Collatz Conjecture
3n+1 trajectory length and step plot
About this calculator
The Collatz Conjecture Calculator runs the 3n+1 process on any positive whole number: divide by two when even, multiply by three and add one when odd, and repeat until you reach 1. It reports the total number of steps, the peak value reached, and the even/odd step split, and plots the full trajectory so you can see the characteristic rises and falls of the 'hailstone' sequence.
How to use the Collatz Conjecture calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- n = 6 → 6, 3, 10, 5, 16, 8, 4, 2, 1 (8 steps, peak 16)
- n = 7 → 16 steps, peak 52
- n = 27 → 111 steps, peak 9232 (a famously long climb)
- n = 1 → 0 steps (already at the fixed point)
Frequently asked questions
How does the Collatz Conjecture calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the Collatz Conjecture calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.