HesapHanem

License Plate Combinations Calculator

Enter the number of letter and digit positions to get the total possible license plates.

How it is calculated

The count is N = 26L × 10D, where L is the number of letter positions and D is the number of digit positions. Every letter slot is assumed to accept all 26 letters A to Z, and every digit slot all ten digits 0 to 9, in any order and with repetition allowed. The tool only accepts whole numbers: L can be 0 to 12 and D 0 to 18, with at least one position in total. A decimal such as 2.5, a negative number or anything above those limits gives no result. For the largest formats the displayed figure is a double-precision number, so its trailing digits are rounded and show as zeros. Real schemes often subtract banned letters, reserved prefixes or sequences, so actual capacity is lower than this upper bound.

Worked example

A format with 3 letters and 3 digits, such as ABC 123. The letters give 26 × 26 × 26 = 17,576 possibilities. The digits give 10 × 10 × 10 = 1,000. Because each choice is independent, multiply the two: 17,576 × 1,000 = 17,576,000. The tool shows 17,576,000 combinations. Adding one more digit would multiply the total by 10, while adding one more letter would multiply it by 26.

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Common mistakes

  • Typing the plate itself or the total number of characters in the letters field. The fields count positions, so ABC 123 is 3 letters and 3 digits, not 6.
  • Forgetting that a hyphen or space on the plate is not a position. Only letter and digit slots count.
  • Treating the result as the number of plates a region can issue. Banned letters, reserved prefixes, special series and the need to avoid awkward words all reduce the usable count.
  • Entering a region code or province number as a digit position when it is a fixed prefix. A fixed part adds no combinations.
  • Expecting 0 letters and 0 digits to return 1. At least one position is required.

About this calculator

This calculator counts how many unique plates a license plate format can produce using the basic combinatorics counting rule: each letter position has 26 possible values and each digit position has 10, so the total is 26^(letters) × 10^(digits). A common US format with 3 letters and 4 digits, for example, yields 26³ × 10⁴ = 175,760,000 possible plates.

DMVs and vehicle registration authorities use this kind of capacity calculation when designing a plate scheme, to make sure a format won't run out of unique combinations before it needs to add a character or switch formats — which is exactly why many regions have moved from all-numeric to mixed alphanumeric plates as their vehicle fleets grew.

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Comments (1)

  • Editorial team

    The tool assumes all 26 letters are allowed in every slot, so treat its answer as a ceiling. Many schemes drop look-alike letters such as I, O and Q. With three letter slots that leaves 23 choices each, and 23 cubed is 12,167 against 17,576, so only about 69% of the combinations survive. Multiply your digit part back in to compare. Which plate format are you working out, and does it skip any letters?

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