How Many Combinations Does a 4 Digit Lock Have?

Exact result

10,000

A 4-position lock code with 10 options per position has 10,000 possible codes.

A typical 4 digit lock has 10 choices on each of 4 ordered dials. Codes like 1234 and 4321 are different, and repeated digits like 0000 are allowed, so the total is 10^4.

Worked steps

Show your work

Inputs: positions = 4, pool size = 10 from range 0 through 9
Formula: n^r
Substitute: 10^4
Steps: 10 x 10 x 10 x 10 = 10,000
Result: A 4-position lock code with 10 options per position has 10,000 possible codes.

Interactive tool

Verify the same values in the calculator

A typical 4 digit lock has 10 choices on each of 4 ordered dials. Codes like 1234 and 4321 are different, and repeated digits like 0000 are allowed, so the total is 10^4.

Number of dials / positions

4

We are given a fixed number of dials or spins.

Dial type Use a define numberic range or custom symbol list on dials. Range start Inclusive first value on every dial. Range end Inclusive last value on every dial. Custom symbol list Enter comma-separated symbols or short tokens. Example: A,B,C,D or 10,20,30,59.

Result

0

Enter values to calculate.

What your result means

The explanation updates with the current inputs.

Calculation work

How many combinations does a 4 digit lock have?

10,000

Show your work

Verify the same values in the calculator

Lock preview