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Collatz conjecture calculator

Trace the Collatz sequence from any positive integer: halve it if even, triple-plus-one if odd, and repeat until you reach 1. The famous unproven conjecture says every number eventually does. See the full trajectory, the number of steps and the peak value it soars to.

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Enter Starting integer and the Collatz conjecture calculator works out Steps to reach 1, Peak value, Sequence straight away. For instance, with Starting integer = 27 it returns Steps to reach 1 = 111, Peak value = 9232 and 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.

How to use it

  1. Enter your values: Starting integer.
  2. Read the result instantly: Steps to reach 1, Peak value, Sequence.

Frequently asked questions

What does the Collatz conjecture calculator actually compute?

It takes Starting integer and derives Steps to reach 1, Peak value and Sequence from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

A single value: Starting integer. Nothing else is required — no account, no file upload.

Can you show a worked example?

With Starting integer = 27, the calculator returns Steps to reach 1 = 111, Peak value = 9232 and 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. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Starting integer = 54 instead, Steps to reach 1 goes from 111 to 112 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to Starting integer = 14, Steps to reach 1 comes out at 17. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Finding the nth term without listing every one before it, summing a long run in one step, and recognising which family a sequence belongs to.

What is the most common mistake?

Starting the index at the wrong end. Whether the first term is a₀ or a₁ shifts every result by one position, and the two conventions are both common.

What is the difference between the Collatz conjecture calculator and the Goldbach conjecture verifier?

This one returns Steps to reach 1 and Peak value; the Goldbach conjecture verifier returns Sum of two primes and Status. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Happy number calculator is the closest one after this: Find out whether a number is 'happy'. Repeatedly replace it with the sum of the squares of its digits: if you reach 1 it is happy; if you fall into the 4-16-37-58-89-145-42-20 loop it is unhappy. See the verdict and the full chain of steps.

What else is worth having open alongside it?

Fibonacci Number Checker and Infinite Series Sum Calculator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
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