What is the Collatz conjecture (the 3n+1 problem)?

It is a famously simple rule with an unsolved outcome. Start from any positive integer. If it is even, divide by 2; if it is odd, multiply by 3 and add 1. Repeat. The conjecture, posed by Lothar Collatz in 1937, claims that no matter which number you start from, you always eventually reach 1. Try 12 and it goes 12, 6, 3, 10, 5, 16, 8, 4, 2, 1. Every number ever tested obeys, but nobody has proven it must hold for all of them.

How does the sequence for 6 work step by step?

Start at 6. It is even, so halve it to 3. Three is odd, so 3 times 3 plus 1 gives 10. Ten halves to 5, which is odd, so 5 times 3 plus 1 is 16. Then 16, 8, 4, 2, 1 by repeated halving. The full path is 6, 3, 10, 5, 16, 8, 4, 2, 1. That is 8 steps to reach 1, and the peak along the way is 16. Enter 6 in the tool and you will see exactly this sequence laid out.

What do stopping time and peak mean here?

Stopping time is the number of steps it takes to first reach 1, counting each halving or each 3n+1 as one move. For 6 that is 8 steps. Peak is the largest value the path ever reaches before it falls to 1. Small seeds can have surprisingly large peaks: 27 takes 111 steps and climbs all the way to 9232 before coming back down. The tool reports both numbers next to the sequence so you can compare seeds at a glance.

Why is the Collatz conjecture still unsolved?

The rule mixes multiplication and division in a way that makes the long-term behaviour hard to pin down. An odd step roughly triples a number, an even step halves it, and the order of those steps depends on bits that change unpredictably as the value grows. Mathematicians including Paul Erdos have called it out of reach of current methods; Erdos said mathematics is not yet ready for such problems. Computers have verified it past 2^68, but verification is not proof.

Why is it also called the hailstone or Kakutani problem?

Hailstone sequence is the picturesque name: the values rise and fall many times, like a hailstone carried up and down inside a storm cloud before it finally drops to the ground, which here is 1. The problem has collected many names from the people who studied it — the Collatz conjecture, the 3n+1 problem, the Ulam conjecture, Kakutani's problem, and the Syracuse problem — but they all describe the very same rule and the same open question.

How large a starting number can this handle?

Because every step runs on BigInt, the arithmetic stays exact no matter how high a peak the path reaches, so you will not see rounding errors that plain JavaScript numbers hit above 9 quadrillion. The practical limit is a step cap that stops a single run from going past a safe number of iterations, which keeps the tab responsive if you feed in a value with an enormous orbit. If a run is capped you will see a note rather than a frozen page.

Explore the 3n+1 problem for a math class

A teacher introducing unsolved problems wants students to feel how wild a simple rule can get. Have each student pick a starting number under 100, run it here, and write down its stopping time and peak. The class quickly notices there is no pattern: 26 falls in 10 steps, but its neighbour 27 takes 111 and spikes to 9232. The shared URL lets a student send their favourite seed straight to the teacher.

Check a hand-computed sequence

You worked out the orbit of 97 on paper and want to confirm it. Paste 97 in, and the tool gives the full path, the step count, and the peak, so you can compare your hand work line by line. Because the values are exact BigInt, even the tall peaks match what a careful computation gives rather than a rounded approximation.

Hunt for long stopping times

You are curious which small numbers take the most steps to reach 1. Run 27, 31, 47, 54, 73, 97 and compare their stopping times — these are the classic record-holders under 100. Copy each sequence into a notes file and you have a quick table of which seeds produce the longest hailstone flights, with the peak listed alongside.

Generate sequence data for a visualization

Building a plot or an animation of hailstone paths? Run a seed, copy the full comma-separated sequence, and paste it straight into your plotting code or a spreadsheet. The copy button hands you clean, exact integers with no scientific notation, so a 9232 peak comes across as 9232, not 9.232e3.

Collatz Conjecture Calculator — 3n+1 Sequence, Steps & Peak

Enter any positive integer, watch 3n+1 run to 1 — full hailstone sequence, stopping time, and peak, exact via BigInt

Runs locally
Category Developer & DevOps
Best for Formatting, validating, shrinking, or inspecting code-adjacent text.

Starting number

Try

Stopping time

111 steps

Peak

9232

Sequence length

112 numbers

Hailstone path

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

What this tool does

A 3n+1 calculator for the Collatz conjecture: pick any positive whole number and the tool runs the rule until it lands on 1 — if the number is even, halve it; if it is odd, triple it and add one. The path it traces is the hailstone sequence, named because the values bounce up and down like a hailstone in a cloud before they finally fall to 1. You get three readouts at once: the complete sequence, the stopping time (how many steps it takes to reach 1), and the peak (the largest value the path ever hits). Try 27 and watch it climb to 9232 over 111 steps before crashing down — a tiny seed with a wild orbit. Everything is computed with BigInt, so the peaks of numbers like 27 or 97 stay exact instead of rounding off the way ordinary JavaScript numbers would past 2^53. One click copies the whole sequence, and the URL carries your starting number so a shared link reopens the exact same run. 100% in your browser, nothing uploaded.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy + Preview; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 12 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Developer & DevOps · Developer; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Collatz Conjecture Calculator fits into your work

Use it in the small gaps between coding, reviewing, debugging, and shipping.

Developer jobs

Formatting, validating, shrinking, or inspecting code-adjacent text.
Preparing snippets for documentation, tickets, commits, or handoff.
Checking a small payload quickly without switching tools.

Developer checks

Run irreversible transforms like minify or obfuscate on a copy.
Keep secrets out of pasted snippets unless the tool explicitly stays local.
Use your normal tests or linter before shipping transformed code.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Explore the 3n+1 problem for a math class
A teacher introducing unsolved problems wants students to feel how wild a simple rule can get. Have each student pick a starting number under 100, run it here, and write down its stopping time and peak. The class quickly notices there is no pattern: 26 falls in 10 steps, but its neighbour 27 takes 111 and spikes to 9232. The shared URL lets a student send their favourite seed straight to the teacher.
Check a hand-computed sequence
You worked out the orbit of 97 on paper and want to confirm it. Paste 97 in, and the tool gives the full path, the step count, and the peak, so you can compare your hand work line by line. Because the values are exact BigInt, even the tall peaks match what a careful computation gives rather than a rounded approximation.
Hunt for long stopping times
You are curious which small numbers take the most steps to reach 1. Run 27, 31, 47, 54, 73, 97 and compare their stopping times — these are the classic record-holders under 100. Copy each sequence into a notes file and you have a quick table of which seeds produce the longest hailstone flights, with the peak listed alongside.
Generate sequence data for a visualization
Building a plot or an animation of hailstone paths? Run a seed, copy the full comma-separated sequence, and paste it straight into your plotting code or a spreadsheet. The copy button hands you clean, exact integers with no scientific notation, so a 9232 peak comes across as 9232, not 9.232e3.

Common pitfalls

Counting steps off by one. The stopping time here counts every operation until the value first equals 1, so 1 itself is the endpoint, not a step. For 6 there are 8 steps and the sequence has 9 entries because the starting number and the final 1 are both listed. If your hand count is one higher, you probably counted the starting number as a step.
Expecting small numbers to be tame. People assume a seed under 100 settles fast, then 27 takes 111 steps and peaks at 9232. There is no relationship between how small the seed is and how long or how high its orbit runs, so do not be surprised by a tiny number with a huge peak.
Feeding in zero, a negative, or a fraction. The rule is defined for positive integers only. Zero loops on itself and negatives fall into different cycles, so the tool treats anything that is not a positive whole number as invalid and returns nothing rather than spinning. Enter 1 or larger, with no decimal point.

Privacy

Every step of the 3n+1 rule, the step count and the peak are plain JavaScript running in your browser tab. The starting number never leaves the page and nothing about your runs is logged. The one thing to know: the shareable URL puts your starting number in the query string, so a link you paste into chat records that number in the recipient server's access log. That is just a small integer, but if you would rather not share it, use the copy button on the sequence instead of the URL.

FAQ

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Collatz Conjecture Calculator — 3n+1 Sequence, Steps & Peak

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Collatz Conjecture Calculator fits into your work

Developer jobs

Developer checks

Good next steps

Real-world use cases

Explore the 3n+1 problem for a math class

Check a hand-computed sequence

Hunt for long stopping times

Generate sequence data for a visualization

Common pitfalls

Privacy

FAQ

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