 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1.

## Key terms

- **Hailstone sequence**: Another name for a Collatz sequence.

## FAQ

**Has the Collatz conjecture been proved?**
No – it remains open.

**Why is 27 famous?**
It takes 111 steps and climbs to 9,232 before falling to 1.

**What is the stopping time?**
The number of steps needed to reach 1.

**Does every number reach 1?**
Every number tested so far does.


## Sources

- [Wolfram MathWorld – Collatz problem](https://mathworld.wolfram.com/CollatzProblem.html)