When to use this
Use this formula when the question matches this rule set
Use this for 4-dial bike locks, luggage locks, letter locks, or any four-position code where each dial can show one value from the same shared pool.
What this result means
Interpret the output, not just the number
The result is the total number of different codes the lock can show. Because 1234 and 4321 are different codes, order matters. Because 0000 is usually allowed, repeats are allowed too, so the count uses n^r.
Formula: n^r
Calculator inputs
Know what to enter in each field
These pages use lock language, but the math is permutation with repetition: order matters, repeats are allowed, and the count is n^r.
Number of dials / positions
This is how many ordered slots the code uses.
What to enter: On the dedicated lock pages this value is preset by the page title.
How to use it: Each extra dial multiplies the total again because a code like 1234 is different from 4321.
Example: A three-dial lock uses 3 positions, and a four-dial lock uses 4.
Pool type
Choose whether each dial uses a generated range or a custom symbol list.
What to enter: Pick Range for numeric spans like 0-9 or 0-59, or Custom list for tokens like A,B,C,D.
How to use it: The calculator counts how many allowed symbols each dial can show, then raises that pool size to the number of positions.
Example: A lock labeled 0-59 uses Range. A puzzle lock with A,B,C,D uses Custom list.
Range start / range end
These define the first and last values available on every dial when using Range.
What to enter: Enter the full inclusive range used on each dial.
How to use it: The pool size is end - start + 1, so 0-9 gives 10 symbols and 0-59 gives 60 symbols.
Example: A three-number locker dial usually uses 0 through 59.
Custom symbol list
This defines the allowed symbols directly when the dials are not a simple numeric range.
What to enter: Enter comma-separated tokens such as A,B,C,D or 10,20,30,59.
How to use it: Each unique trimmed token becomes one available dial symbol. Duplicates and empty entries should be removed before solving.
Example: A letter lock using A,B,C,D,E has 5 possible symbols on each dial.
Worked examples
Quick checks with realistic inputs
Typical 0-9 bike lock
A four-dial lock where each dial shows one digit from 0 through 9. That's 10 choices.
A 4-position lock code with 10 options per position has 10,000 possible codes.
Load this example into the calculatorLetter lock with four symbols
A four-dial letter lock where each dial can show A, B, C, or D.
A 4-position lock code with 4 options per position has 256 possible codes.
Load this example into the calculator