Case 1
- Starting number
- 27
111
Open with these valuesCollatz Steps Calculator
111steps
Result: 111 stepsHalve an even number, take 3n + 1 for an odd one, repeat until you land on 1. The answer is how many of those steps it takes: 27 needs 111 and peaks at 9232, while its neighbour 28 needs only 18. Nobody has proved every number reaches 1, but every number this calculator accepts has been checked.
The numbers at a glance
| Starting number | Result |
|---|---|
| 10 | 6 |
| 20 | 7 |
| 27Your value | 111 |
| 30 | 18 |
| 40 | 8 |
| 50 | 24 |
Worked examples
Case 2
- Starting number
- 7
16
Open with these valuesCase 3
- Starting number
- 97
118
Open with these valuesHow it's calculated
even → n ÷ 2, odd → 3n + 1, repeat until n = 1
- StepEnter a positive whole number from 1 to one billion.
- StepHalve it while it is even; when it is odd, take 3n + 1 instead.
- StepCount every one of those operations as a single step.
- ResultStop at 1 — a start of 1 therefore needs zero steps.
Reference table
| Starting number | Highest value reached | Steps |
|---|---|---|
| 1 | 1 | 0 |
| 6 | 16 | 8 |
| 7 | 52 | 16 |
| 27 | 9232 | 111 |
| 97 | 9232 | 118 |
Questions
What is the Collatz conjecture?
It says that starting from any positive whole number, repeatedly halving even numbers and applying 3n + 1 to odd ones always eventually reaches 1. It has been verified for every start up to at least 2^68 but never proved, which makes it one of the most famous open problems in mathematics.
How many steps does 27 take?
111 steps, climbing to a maximum of 9232 on the way — more than 340 times the starting number. That is why 27 is the classic example of a small start producing a long, dramatic sequence.
What counts as one step?
A single application of the rule: either halving an even number, or computing 3n + 1 for an odd one. The count is how many of those it takes before the sequence reaches 1, so starting at 1 gives zero.
Is it proven that the sequence always reaches 1?
Not in general, and that is exactly why the conjecture is famous. Computers have checked every start up to at least 2^68, so every value this calculator accepts is guaranteed to terminate, but no proof covers all whole numbers.
Which numbers have the longest sequences?
There is no simple pattern; record holders tend to sit just above a power of two. The step count does not grow with the starting value either — 27 takes 111 steps while 28 takes 18.
Sources and last check
Information, not professional advice.